preprocessing¶

image transforms¶

functions adjusting the gray scale of an image

dhdt.preprocessing.image_transforms.cum_hist(img)¶

compute the cumulative histogram of an image

Parameters: img (numpy.array, size=(m,n), ndim=2) – grid with intensity values
Returns: cdf – emperical cumulative distribution function, i.e. a cumulative histogram.
Return type: numpy.array, size=(2**n,), dtype=integer

dhdt.preprocessing.image_transforms.gamma_adjustment(Z, gamma=1.0)¶

transform intensity in non-linear way

enhances high intensities when gamma>1

Parameters

Z (numpy.ndarray, size=(m,n), dtype=integer) – array with intensity values
gamma (float) – power law parameter

Returns

Z_new – array with transform

Return type

numpy.ndarray, size=(m,n)

dhdt.preprocessing.image_transforms.general_midway_equalization(Z)¶

equalization of multiple imagery, based on [De04].

Parameters: Z (numpy.array, dim=3, type={uint8,uint16}) – stack of imagery
Returns: Z_new – harmonized stack of imagery
Return type: numpy.array, dim=3, type={uint8,uint16}

References

De04: Delon, “Midway image equalization”, Journal of mathematical imaging and Vision”, vol.21(2) pp.119-134, 2004

Notes

The following acronyms are used:

CDF - cumulative distribution function

dhdt.preprocessing.image_transforms.get_histogram(img)¶

calculate the normalized histogram of an image

Parameters: img (numpy.ndarray, size=(m,n)) – gray scale image array
Returns: hist – histogram array
Return type: numpy.ndarray, size={(2**8,2), (2**16,2)}

dhdt.preprocessing.image_transforms.gompertz_adjustment(Z, a=None, b=None)¶

transform intensity in non-linear way, so high reflected surfaces like snow have more emphasized.

Parameters

Z (numpy.ndarray, size=(m,n), dtype=integer) – array with intensity values
a (float) – parameters for the Gompertz function
b (float) – parameters for the Gompertz function

Returns

Z_new – grid with transform

Return type

numpy.ndarray, size=(m,n)

dhdt.preprocessing.image_transforms.high_pass_im(Im, radius=10)¶

Parameters

Im (numpy.array, ndim={2,3}, size=(m,n,_)) – data array with intensities
radius (float, unit=pixels) – hard threshold of the sphere in Fourier space

Returns

Inew – data array with high-frequency signal

Return type

numpy.array, ndim={2,3}, size=(m,n,_)

dhdt.preprocessing.image_transforms.histogram_equalization(img, img_ref)¶

transform the intensity values of an array, so they have a similar histogram as the reference.

Parameters

img (numpy.array, size=(m,n), ndim=2) – asd
img_ref (numpy.array, size=(m,n), ndim=2) –

Returns

img – transformed image

Return type

numpy.array, size=(m,n), ndim=2

See also

normalize_histogram

general_midway_equalization: equalize multiple imagery

dhdt.preprocessing.image_transforms.hyperbolic_adjustment(Z, intercept)¶

transform intensity through an hyperbolic sine function

Parameters: Z (numpy.ndarray, size=(m,n), dtype=float) – grid with intensity values
Returns: Z_new – grid with transform
Return type: numpy.ndarray, size=(m,n), dtype=float, range=-1…+1

dhdt.preprocessing.image_transforms.inverse_tangent_transformation(x)¶

enhances high and low intensities

Parameters: x (numpy.ndarray, size=(m,n)) – grid with intensity values
Returns: fx – grid with transform
Return type: numpy.ndarray, size=(_,_)

Examples

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> x = np.arange(-1,1,.001)
>>> y = inverse_tangent_transformation(x)
>>> plt.figure(), plt.plot(x,y), plt.show()
shows the mapping function

dhdt.preprocessing.image_transforms.log_adjustment(Z)¶

transform intensity in non-linear way

enhances low intensities

Parameters: Z (numpy.ndarray, size=(m,n)) – grid with intensity values
Returns: Z_new – grid with transform
Return type: numpy.ndarray, size=(m,n)

dhdt.preprocessing.image_transforms.mat_to_gray(Z, notZ=None, vmin=None, vmax=None)¶

transform matix array to float, omitting nodata values

Parameters

Z (numpy.ndarray, size=(m,n), dtype={integer,float}) – matrix of integers with data
notZ (numpy.ndarray, size=(m,n), dtype=bool) – matrix assigning which is a no data. The default is None.

Returns

Znew – array with normalized intensity values

Return type

numpy.ndarray, size=(m,n), dtype=float, range=0…1

Examples

>>> import numpy as np
>>> from skimage import data
>>> img = data.astronaut()
>>> np.max(img)
255
>>> gray = mat_to_gray(img[:,:,0], img[:,:,0]==0)
>>> np.max(gray)
1.0

dhdt.preprocessing.image_transforms.multi_spectral_grad(Ims)¶

get the dominant multi-spectral gradient of the stack, stripped down version of the fusion technique, described in [SW02].

Parameters: Ims (numpy.array, dim=3, dtype=float) – stack of imagery
Returns: grad_I – fused gradient of the image stack
Return type: numpy.array, dim=2, dtype=complex

References

SW02: Socolinsky & Wolff, “Multispectral image visualization through first-order fusion”, IEEE transactions on image fusion, vol.11(8) pp.923-931, 2002.

dhdt.preprocessing.image_transforms.normalize_histogram(img)¶

transform image to have a uniform distribution

Parameters: img (numpy.ndarray, size=(m,n), dtype={uint8,unit16}) – image array
Returns: new_img – transfrormed image
Return type: numpy.ndarray, size=(m,n), dtype={uint8,unit16}

See also

histogram_equalization

dhdt.preprocessing.image_transforms.psuedo_inv(cumhist, val)¶

Parameters

cumhist (numpy.array, size=(2**n,), dtype={integer, float}) – emperical cumulative distribution function, i.e. a cumulative histogram.
val ({integer,float}) –

Returns

res – the pseudo-inverse of cumhist

Return type

{integer,float}

Notes

The following acronyms are used:

CDF - cumulative distribution function

color transforms¶

functions transforming to and from different color spaces

dhdt.preprocessing.color_transforms.erdas2hsi(Blue, Green, Red)¶

transform red, green, blue arrays to hue, saturation, intensity arrays

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Red (numpy.array, size=(m,n)) – red band of satellite image

Returns

Hue (numpy.array, size=(m,n), float) – hue
Sat (numpy.array, size=(m,n), float) – saturation
Int (numpy.array, size=(m,n), float) – intensity

See also

rgb2hsi

References

ER13: ERDAS, “User handbook”, 2013.

dhdt.preprocessing.color_transforms.hcv2rgb(H, C, V)¶

transform a color bubble model to red green blue arrays, following [Sh95].

Parameters

H (numpy.array, size=(m,n)) – array with amount of color
C (numpy.array, size=(m,n)) – luminance
V (numpy.array, size=(m,n)) – array with dominant frequency

Returns

Red, Green, Blue – array with colours

Return type

numpy.array, size=(m,n)

References

Sh95: Shih, “The reversibility of six geometric color spaces”, Photogrammetric engineering & remote sensing, vol.61(10) pp.1223-1232, 1995.

dhdt.preprocessing.color_transforms.lab2lch(L, a, b)¶

transform XYZ tristimulus arrays to Lab values

Parameters

L (numpy.array, size=(m,n)) –
a (numpy.array, size=(m,n)) –
b (numpy.array, size=(m,n)) –

Returns

C,h

Return type

numpy.array, size=(m,n)

See also

rgb2xyz, xyz2lms, xyz2lab

References

FR98: Ford & Roberts. “Color space conversion”, pp. 1–31, 1998.
Si18: Silva et al. “Near real-time shadow detection and removal in aerial motion imagery application” ISPRS journal of photogrammetry and remote sensing, vol.140 pp.104–121, 2018.

dhdt.preprocessing.color_transforms.lms2lab(L, M, S)¶

transform L, M, S arrays to lab color space

Parameters

L (numpy.array, size=(m,n)) –
M (numpy.array, size=(m,n)) –
S (numpy.array, size=(m,n)) –

Returns

l,a,b

Return type

numpy.array, size=(m,n)

References

Re01: Reinhard et al. “Color transfer between images” IEEE Computer graphics and applications vol.21(5) pp.34-41, 2001.

dhdt.preprocessing.color_transforms.rgb2hcv(Blue, Green, Red)¶

transform red green blue arrays to a color space

Parameters

Blue (numpy.array, size=(m,n)) – Blue band of satellite image
Green (numpy.array, size=(m,n)) – Green band of satellite image
Red (numpy.array, size=(m,n)) – Red band of satellite image

Returns

H (numpy.array, size=(m,n)) – array with amount of color
C (numpy.array, size=(m,n)) – luminance
V (numpy.array, size=(m,n)) – array with dominant frequency

References

Sm93: Smith, “Putting colors in order”, Dr. Dobb’s Journal, pp 40, 1993.
Ts06: Tsai, “A comparative study on shadow compensation of color aerial images in invariant color models”, IEEE transactions in geoscience and remote sensing, vol. 44(6) pp. 1661–1671, 2006.

dhdt.preprocessing.color_transforms.rgb2hsi(Red, Green, Blue)¶

transform red, green, blue arrays to hue, saturation, intensity arrays

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Blue (numpy.array, size=(m,n)) – blue band of satellite image

Returns

Hue (numpy.array, size=(m,n), range=0…1) – Hue
Sat (numpy.array, size=(m,n), range=0…1) – Saturation
Int (numpy.array, size=(m,n), range=0…1) – Intensity

References

Ts06: Tsai, “A comparative study on shadow compensation of color aerial images in invariant color models”, IEEE transactions in geoscience and remote sensing, vol. 44(6) pp. 1661–1671, 2006.
Pr91: Pratt, “Digital image processing” Wiley, 1991.

dhdt.preprocessing.color_transforms.rgb2lms(Red, Green, Blue)¶

transform red, green, blue arrays to XYZ tristimulus values

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Blue (numpy.array, size=(m,n)) – blue band of satellite image

Returns

L,M,S

Return type

numpy.array, size=(m,n)

References

Re01: Reinhard et al. “Color transfer between images” IEEE Computer graphics and applications vol.21(5) pp.34-41, 2001.

dhdt.preprocessing.color_transforms.rgb2xyz(Red, Green, Blue, method='reinhardt')¶

transform red, green, blue arrays to XYZ tristimulus values

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Blue (numpy.array, size=(m,n)) – blue band of satellite image
method –

‘reinhardt’
XYZitu601-1 axis

’ford’
D65 illuminant

Returns

X,Y,Z

Return type

numpy.array, size=(m,n)

References

Re01: Reinhard et al. “Color transfer between images” IEEE Computer graphics and applications vol.21(5) pp.34-41, 2001.
FR98: Ford & Roberts. “Color space conversion”, pp. 1–31, 1998.

dhdt.preprocessing.color_transforms.rgb2ycbcr(Red, Green, Blue)¶

transform red, green, blue arrays to luna and chroma values

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Blue (numpy.array, size=(m,n)) – blue band of satellite image

Returns

Y (numpy.array, size=(m,n)) – luma
Cb (numpy.array, size=(m,n)) – chroma
Cr (numpy.array, size=(m,n)) – chroma

References

Ts06: Tsai, “A comparative study on shadow compensation of color aerial images in invariant color models”, IEEE transactions in geoscience and remote sensing, vol. 44(6) pp. 1661–1671, 2006.

dhdt.preprocessing.color_transforms.rgb2yiq(Red, Green, Blue)¶

transform red, green, blue to luminance, inphase, quadrature values

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Blue (numpy.array, size=(m,n)) – blue band of satellite image

Returns

Y (numpy.array, size=(m,n)) – luminance
I (numpy.array, size=(m,n)) – inphase
Q (numpy.array, size=(m,n)) – quadrature

References

GW92: Gonzalez & Woods “Digital image processing”, 1992.

dhdt.preprocessing.color_transforms.xyz2lab(X, Y, Z, th=0.008856)¶

transform XYZ tristimulus arrays to Lab values

Parameters

X (numpy.array, size=(m,n)) –
Y (numpy.array, size=(m,n)) –
Z (numpy.array, size=(m,n)) –

Returns

L,a,b

Return type

numpy.array, size=(m,n)

See also

rgb2xyz, xyz2lms, lms2lch

References

FR98: Ford & Roberts. “Color space conversion”, pp. 1–31, 1998.
Si18: Silva et al. “Near real-time shadow detection and removal in aerial motion imagery application” ISPRS journal of photogrammetry and remote sensing, vol.140 pp.104–121, 2018.

dhdt.preprocessing.color_transforms.xyz2lms(X, Y, Z)¶

transform XYZ tristimulus arrays to LMS values

Parameters

X (numpy.array, size=(m,n)) – modified XYZitu601-1 axis
Y (numpy.array, size=(m,n)) – modified XYZitu601-1 axis
Z (numpy.array, size=(m,n)) – modified XYZitu601-1 axis

Returns

L,M,S

Return type

numpy.array, size=(m,n)

References

Re01: Reinhard et al. “Color transfer between images” IEEE Computer graphics and applications vol.21(5) pp.34-41, 2001.

dhdt.preprocessing.color_transforms.yiq2rgb(Y, Inph, Quadr)¶

transform luminance, inphase, quadrature values to red, green, blue

Parameters

Y (numpy.array, size=(m,n)) – luminance
Inph (numpy.array, size=(m,n)) – inphase
Quadr (numpy.array, size=(m,n)) – quadrature

Returns

Red (numpy.array, size=(m,n)) – red band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Blue (numpy.array, size=(m,n)) – blue band of satellite image

See also

rgb2yiq

References

GW92: Gonzalez & Woods “Digital image processing”, 1992.

acquisition geometry¶

functions of use for geometric information extraction and retrival

dhdt.preprocessing.acquisition_geometry.compensate_ortho_offset(Img, Z, dx, dy, obs_az, obs_zn, geoTransform)¶

Parameters

Img (numpy.array, size=(m,n), ndim=2, dtype={float,integer}) – grid with intensities to be compensated
Z (numpy.array, size=(m,n), ndim=2, dtype={float,integer}, unit=meters) – grid with elevations
dx (float, unit=meter) – mis-registration offset
dy (float, unit=meter) – mis-registration offset
obs_az (numpy.array, size=(m,n), unit=degrees) – azimuth angle of observation
obs_zn (numpy.ndarray, size=(m,n), unit=degrees) – zenith angle of observation
geoTransform1 (tuple) – affine transformation coefficients of array Z

Returns

Img_cor – corrected intensities

Return type

numpy.array, size=(m,n), ndim=2, dtype=float

See also

get_ortho_offset

dhdt.preprocessing.acquisition_geometry.get_ortho_offset(Z, dx, dy, obs_az, obs_zn, geoTransform)¶

get terrain displacement due to miss-registration

Parameters

Z (numpy.array, size=(m,n), unit=meter) – elevation model
dx (float, unit=meter) – mis-registration
dy (float, unit=meter) – mis-registration
obs_az (numpy.array, size=(m,n), unit=degrees) – azimuth angle of observation
obs_zn (numpy.ndarray, size=(m,n), unit=degrees) – zenith angle of observation
geoTransform (tuple, size={(6,), (8,)}) – affine transformation coefficients of array Z

Returns

dI, dJ – terrain displacements

Return type

numpy.ndarray, size=(m,n), unit=pixels

Notes

It is important to know what type of coordinate systems exist, hence:

coordinate |           coordinate  ^ y
system 'ij'|           system 'xy' |
           |                       |
           |       j               |       x
   --------+-------->      --------+-------->
           |                       |
           |                       |
           | i                     |
           v                       |

The azimuth angle is declared in the following coordinate frame:

     ^ North & y
     |
- <--|--> +
     |
     +----> East & x

The angles related to the satellite are as follows:

     #*#                   #*# satellite
^    /                ^    /|
|   /                 |   / | nadir
|-- zenith angle      |  /  v
| /                   | /|
|/                    |/ | elevation angle
+----- surface        +------

dhdt.preprocessing.acquisition_geometry.get_template_acquisition_angles(Az, Zn, Det, i_samp, j_samp, t_size)¶

Parameters

Az (numpy.ndarray, size=(m,n), float) – array with sensor azimuth angles
Zn (numpy.ndarray, size=(m,n), float) – array with sensor zenith angles
Det (numpy.ndarray, size=(m,n), bool) – array with sensor detector ids
i_samp (numpy.ndarray, size=(k,l), integer) – array with collumn coordinates of the template centers
j_samp (numpy.ndarray, size=(k,l), integer) – array with row coordinates of the template centers
t_size (integer, {x ∈ ℕ | x ≥ 1}, unit=pixels) – size of the template

Returns

Azimuth, Zenith – mean observation angles, that is, azimuth and zenith

Return type

np.array, size=(k,l), float

Notes

The azimuth angle declared in the following coordinate frame:

     ^ North & y
     |
- <--|--> +
     |
     +----> East & x

dhdt.preprocessing.acquisition_geometry.get_template_aspect_slope(Z, i_samp, j_samp, t_size, spac=10.0)¶

Parameters

Z (numpy.ndarray, size=(m,n), float, unit=meters) – array with elevation values
i_samp (numpy.ndarray, size=(k,l), integer, unit=pixels) – array with collumn coordinates of the template centers
j_samp (numpy.ndarray, size=(k,l), integer, unit=pixels) – array with row coordinates of the template centers
t_size (integer, {x ∈ ℕ | x ≥ 1}, unit=pixels) – size of the template
spac (float, unit=meters) – spacing of the elevation grid

Returns

Slope, Aspect – mean slope and aspect angle in the template

Return type

numpy.ndarray, size=(k,l), float

See also

get_aspect_slope

Notes

It is important to know what type of coordinate systems exist, hence:

coordinate |           coordinate  ^ y
system 'ij'|           system 'xy' |
           |                       |
           |       j               |       x
   --------+-------->      --------+-------->
           |                       |
           |                       |
           | i                     |
           v                       |

dhdt.preprocessing.acquisition_geometry.slope_along_perp(Z, Az, spac=10)¶

get the slope of the terrain along a specific direction

Parameters

Z (numpy.ndarray, size=(m,n), units=meters) – elevation model
Az ({numpy.ndarray, float}, units=degrees) – argument or azimuth angle of interest
spac (float, units=meters) – spacing used for the elevation model

Returns

Slp_para (numpy.ndarray, size=(m,n), units=degrees) – slope in the along direction of the azimuth angle
Slp_perp (numpy.ndarray, size=(m,n), units=degrees) – slope in the perpendicular direction of the azimuth angle

aquatic transforms¶

functions of use for enhancement of water or suspended material

dhdt.preprocessing.aquatic_transforms.alternative_floating_algae_index(Red, Rededge, Near)¶

transform near and short wave infrared arrays to get a algae-index. Based upon [Wa18]

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Rededge (numpy.ndarray, size=(m,n)) – rededge band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

AFAI – array with floating algae transform

Return type

numpy.ndarray, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[AFAI=(B_{06} - B_{04})/(B_{8A} - B_{04})\]

References

Wa18: Wang, et al. “Remote sensing of Sargassum biomass, nutrients, and pigments” Geophysical Research Letters, vol.45(22) pp.12-359, 2018.

dhdt.preprocessing.aquatic_transforms.atmospherically_resistant_vegetation_index(Blue, Red, Near, gamma=1.0, L=0.5)¶

Based upon [KT92]

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

ARVI – array with atmospherically resistant vegetation index

Return type

numpy.ndarray, size=(m,n)

References

KT92: Kaufman & Tanre, “Atmospherically resistant vegetation index (ARVI)” IEEE transactions in geoscience and remote sensing, vol.30 pp.261–270, 1992.

dhdt.preprocessing.aquatic_transforms.floating_algae_index(Red, Near, Swir, df)¶

Following [Hu09]

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image
Swir (numpy.ndarray, size=(m,n)) – shortwave infrared band of satellite image
df (datafram) –

Returns

FAI – array with floating algae index

Return type

numpy.ndarray, size=(m,n)

References

Hu09: Hu, “A novel ocean color index to detect floating algae in the global oceans” Remote sensing of the enviroment, vol.113(10) pp.2188-2129, 2009

dhdt.preprocessing.aquatic_transforms.infrared_percentage_vegetation_index(Red, Near)¶

adjustment over the NDVI, see [Cr90].

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

NPVI – array with infrared percentage vegetation index

Return type

numpy.ndarray, size=(m,n), range=0…1

References

Cr90: Crippen “Calculating the vegetation index faster” Remote sensing of environment, vol.34 pp.71-73, 1990.

dhdt.preprocessing.aquatic_transforms.modified_chlorophyll_absorption_index(Green, Red, Rededge)¶

Based upon [Da00]

Parameters

Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Rededgde (numpy.ndarray, size=(m,n)) – rededge band of satellite image

Returns

MCARI – array with atmospherically resistant vegetation index

Return type

numpy.ndarray, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[MCARI= ((B_{05} - B_{04}) - .2(B_{05} - B_{03})) * (B_{04})/(B_{03})\]

References

Da00: Daughtry et al. “Estimating corn leaf chlorophyll concentration from leaf and canopy reflectance” Remote sensing of environment vol.74 pp.229–239, 2000.

dhdt.preprocessing.aquatic_transforms.modified_simple_ratio(Red, Near)¶

Based upon [Ch96]

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

SR – array with simple ratio

Return type

numpy.ndarray, size=(m,n)

References

Ch96: Chen, “Evaluation of vegetation indices and modified simple ratio for boreal applications” Canadian journal of remote sensing, vol.22 pp.229–242, 1996.

dhdt.preprocessing.aquatic_transforms.modified_soil_adjusted_vegetation_index(Red, Near)¶

Based upon [Qi94]

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

MSAVI – array with modified soil adjusted vegetation index

Return type

numpy.ndarray, size=(m,n)

References

Qi94: Qi et al., “A modified soil vegetation adjusted index” Remote sensing of environment, vol.48, pp.119–126, 1994.

dhdt.preprocessing.aquatic_transforms.normalized_difference_vegetation_index(Red, Near)¶

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

NDVI – array with normalized difference vegetation index

Return type

numpy.ndarray, size=(m,n)

References

Ro74: Rouse et al. “Monitoring the vernal advancements and retrogradation of natural vegetation” in NASA/GSFC final report, pp.1–137, 1974.

dhdt.preprocessing.aquatic_transforms.renormalized_difference_vegetation_index(Red, Near)¶

Based upon [RB95]

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

NDVI – array with renormalized difference vegetation index

Return type

numpy.ndarray, size=(m,n)

References

RB95: Rougean & Breon, “Estimating PAR absorbed by vegetation from bidirectional reflectance measurements” Remote sensing of environment, vol.51 pp.375–384, 1995.

dhdt.preprocessing.aquatic_transforms.simple_ratio(Red, Near)¶

Based upon [Jo69]

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

SR – array with simple ratio

Return type

numpy.ndarray, size=(m,n)

References

Jo69: Jordan, “Derivation of leaf area index from quality of light on the forest floor” Ecology vol.50 pp.663–666, 1969.

dhdt.preprocessing.aquatic_transforms.soil_adjusted_vegetation_index(Red, Near, L=0.5)¶

Based upon [Hu88]

Parameters

Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image
L (float, default=.5) – multiplication factor

Returns

SAVI – array with soil adjusted vegetation index

Return type

numpy.ndarray, size=(m,n)

References

Hu88: Huete, “A soil vegetation adjusted index (SAVI)” Remote sensing of environment, vol.25 pp.295–309, 1988.

dhdt.preprocessing.aquatic_transforms.triangular_vegetation_index(Green, Red, Rededge)¶

Based upon [BL00]

Parameters

Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Rededgde (numpy.ndarray, size=(m,n)) – rededge band of satellite image

Returns

TVI – array with triangular vegetation index

Return type

numpy.ndarray, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[TVI= .5 (120(B_{06} - B_{03}) - 200(B_{04} - B_{03}))\]

References

BL00: Broge & Leblanc, “Comparing prediction power and stability of broadband and hyperspectral vegetation indices for estimation of green leaf area index and canopy chlorophyll density” Remote sensing of environment, vol.76 pp.156–172, 2000.

snow transforms¶

functions of use for enhancement of snow and ice

dhdt.preprocessing.snow_transforms.automated_glacier_extraction_index(Red, Near, Short, alpha=0.5)¶

transform red, near and shortwave infrared arrays to AGEI, based on [Zh19].

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Near (numpy.array, size=(m,n)) – near infrared band of satellite image
Short (numpy.array, size=(m,n)) – shortwave infrared band of satellite image
alpha (float) –

Returns

AGEI – array with AGEI transform

Return type

numpy.array, size=(m,n)

See also

snow_cover_fraction, snow_fraction

Notes

Based on the bands of Sentinel-2:

\[AGEI = (B_{3}-B_{8}) / (B_{3}+B_{8})\]

References

Zh19: Zhang et al. “Automated glacier extraction index by optimization of red/SWIR and NIR/SWIR ratio index for glacier mapping using Landsat imagery” Water, vol.11 pp.1233, 2019.

dhdt.preprocessing.snow_transforms.normalized_difference_snow_ice_index(Red, Short)¶

transform red and short wave infrared arrays NDSII-index, see also [Xi01]

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Short (numpy.array, size=(m,n)) – shortwave infrared band of satellite image

Returns

NDSII – array with NDSII transform

Return type

numpy.array, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[NDSII = (B_{4}-B_{11}) / (B_{4}+B_{11})\]

The bands of Sentinel-2 correspond to the following spectral range:

\(B_{4}\) : red

\(B_{11}\) : shortwave infrared

References

Xi01: Xiao et al. “Assessing the potential of Vegetation sensor data for mapping snow and ice cover: A normalized snow and ice index” International journal of remote sensing, vol.22(13) pp.2479-2487, 2001.

dhdt.preprocessing.snow_transforms.normalized_difference_snow_index(Green, Short)¶

transform red and short wave infrared arrays NDSII-index, see also [Do89].

Parameters

Green (numpy.array, size=(m,n)) – green band of satellite image
Short (numpy.array, size=(m,n)) – shortwave infrared band of satellite image

Returns

NDSI – array with NDSI transform

Return type

numpy.array, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[NDSI = (B_{3}-B_{8}) / (B_{3}+B_{8})\]

The bands of Sentinel-2 correspond to the following spectral range:

\(B_{3}\) : green
\(B_{8}\) : near infrared

See also

normalized_difference_snow_ice_index

References

Do89: Dozier. “Spectral signature of alpine snow cover from the Landsat Thematic Mapper” Remote sensing of environment, vol.28 pp.9-22, 1989.

dhdt.preprocessing.snow_transforms.s3(Red, Near, Short)¶

transform red, near and shortwave infrared arrays to s3, see [SY99].

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Near (numpy.array, size=(m,n)) – near infrared band of satellite image
Short (numpy.array, size=(m,n)) – shortwave infrared band of satellite image

Returns

S3 – array with S3 transform

Return type

numpy.array, size=(m,n)

See also

snow_water_index

Notes

Based on the bands of Sentinel-2:

\[S3 = B_{8}(B_{4}-B_{11}) / ((B_{4} + B_{8})(B_{4} + B_{11}))\]

The bands of Sentinel-2 correspond to the following spectral range:

\(B_{4}\) : red

\(B_{8}\) : near infrared

\(B_{11}\) : shortwave infrared

See also

snow_water_index

References

SY99: Saito & Yamazaki. “Characteristics of spectral reflectance for vegetation ground surfaces with snowcover; Vegetation indeces and snow indices” Journal of Japan society of hydrology and water resources, vol.12(1) pp.28-38, 1999.

dhdt.preprocessing.snow_transforms.snow_cover_fraction(Near, Short)¶

transform near and short wave infrared arrays to get a snow-index, from [Pa02].

Parameters

Near (numpy.array, size=(m,n)) – near infrared band of satellite image
Short (numpy.array, size=(m,n)) – shortwave infrared band of satellite image

Returns

NDSII – array with NDSII transform

Return type

numpy.array, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[SCF= B_{8} / B_{11}\]

The bands of Sentinel-2 correspond to the following spectral range:

\(B_{8}\) : near infrared

\(B_{11}\) : shortwave infrared

References

Pa02: Paul et al. “The new remote-sensing-derived Swiss glacier inventory: I methods” Annuals of glaciology, vol.34 pp.355-361, 2002.

dhdt.preprocessing.snow_transforms.snow_fraction(Red, Short)¶

transform red and short wave infrared arrays to get a snow-index, see also [PK05].

Parameters

Red (numpy.array, size=(m,n)) – red band of satellite image
Short (numpy.array, size=(m,n)) – shortwave infrared band of satellite image

Returns

SF – array with snow fraction transform

Return type

numpy.array, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[SF = B_{4} / B_{11}\]

The bands of Sentinel-2 correspond to the following spectral range:

\(B_{4}\) : red

\(B_{11}\) : shortwave infrared

References

PK05: Paul & Kääb “Perspectives on the production of a glacier inventory from multispectral satellite data in Arctic Canada: Cumberland peninsula, Baffin Island” Annuals of glaciology, vol.42 pp.59-66, 2005.

dhdt.preprocessing.snow_transforms.snow_water_index(Green, Near, Short)¶

transform green, near and shortwave infrared arrays to snow water index, as described in [Di19].

Parameters

Green (numpy.array, size=(m,n)) – green band of satellite image
Near (numpy.array, size=(m,n)) – near infrared band of satellite image
Short (numpy.array, size=(m,n)) – shortwave infrared band of satellite image

Returns

SWI – array with SWI transform

Return type

numpy.array, size=(m,n)

See also

s3

Notes

Based on the bands of Sentinel-2:

\[SWI = B_{8}(B_{3}-B_{11}) / ((B_{3} + B_{8})(B_{3} + B_{11}))\]

The bands of Sentinel-2 correspond to the following spectral range:

\(B_{3}\) : green

\(B_{8}\) : near infrared

\(B_{11}\) : shortwave infrared

References

Di19: Dixit et al. “Development and evaluation of a new snow water index (SWI) for accurate snow cover delineation” Remote sensing, vol.11(23) pp.2774, 2019.

shadow transforms¶

functions of use for enhancement of intensities, making use of spectral properties

dhdt.preprocessing.shadow_transforms.apply_shadow_transform(method, Blue, Green, Red, RedEdge, Near, Shw, **kwargs)¶

Given a specific method, employ shadow transform

Parameters

method ({‘siz’,’ isi’,’ sei’,’ fcsdi’, ‘nsvi’, ‘nsvdi’, ‘sil’, ‘sr’, ‘sdi’, ‘sisdi’, ‘mixed’, ‘c3’, ‘entropy’, ‘shi’,’ sp’, 'nri'}) –
method name to be implemented,can be one of the following:
- ’siz’ : shadow index first version
- ’isi’ : improved shadow index
- ’sei’ : shadow enhancement index
- ’fcsdi’ : false color shadow difference index
- ’csi’ : combinational shadow index
- ’nsvdi’ : normalized saturation value difference index
- ’sil’ : shadow index second
- ’sr’ : specthem ratio
- ’sdi’ : shadow detector index
- ’sisdi’ : saturation intensity shadow detector index
- ’mixed’ : mixed property based shadow index
- ’msf’ : modified shadow fraction
- ’c3’ : color invariant
- ’entropy’ : entropy shade removal
- ’shi’ : shade index
- ’sp’ : shadow probabilities
- ’nri’ : normalized range shadow index
Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
RedEdge (numpy.ndarray, size=(m,n)) – red edge band of satellite image
Near (numpy.ndarray, size=(m,n)) – near-infrared band of satellite image
Shw (numpy.ndarray, size=(m,n)) – synthetic shading from for example a digital elevation model

Returns

M – shadow enhanced satellite image

Return type

numpy.ndarray, size=(m,n)

See also

handler_multispec.get_shadow_bands: provides Blue, Green, Red bandnumbers for a specific satellite
handler_multispec.read_shadow_bands: reads the specific bands given

dhdt.preprocessing.shadow_transforms.color_invariant(Blue, Green, Red)¶

transform red, green, blue arrays to color invariant (c3), see also [GS99] and [AA08].

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Red (numpy.array, size=(m,n)) – red band of satellite image

Returns

c3 – array with shadow enhancement

Return type

numpy.array, size=(m,n)

References

GS99: Gevers & Smeulders. “Color-based object recognition” Pattern recognition, vol.32 pp.453–464, 1999
AA08: Arévalo González & Ambrosio. “Shadow detection in colour high‐resolution satellite images” International journal of remote sensing, vol.29(7) pp.1945–1963, 2008

dhdt.preprocessing.shadow_transforms.combinational_shadow_index(Blue, Green, Red, Near)¶

transform red, green, blue arrays to combined shadow index. See also [Su19].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

CSI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

See also

shadow_enhancement_index

References

Su19: Sun et al. “Combinational shadow index for building shadow extraction in urban areas from Sentinel-2A MSI imagery” International journal of applied earth observation and geoinformation, vol.78 pp.53–65, 2019.

dhdt.preprocessing.shadow_transforms.entropy_shade_removal(Ia, Ib, Ic, a=None)¶

Make use of Wiens’ law to get illumination component, see also [Fi09].

Parameters

Ia (numpy.array, size=(m,n)) – highest frequency band of satellite image
Ib (numpy.array, size=(m,n)) – lower frequency band of satellite image
Ic (numpy.array, size=(m,n)) – lowest frequency band of satellite image
a (float, default=-1, unit=degrees) – angle of the coordinate rotation

Returns

S – shadow enhanced band

Return type

numpy.array, size=(m,n)

References

Fi09: Finlayson et al. “Entropy minimization for shadow removal” International journal of computer vision vol.85(1) pp.35-57 2009.

dhdt.preprocessing.shadow_transforms.false_color_shadow_difference_index(Green, Red, Near)¶

transform red and near infrared arrays to shadow index. See also [Te11].

Parameters

Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

FCSI – array with shadow enhancement

Return type

numpy.ndarray, size=(m,n)

Notes

\[FCSI = (I_{sat} - I_{int}) / (I_{sat} + I_{int})\]

References

Te11: Teke et al. “Multi-spectral false color shadow detection”, Proceedings of the ISPRS conference on photogrammetric image analysis, pp.109-119, 2011.

dhdt.preprocessing.shadow_transforms.fractional_range_shadow_index(*args)¶

transform multi-spectral arrays to shadow index

Parameters: *args (numpy.array, size=(m,n)) – different bands of a satellite image, all of the same extent
Returns: SI – shadow enhanced band
Return type: numpy.array, size=(m,n)

Notes

Schematically this looks like:

I1    ┌-----┐
 -┬---┤     |
I2|┌--┤     | Imin
 -┼┼┬-┤ min ├------┐
  |||┌┤     |      |┌-------┐
  ||||└-----┘      └┤ a / b |   SI
I3||||┌-----┐      ┌┤       ├------
 -┼┴┼┼┤     | Imax |└-------┘
I4└-┼┼┤     ├------┘
----┼┴┤ max |
    └-┤     |
      └-----┘

dhdt.preprocessing.shadow_transforms.improved_shadow_index(Blue, Green, Red, Near)¶

transform red, green, blue arrays to improved shadow index. Based upon [Zh21].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

ISI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

See also

shadow_index_zhou

Notes

\[ISI = (SI + (1-I_{near}))/(SI + (1+I_{near}))\]

References

Zh21: Zhou et al. “Shadow detection and compensation from remote sensing images under complex urban conditions”, 2021.

dhdt.preprocessing.shadow_transforms.mixed_property_based_shadow_index(Blue, Green, Red)¶

transform red, green, blue arrays to Mixed property-based shadow index, see also [Ha18].

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Red (numpy.array, size=(m,n)) – red band of satellite image

Returns

MPSI – array with shadow enhancement

Return type

numpy.array, size=(m,n)

References

Ha18: Han et al. “A mixed property-based automatic shadow detection approach for VHR multispectral remote sensing images” Applied sciences vol.8(10) pp.1883, 2018.

dhdt.preprocessing.shadow_transforms.modified_color_invariant(Blue, Green, Red, Near)¶

transform red, green, blue arrays to color invariant (c3), see also [GS99] and [BA15].

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Red (numpy.array, size=(m,n)) – red band of satellite image
Near (numpy.array, size=(m,n)) – near infrared band of satellite image

Returns

c3 – array with shadow enhancement

Return type

numpy.array, size=(m,n)

References

GS99: Gevers & Smeulders. “Color-based object recognition” Pattern recognition, vol.32 pp.453–464, 1999
BA15: Besheer & Abdelhafiz. “Modified invariant colour model for shadow detection” International journal of remote sensing, vol.36(24) pp.6214–6223, 2015.

dhdt.preprocessing.shadow_transforms.modified_normalized_difference_water_index(Green, Shortwave)¶

transform green and shortwave infrared arrays to modified NDW-index. See also [Xu06].

Parameters

Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Shortwave (numpy.ndarray, size=(m,n)) – shortwave infrared band of satellite image, for Sentinel-2 this is B11, originally the Landsat TM band 5 was used in [Xu06].

Returns

NDWI – array with NDWI transform

Return type

numpy.ndarray, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[NDWI = [B_{3}-B_{11}]/[B_{3}+B_{11}]\]

References

Xu06(1,2): Xu, “Modification of normalized difference water index (NDWI) to enhance open water features in remotely sensed imagery” International journal of remote sensing, vol.27(14) pp.3025–3033, 2006.

dhdt.preprocessing.shadow_transforms.modified_shadow_fraction(Blue, Green, Red, P_S=0.95)¶

transform red, green, blue arrays to shadow index. Based upon [Ch09].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
P_S (float, range=0...1) – threshold value for classification, based on the quantile

Returns

SI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

See also

shadow_hsv_fraction

References

Ch09: Chung, et al. “Efficient shadow detection of color aerial images based on successive thresholding scheme.” IEEE transactions on geoscience and remote sensing vol.47, pp.671–682, 2009.

dhdt.preprocessing.shadow_transforms.normalized_difference_blue_water_index(Blue, Near)¶

transform green and near infrared arrays NDW-index. See also [Qu11].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

NDWI – array with NDWI transform

Return type

numpy.ndarray, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[NDWI = [B_{3}-B_{8}]/[B_{3}+B_{8}]\]

References

Qu11: Qu et al, “Research on automatic extraction of water bodies and wetlands on HJU satellite CCD images” Remote sensing information, vol.4 pp.28–33, 2011

dhdt.preprocessing.shadow_transforms.normalized_difference_moisture_index(Near, Shortwave)¶

transform near and shortwave infrared arrays to NDM-index. See also [Wi02].

Parameters

Near (numpy.ndarray, size=(m,n)) – green band of satellite image
Shortwave (numpy.ndarray, size=(m,n)) – shortwave infrared band of satellite image

Returns

NDMI – array with NDMI transform

Return type

numpy.ndarray, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[NDMI = [B_{8}-B_{11}]/[B_{8}+B_{11}]\]

References

Wi02: Wilson, “Detection of forest harvest type using multiple dates of Landsat TM imagery” Remote sensing of environment, vol.80 pp.385–396, 2002.

dhdt.preprocessing.shadow_transforms.normalized_difference_water_index(Green, Near)¶

transform green and near infrared arrays NDW-index. See also [Ga96].

Parameters

Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

NDWI – array with NDWI transform

Return type

numpy.ndarray, size=(m,n)

Notes

Based on the bands of Sentinel-2:

\[NDWI = [B_{3}-B_{8}]/[B_{3}+B_{8}]\]

References

Ga96: Gao, “NDWI - a normalized difference water index for remote sensing of vegetation liquid water from space” Remote sensing of environonment, vol.58 pp.257–266, 1996

dhdt.preprocessing.shadow_transforms.normalized_range_shadow_index(*args)¶

transform multi-spectral arrays to shadow index

Parameters: *args (numpy.array, size=(m,n)) – different bands of a satellite image, all of the same extent
Returns: SI – shadow enhanced band
Return type: numpy.array, size=(m,n)

Notes

Schematically this looks like:

I1    ┌-----┐
 -┬---┤     |
I2|┌--┤     | Imin
 -┼┼┬-┤ min ├------┐
  |||┌┤     |      |┌-------┐
  ||||└-----┘      └┤(a-b)/ |   SI
I3||||┌-----┐      ┌┤  (a+b)├------
 -┼┴┼┼┤     | Imax |└-------┘
I4└-┼┼┤     ├------┘
----┼┴┤ max |
    └-┤     |
      └-----┘

dhdt.preprocessing.shadow_transforms.normalized_sat_value_difference_index(Blue, Green, Red)¶

transform red, green, blue arrays to normalized sat-value difference. See also [Ma08].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

NSVDI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

Notes

\[NSVDI = (I_{sat} - I_{int}) / (I_{sat} + I_{int})\]

References

Ma08: Ma et al. “Shadow segmentation and compensation in high resolution satellite images”, Proceedings of IEEE IGARSS, pp.II-1036–II-1039, 2008.

dhdt.preprocessing.shadow_transforms.reinhard(Blue, Green, Red)¶

transform red, green, blue arrays to luminance, see also [Re01].

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Red (numpy.array, size=(m,n)) – red band of satellite image

Returns

l – shadow enhanced band

Return type

numpy.array, size=(m,n)

References

Re01: Reinhard et al. “Color transfer between images” IEEE Computer graphics and applications vol.21(5) pp.34-41, 2001.

dhdt.preprocessing.shadow_transforms.sat_int_shadow_detector_index(Blue, RedEdge, Near)¶

transform red, green, blue arrays to sat-int shadow detector index, see also [MA18].

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
RedEdge (numpy.array, size=(m,n)) – rededge band of satellite image
Near (numpy.array, size=(m,n)) – near infrared band of satellite image

Returns

SISDI – array with shadow enhancement

Return type

numpy.array, size=(m,n)

References

MA18: Mustafa & Abedelwahab. “Corresponding regions for shadow restoration in satellite high-resolution images” International journal of remote sensing, vol.39(20) pp.7014–7028, 2018.

dhdt.preprocessing.shadow_transforms.shade_index(*args)¶

transform multi-spectral arrays to shade index, see also [HS10] and [Al12].

Parameters: *args (numpy.array, size=(m,n)) – different bands of a satellite image, all of the same extent
Returns: SI – shadow enhanced band
Return type: numpy.array, size=(m,n)

Notes

Amplify dark regions by simple multiplication:

\[SI = Pi_{i}^{N}{[1 - B_{i}]}\]

References

HS10: Hogan & Smith, “Refinement of digital elvation models from shadowing cues” IEEE computer society conference on computer vision and pattern recognition, 2010.
Al12: Altena, “Filling the white gap on the map: Photoclinometry for glacier elevation modelling” MSc thesis TU Delft, 2012.

dhdt.preprocessing.shadow_transforms.shadow_detector_index(Blue, Green, Red)¶

transform red, green, blue arrays to shadow detector index, see [MA17].

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Red (numpy.array, size=(m,n)) – red band of satellite image

Returns

SDI – array with shadow enhancement

Return type

numpy.array, size=(m,n)

References

MA17: Mustafa & Abedehafez. “Accurate shadow detection from high-resolution satellite images” IEEE geoscience and remote sensing letters, vol.14(4) pp.494–498, 2017.

dhdt.preprocessing.shadow_transforms.shadow_enhancement_index(Blue, Green, Red, Near)¶

transform red, green, blue arrays to SEI index. See also [Su19].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image
Near (numpy.ndarray, size=(m,n)) – near infrared band of satellite image

Returns

SEI – array with sei transform

Return type

numpy.ndarray, size=(m,n)

See also

combinational_shadow_index

Notes

Based on the bands of Sentinel-2:

\[SEI = [(B_{1}+B_{9})-(B_{3}+B_{8})]/[(B_{1}+B_{9})+(B_{3}+B_{8})]\]

References

Su19: Sun et al. “Combinational shadow index for building shadow extraction in urban areas from Sentinel-2A MSI imagery” International journal of applied earth observation and geoinformation, vol.78 pp.53–65, 2019.

dhdt.preprocessing.shadow_transforms.shadow_hcv_fraction(Blue, Green, Red)¶

transform red, green, blue arrays to shadow index. Based upon [Ts06].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

SI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

References

Ts06: Tsai. “A comparative study on shadow compensation of color aerial images in invariant color models.” IEEE Transactions on geoscience and remote sensing vol.44 pp.1661–1671, 2006.

dhdt.preprocessing.shadow_transforms.shadow_hsv_fraction(Blue, Green, Red)¶

transform red, green, blue arrays to shadow index. Based upon [Ts06].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

SI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

References

Ts06: Tsai. “A comparative study on shadow compensation of color aerial images in invariant color models.” IEEE Transactions on geoscience and remote sensing vol.44 pp.1661–1671, 2006.

dhdt.preprocessing.shadow_transforms.shadow_identification(Blue, Green, Red)¶

transform red, green, blue arrays to sat-value difference, following [Po03].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

SI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

Notes

\[SI = I_{sat} - I_{int}\]

References

Po03: Polidorio et al. “Automatic shadow segmentation in aerial color images”, Proceedings of the 16th Brazilian symposium on computer graphics and image processing, pp.270-277, 2003.

dhdt.preprocessing.shadow_transforms.shadow_index_liu(Blue, Green, Red)¶

transform red, green, blue arrays to shadow index, see [LX13] and [Su19].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

SI – array with shadow enhancement

Return type

numpy.ndarray, size=(m,n)

References

LX13: Liu & Xie. “Study on shadow detection in high resolution remote sensing image of PCA and HIS model”, Remote sensing technology and application, vol.28(1) pp. 78–84, 2013.
Su19: Sun et al. “Combinational shadow index for building shadow extraction in urban areas from Sentinel-2A MSI imagery” International journal of applied earth observation and geoinformation, vol.78 pp.53–65, 2019.

dhdt.preprocessing.shadow_transforms.shadow_index_zhou(Blue, Green, Red)¶

transform red, green, blue arrays to shadow index, based upon [Zh21].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

SI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

See also

improved_shadow_index

References

Zh21: Zhou et al. “Shadow detection and compensation from remote sensing images under complex urban conditions”, 2021.

dhdt.preprocessing.shadow_transforms.shadow_probabilities(Blue, Green, Red, Near, **kwargs)¶

transform blue, green, red and near infrared to shade probabilities, see also [FS10] and [Rü13].

Parameters

Blue (numpy.array, size=(m,n)) – blue band of satellite image
Green (numpy.array, size=(m,n)) – green band of satellite image
Red (numpy.array, size=(m,n)) – red band of satellite image
Near (numpy.array, size=(m,n)) – near infrared band of satellite image

Returns

M – shadow enhanced band

Return type

numpy.array, size=(m,n)

References

FS10: Fredembach & Süsstrunk. “Automatic and accurate shadow detection from (potentially) a single image using near-infrared information” EPFL Tech Report 165527, 2010.
Rü13: Rüfenacht et al. “Automatic and accurate shadow detection using near-infrared information” IEEE transactions on pattern analysis and machine intelligence, vol.36(8) pp.1672-1678, 2013.

dhdt.preprocessing.shadow_transforms.shadow_ycbcr_fraction(Blue, Green, Red)¶

transform red, green, blue arrays to shadow index. Based upon [Ts06].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

SI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

References

Ts06: Tsai. “A comparative study on shadow compensation of color aerial images in invariant color models.” IEEE Transactions on geoscience and remote sensing vol.44 pp.1661–1671, 2006.

dhdt.preprocessing.shadow_transforms.shadow_yiq_fraction(Blue, Green, Red)¶

transform red, green, blue arrays to shadow index. Based upon [Ts06].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

SI – array with shadow transform

Return type

numpy.ndarray, size=(m,n)

References

Ts06: Tsai. “A comparative study on shadow compensation of color aerial images in invariant color models.” IEEE Transactions on geoscience and remote sensing vol.44 pp.1661–1671, 2006.

dhdt.preprocessing.shadow_transforms.shannon_entropy(X, band_width=100)¶

calculate shanon entropy from data sample

Parameters

X (numpy.ndarray, size=(m,1)) – data array
band_width (integer, optional) – sample bandwith

Returns

shannon – entropy value of the total data sample

Return type

float

dhdt.preprocessing.shadow_transforms.specthem_ratio(Blue, Green, Red)¶

transform red, green, blue arrays to specthem ratio, see [Si18].

Parameters

Blue (numpy.ndarray, size=(m,n)) – blue band of satellite image
Green (numpy.ndarray, size=(m,n)) – green band of satellite image
Red (numpy.ndarray, size=(m,n)) – red band of satellite image

Returns

Sr – array with shadow enhancement

Return type

numpy.ndarray, size=(m,n)

Notes

In the paper the logarithmic is also used further to enhance the shadows,

\[Sr = log{[Sr+1]}\]

References

Si18: Silva et al. “Near real-time shadow detection and removal in aerial motion imagery application” ISPRS journal of photogrammetry and remote sensing, vol.140 pp.104–121, 2018.

shadow filters¶

functions of use for enhancement of intensities, making use of spatial properties

dhdt.preprocessing.shadow_filters.L0_smoothing(Z, lamb=0.02, kappa=2.0, beta_max=100000.0)¶

Parameters

Z (numpy.ndarray, size={(m,n), (m,n,b)}, dtype=float) – grid with intensity values
lamb (float, default=.002) –
kappa (float, default=2.) –
beta_max (float, default=10000) –

Returns

Z – modified intensity image

Return type

numpy.ndarray, size={(m,n), (m,n,b)}, dtype=float

References

Xu11: Xu et al. “Image smoothing via L0 gradient minimization” ACM transactions on graphics, 2011.

dhdt.preprocessing.shadow_filters.anistropic_diffusion_scalar(Z, iter=10, K=0.15, s=0.25, n=4)¶

non-linear anistropic diffusion filter of a scalar field

Parameters

Z (np.array, size=(m,n), dtype={float,complex}, ndim={2,3}) – intensity array
iter (integer, {x ∈ ℕ | x ≥ 0}) – amount of iterations
K (float, default=.15) – parameter based upon the noise level
s (float, default=.25) – parameter for the integration constant
n ({4,8}) – amount of neighbors used

Returns

I

Return type

np.array, size=(m,n)

References

PM87: Perona & Malik “Scale space and edge detection using anisotropic diffusion” Proceedings of the IEEE workshop on computer vision, pp.16-22, 1987
Ge92: Gerig et al. “Nonlinear anisotropic filtering of MRI data” IEEE transactions on medical imaging, vol.11(2), pp.221-232, 1992

dhdt.preprocessing.shadow_filters.diffusion_strength_1(Z, K)¶

first diffusion function, proposed by [PM87], when a complex array is provided the absolute magnitude is used, following [Ge92]

Parameters

Z (np.array, size=(m,n), dtype={float,complex}, ndim={2,3}) – array with intensities
K (float) – parameter based upon the noise level

Returns

g – array with diffusion parameters

Return type

np.array, size=(m,n), dtype=float

References

PM87: Perona & Malik “Scale space and edge detection using anisotropic diffusion” Proceedings of the IEEE workshop on computer vision, pp.16-22, 1987
Ge92: Gerig et al. “Nonlinear anisotropic filtering of MRI data” IEEE transactions on medical imaging, vol.11(2), pp.221-232, 1992

dhdt.preprocessing.shadow_filters.diffusion_strength_2(Z, K)¶

second diffusion function, proposed by [PM87], when a complex array is provided the absolute magnitude is used, following [Ge82].

Parameters

Z (np.array, size=(m,n), dtype={float,complex}) – array with intensities
K (float) – parameter based upon the noise level

Returns

g – array with diffusion parameters

Return type

np.array, size=(m,n), dtype=float

References

PM87: Perona & Malik “Scale space and edge detection using anisotropic diffusion” Proceedings of the IEEE workshop on computer vision, pp.16-22, 1987.
Ge92: Gerig et al. “Nonlinear anisotropic filtering of MRI data” IEEE transactions on medical imaging, vol.11(2), pp.221-232, 1992.

dhdt.preprocessing.shadow_filters.enhance_shadows(Shw, method, **kwargs)¶

Given a specific method, employ shadow transform

Parameters

Shw (np.array, size=(m,n), dtype={float,integer}) – array with intensities of shading and shadowing
method ({‘mean’,’kuwahara’,’median’,’otsu’,'anistropic'}) –
method name to be implemented,can be one of the following:
- ’mean’ : mean shift filter
- ’kuwahara’ : kuwahara filter
- ’median’ : iterative median filter
- ’anistropic’ : anistropic diffusion filter

Returns

M – shadow enhanced image, done through the given method

Return type

np.array, size=(m,n), dtype={float,integer}

dhdt.preprocessing.shadow_filters.fade_shadow_cast(Shw, az, t_size=9)¶

Parameters

Shw (np.array, size=(m,n)) – image with mask of shadows
az (float, unit=degrees) – illumination orientation
t_size (integer, {x ∈ ℕ | x ≥ 1}) – buffer size of the Gaussian blur

Returns

Shw – image with faded shadows on the occluding end

Return type

np.array, size=(m,n), dtype=float, range=0…1

dhdt.preprocessing.shadow_filters.iterative_median_filter(Z, tsize=5, loop=50)¶

Transform intensity to more clustered intensity, through iterative filtering with a median operation

Parameters

Z (np.array, size=(m,n), dtype=float) – array with intensity values
tsize (integer, {x ∈ ℕ | x ≥ 1}) – dimension of the kernel
loop (integer, {x ∈ ℕ | x ≥ 0}) – amount of iterations

Returns

I_new – array with stark edges

Return type

np.array, size=(m,n), dtype=float

See also

kuwahara_filter

dhdt.preprocessing.shadow_filters.kuwahara_filter(Z, tsize=5)¶

Transform intensity to more clustered intensity

Parameters

Z (np.array, size=(m,n), dtype=float) – array with intensity values
tsize (integer, {x ∈ ℕ | x ≥ 1}) – dimension of the kernel

Returns

Z_new

Return type

np.array, size=(m,n), dtype=float

Notes

The template is subdivided into four blocks, where the sampled mean and standard deviation are calculated. Then mean of the block with the lowest variance is assigned to the central pixel. The configuration of the blocks look like:

┌-----┬-┬-----┐ ^
|  A  | |  B  | |
├-----┼-┼-----┤ | tsize
├-----┼-┼-----┤ |
|  C  | |  D  | |
└-----┴-┴-----┘ v

See also

iterative_median_filter

dhdt.preprocessing.shadow_filters.mean_shift_filter(Z, quantile=0.1)¶

Transform intensity to more clustered intensity, through mean-shift

Parameters

Z (np.array, size=(m,n), dtype=float) – array with intensity values
quantile (float, range=0...1) –

Returns

labels – array with numbered labels

Return type

np.array, size=(m,n), dtype=integer

composition and geometry of the atmosphere¶

functions of use for describing the refractive properties of the atmosphere

dhdt.preprocessing.atmospheric_geometry.ciddor_eq5(ρ_a, ρ_w, n_axs, n_ws, ρ_axs, ρ_ws)¶

estimating the refractive index through summation

Parameters

ρ_a ({numpy.array, float}, unit=kg m-3) – density of dry air
ρ_w ((numpy.array, float}, unit=kg m-3) – density of moist air
n_axs (numpy.array, size=(k,)) – refractive index for dry air at sea level at a specific wavelength
n_ws (numpy.array, size=(k,)) – refractive index for standard moist air at sea level for a specific wavelength
ρ_axs (float, unit=kg m-3) – density of standard dry air at sea level
ρ_ws (float, unit=kg m-3) – density of standard moist air at sea level

Returns

n_prop – refractive index

Return type

float

References

Ow67: Owens, “Optical refractive index of air: Dependence on pressure, temperature and composition”, Applied optics, vol.6(1) pp.51-59, 1967.

dhdt.preprocessing.atmospheric_geometry.ciddor_eq6(ρ_a, ρ_w, n_axs, n_ws, ρ_axs, ρ_ws)¶

estimating the refractive index through the Lorenz-Lorentz relation

Parameters

ρ_a (float, unit=kg m-3) – density of dry air
ρ_w (float, unit=kg m-3) –
n_axs (float) – refractive index for dry air at sea level
n_ws (float) – refractive index for standard moist air at sea level
ρ_axs (float, unit=kg m-3) – density of standard dry air at sea level
ρ_ws (float, unit=kg m-3) – density of standard moist air at sea level

Returns

n_LL – refractive index

Return type

float

References

Ow67: Owens, “Optical refractive index of air: Dependence on pressure, temperature and composition”, Applied optics, vol.6(1) pp.51-59, 1967.
Ci96: Ciddor, “Refractive index of air: new equations for the visible and near infrared”, Applied optics, vol.35(9) pp.1566-1573, 1996.

dhdt.preprocessing.atmospheric_geometry.compressability_moist_air(p, T, x_w)¶

Parameters

p (float, unit=Pascal) – total pressure
T (float, unit=Kelvin) – temperature
x_w (float) – molar fraction of water vapor in moist air

Returns

Z – compressability factor

Return type

float

See also

water_vapor_frac

References

Ci96: Ciddor, “Refractive index of air: new equations for the visible and near infrared”, Applied optics, vol.35(9) pp.1566-1573, 1996.
DaXX: Davis, “Equation for the determination of the density of moist air (1981/91)” Metrologica, vol.29 pp.67-70.

dhdt.preprocessing.atmospheric_geometry.get_CO2_level(lat, date, m=3, nb=3)¶

Rough estimation of CO₂, based upon measurements of global ‘Station data’__

The annual trend is based upon the ‘Global trend’__ in CO₂ while the seasonal trend is based upon relations as shown in Figure 1 in [Ba16]. Where a latitudal component is present in the ampltitude, as well as, an asymmetric triangular wave.

Parameters

lat (float, unit=degrees, range=-90...+90) – latitude of the location of interest
date (np.datetime64, range=1950...2030) – time of interest
m (float, default=3) – assymetry of the wave - m<=2: crest is leftwards leaning - m==2: symmetric wave - m>=2: the ramp is leftwards leaning
nb (integer, default=3) – number of base functions to use, higher numbers will give a more pointy wave function

Returns

total_co2 – estimate of spatial temporal carbon dioxide (CO₂) value

Return type

float, unit=ppm

Notes

Data where this fitting is based on, can be found here:

The following acronyms are used:

CO2 : carbon dioxide

ppm : parts per million

Examples

>>> import numpy as np
>>> import matplotlib.pyplot as plt

Plot the annual trend at 60ºN

>>> t = np.arange("1950-01-01","2022-01-01",dtype="M8[Y]")
>>> co2 = get_CO2_level(60., t)
>>> plt.plot(t, co2)

Plot seasonal signal

>>> t = np.arange("2018-01-01","2022-01-01",dtype="M8[D]")
>>> co2 = get_CO2_level(60., t)
>>> plt.plot(t, co2)

References

Ba16: Barnes et al. “Isentropic transport and the seasonal cycle amplitude of CO₂” Journal of geophysical research: atmosphere, vol.121 pp.8106-8124, 2016.

dhdt.preprocessing.atmospheric_geometry.get_T_in_troposphere(h, T_0)¶

Using parameters of the first layer of the eight layer atmospheric model of ISO 2533:1970 to estimate the temperature at different altitudes

Parameters

h ({float, numpy.array}, unit=m) – altitude above sea-level
T_0 (float, unit=Kelvin) – temperature at the surface (reference)

Returns

T_h – temperature in the troposphere

Return type

{float, numpy.array}, unit=Kelvin

References

Ya16: Yan et al, “Correction of atmospheric refraction geolocation error of high resolution optical satellite pushbroom images” Photogrammetric engineering & remote sensing, vol.82(6) pp.427-435, 2016.

dhdt.preprocessing.atmospheric_geometry.get_T_sealevel(lat, method='noerdlinger')¶

The temperature at sea level can be related to its latitude [Al73] and a least squares fit is given in [No99] and [Ya16].

Parameters

lat ({float, numpy.ndarray}, unit=degrees, range=-90...+90) – latitude of interest

Returns

T_sl ({float, numpy.array}, unit=Kelvin) – estimate of temperature at sea level
method ({‘noerdlinger’, ‘yan’}) –
- ‘noerdlinger’, from [2] has no dependency between hemispheres
- ’yan’, from [3] is hemisphere dependent

References

Al73: Allen, “Astrophysical quantities”, pp.121-124, 1973.
No99: Noerdlinger, “Atmospheric refraction effects in Earth remote sensing” ISPRS journal of photogrammetry and remote sensing, vol.54, pp.360-373, 1999.
Ya16: Yan et al, “Correction of atmospheric refraction geolocation error of high resolution optical satellite pushbroom images” Photogrammetric engineering & remote sensing, vol.82(6) pp.427-435, 2016.

dhdt.preprocessing.atmospheric_geometry.get_density_air(T, P, fH, moist=True, CO2=450, M_w=0.018015, R=8.31451, saturation=False)¶

Parameters

T (float, unit=Kelvin) – temperature at location
P (float, unit=Pascal) – the total pressure in Pascals
fH (float, range=0...1) – fractional humidity
moist (bool) – estimate moist (True) or dry air (False)
CO2 (float, unit=ppm of CO₂) – parts per million of CO₂ in the atmosphere
M_w (float, unit=kg mol-1) – molar mass of water vapor
R (float, unit=J mol-1 K-1) – universal gas constant

Returns

ρ – density of moist air

Return type

float, unit=kg m3

Notes

The following parameters are used in this function:

M_a : unit=kg mol-1, molar mass of dry air

x_w : molecular fraction of water vapor

Z : compressibility of moist air

CO2 : unit=ppm, carbon dioxide

ppm : parts per million volume

References

Ci96: Ciddor, “Refractive index of air: new equations for the visible and near infrared”, Applied optics, vol.35(9) pp.1566-1573, 1996.
Da92: Davis, “Equation for the determination of the density of moist air (1981/91)” Metrologica, vol.29 pp.67-70, 1992.

dhdt.preprocessing.atmospheric_geometry.get_density_fraction(φ, h_0, alpha=0.0065, R=8314.36, M_t=28.825)¶

Parameters

ϕ (unit=degrees) – latitude of point of interest
h_0 (float, unit=meters) – initial altitude above geoid
alpha (float, unit=K km-1, default=0.0065) – lapse rate in the Troposphere
R (float, unit=J kmol-1 K-1, default=8314.36) – universal gas constant
M_t (float, unit=kg kmol-1, default=28.825) – mean moleculear mass in the Troposphere

Returns

ρ_frac – fraction of density in relation to density as sea-level

Return type

float

Notes

The following parameters are used

T_sl : unit=Kelvin, temperature at sea level T_t : unit=Kelvin, temperature at the Tropopause h_t : unit=meters, altitude of the Tropopause g : unit=m s-2, acceleration due to gravity

References

No99: Noerdlinger, “Atmospheric refraction effects in Earth remote sensing” ISPRS journal of photogrammetry and remote sensing, vol.54, pp.360-373, 1999.

dhdt.preprocessing.atmospheric_geometry.get_height_tropopause(φ)¶

The tropopause can be related to its latitude [Al73] and a least squares fit is given in [No99].

Parameters: ϕ ({float, numpy.ndarray}, unit=degrees, range=-90...+90) – latitude of interest
Returns: h_t – estimate of tropopause, that is the layer between the troposphere and the stratosphere
Return type: {float, numpy.ndarray}, unit=meters

See also

get_mean_lat

Notes

The Strato- and Troposphere have different refractive behaviour. A simplified view of this can be like:

                    z_s
  Mesosphere       /
┌-----------------/-┐  ↑ 80 km    |   *       T_s  |*
|                /  |  |          |   *            |*
| Stratosphere  /   |  |          |  *             |*
|              /    |  |          |  *             |*
├--Tropopause-/-----┤  |  ↑ 11 km |_*_________T_t  |*________
|            |      |  |  |       | **             | *
|  Tropo     |      |  |  |       |    **          |  **
|  sphere    | z_h  |  |  |       |       **  T_h  |     ****
└------------#------┘  ↓  ↓       └-----------T_0  └---------
 Earth surface                    Temperature      Pressure

References

Al73: Allen, “Astrophysical quantities”, pp.121-124, 1973.
No99: Noerdlinger, “Atmospheric refraction effects in Earth remote sensing” ISPRS journal of photogrammetry and remote sensing, vol.54, pp.360-373, 1999.

dhdt.preprocessing.atmospheric_geometry.get_sat_vapor_press(T, method='IAPWS')¶

uses either [1] or the international standard of IAPWS [2].

Parameters: T ({float, numpy.array}, unit=Kelvin) – temperature
Returns: svp – saturation vapor pressure
Return type: {float, numpy.array}

References

Gi82: Giacomo, “Equation for the determination of the density of moist air” Metrologica, vol.18, pp.33-40, 1982.
WP02: Wagner and Pruß, “The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use.” Journal of physical and chemical reference data, vol.31(2), pp.387-535, 2002.

dhdt.preprocessing.atmospheric_geometry.get_sat_vapor_press_ice(T)¶

following the international standard of IAPWS [2].

Parameters: T ({float, numpy.array}, unit=Kelvin) – temperature
Returns: svp – saturation vapor pressure
Return type: {float, numpy.array}

References

WP02: Wagner and Pruß, “The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use.” Journal of physical and chemical reference data, vol.31(2), pp.387-535, 2002.

dhdt.preprocessing.atmospheric_geometry.get_simple_density_fraction(φ)¶

The density fraction is related to latitude through a least squares fit as is given in [No99].

Parameters: ϕ ({float, numpy.array}, unit=degrees, range=-90...+90) – latitude of interest
Returns: densFrac – estimate of the density fraction
Return type: {float, numpy.array}

See also

get_mean_lat

References

No99: Noerdlinger, “Atmospheric refraction effects in Earth remote sensing” ISPRS journal of photogrammetry and remote sensing, vol.54, pp.360-373, 1999.

dhdt.preprocessing.atmospheric_geometry.get_water_vapor_enhancement(t, p)¶

estimate the enhancement factor for the humidity calculation

Parameters

t ({float, numpy.array}, unit=Celsius) – temperature
p ({float, numpy.array}, unit=Pascal) – atmospheric pressure

Returns

f – enhancement factor

Return type

{float, numpy.array}

References

Gi82: Giacomo, “Equation for the determination of the density of moist air” Metrologica, vol.18, pp.33-40, 1982.

dhdt.preprocessing.atmospheric_geometry.get_water_vapor_press(T)¶

Parameters: t ({float, numpy.array}, unit=Kelvin) – temperature
Returns: P_w – water vapor pressure
Return type: {float, numpy.array}, unit=Pascal

See also

get_sat_vapor_press

References

Ya16: Yan et al, “Correction of atmospheric refraction geolocation error of high resolution optical satellite pushbroom images” Photogrammetric engineering & remote sensing, vol.82(6) pp.427-435, 2016.

dhdt.preprocessing.atmospheric_geometry.get_water_vapor_press_ice(T)¶

Parameters: T ({float, numpy.array}, unit=Kelvin) – temperature
Returns: P_w – water vapor pressure
Return type: {float, numpy.array}, unit=Pascal

References

MM93: Marti & Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250K” Geophysical research letters, vol.20(5) pp.363-366, 1993.

dhdt.preprocessing.atmospheric_geometry.refraction_angle_analytical(zn_0, n_0)¶

Parameters

zn_0 ({float, numpy.array}, unit=degrees) – observation angle, when atmosphere is not taken into account
n_0 ({float, numpy.array}) – refractive index at the surface

Returns

zn – corrected observation angle, taking refraction into account

Return type

{float, numpy.array}, unit=degrees

References

No99: Noerdlinger, “Atmospheric refraction effects in Earth remote sensing” ISPRS journal of photogrammetry and remote sensing, vol.54, pp.360-373, 1999.

dhdt.preprocessing.atmospheric_geometry.refraction_spherical_symmetric(zn_0, lat=None, h_0=None)¶

Parameters

zn_0 – observation angle, when atmosphere is not taken into account
float – observation angle, when atmosphere is not taken into account
lat (float, unit=degrees, range=-90...+90) – latitude of point of interest
h_0 (float, unit=meters) – initial altitude above geoid

Returns

zn_hat – analytical refraction angle

Return type

float

See also

get_mean_lat

Notes

The angles related to the sun are as follows:

surface normal              * sun
↑                     ↑    /
|                     |   /
|-- zenith angle      |  /
| /                   | /|
|/                    |/ | elevation angle
+----                 +------

References

No99: Noerdlinger, “Atmospheric refraction effects in Earth remote sensing” ISPRS journal of photogrammetry and remote sensing, vol.54, pp.360-373, 1999.
BJ94: Birch and Jones, “Correction to the updated Edlen equation for the refractive index of air”, Metrologica, vol.31(4) pp.315-316, 1994.

dhdt.preprocessing.atmospheric_geometry.refractive_index_CO2(n_s, CO2)¶

correct standard refractivity for diffferent carbon dioxide concentrations, see [2] for more information.

Parameters

n_s ({float, numpy.array}) – refractivity of standard air
CO2 ({float, numpy.array}, unit=ppm) – concentration of carbon dioxide (CO₂) in the atmosphere

Returns

n_x – refractivity of standard air at a given CO₂ concentration

Return type

{float, numpy.array}

Notes

The following acronyms are used:

CO2 : carbon dioxide

ppm : parts per million

References

BD93: Birch & Downs, “An updated Edlen equation for the refractive index of air” Metrologica, vol.30(155) pp.155-162, 1993.
Ed66: Edlén, “The refractive index of air”, Metrologica, vol.2(2) pp.71-80, 1966.

dhdt.preprocessing.atmospheric_geometry.refractive_index_broadband(df, T_0, P_0, fH_0, CO2=450.0, T_a=15.0, P_a=101325.0, T_w=20.0, P_w=1333.0, LorentzLorenz=False)¶

Estimate the refractive index in for wavelengths in the range of 300…1700 nm, see also [1].

Parameters

df ({dataframe, float}, unit=µm) – central wavelengths of the spectral bands
CO2 (float, unit=ppm of CO₂, default=450.) – parts per million of CO₂
T_0 (float, unit=Celsius) – temperature at location
P_0 (float, unit=Pascal) – the total pressure in Pascal
fH_0 (float, range=0...1) – fractional humidity
T_a (float, unit=Celcius) – temperature of standard dry air, see Notes
P_a (float, unit=Pascal) – pressure of standard dry air, see Notes
T_w (float, unit=Celsius) – temperature of standard moist air, see [1]
P_w (float, unit=Pascal) – pressure of standard moist air, see [1]
LorentzLorenz (bool) –
Two ways are possible to calculate the proportional refraction index, when
- True : the Lorentz-Lorenz relationship is used.
- False : component wise addition is used

Returns

n – index of refraction

Return type

{float, numpy.array}

Notes

Standard air [2] is defined to be dry air at a temperature of 15 degrees Celsius and a total pressure of 1013.25 mb, having the following composition by molar percentage:

78.09% nitrogen (N₂)

20.95% oxygen (O₂)

0.93% argon (Ar)

0.03% carbon dioxide (C0₂)

See also

ciddor_eq5: calculation used for the Lorentz-Lorenz relationship
ciddor_eq6: calculation used for component wise addition

refractive_index_visible

References

Ci96: Ciddor, “Refractive index of air: new equations for the visible and near infrared”, Applied optics, vol.35(9) pp.1566-1573, 1996.
Ow67: Owens, “Optical refractive index of air: Dependence on pressure, temperature and composition”, Applied optics, vol.6(1) pp.51-59, 1967.

dhdt.preprocessing.atmospheric_geometry.refractive_index_broadband_vapour(σ)¶

Parameters: σ ({float, numpy.array}, unit=µm-1) – vacuum wavenumber, that is the reciprocal of the vacuum wavelength
Returns: n_ws – refractive index for standard moist air at sea level
Return type: {float, numpy.array}

References

Ow67: Owens, “Optical refractive index of air: Dependence on pressure, temperature and composition”, Applied optics, vol.6(1) pp.51-59, 1967.
Ci96: Ciddor, “Refractive index of air: new equations for the visible and near infrared”, Applied optics, vol.35(9) pp.1566-1573, 1996.

dhdt.preprocessing.atmospheric_geometry.refractive_index_simple(p, RH, t)¶

simple shop-floor formula fro refraction, see appendix B in [1].

Parameters

p ({numpy.array, float}, unit=kPa) – pressure
RH ({numpy.array, float}, unit=percent) – relative humidity
t ({numpy.array, float}, unit=Celsius) – temperature

Returns

n – refractive index

Return type

{numpy.array, float}

References

1: https://emtoolbox.nist.gov/wavelength/Documentation.asp#AppendixB

dhdt.preprocessing.atmospheric_geometry.refractive_index_visible(df, T, P, p_w=None, CO2=None)¶

calculate refractive index, based on measurement around 633nm, see [1].

It applies to ambient atmospheric conditions over the range of wavelengths 350 nm to 650 nm.

Parameters

df ({dataframe, float}, unit=µm) – central wavelengths of the spectral bands
T ({float, numpy.array}, unit=Celcius) – temperature at location
P ({float, numpy.array}, unit=Pascal) – atmospheric pressure at location
CO2 ({float, numpy.array}, unit=ppm) – concentration of carbon dioxide (CO₂) in the atmosphere

Returns

n_0 – index of refraction

Return type

numpy.array

See also

refractive_index_broadband

References

BJ94: Birch and Jones, “Correction to the updated Edlén equation for the refractive index of air”, Metrologica, vol.31(4) pp.315-316, 1994.
Ed66: Edlén, “The refractive index of air”, Metrologica, vol.2(2) pp.71-80, 1966.
BJ94: Birch and Jones, “An updated Edlén equation for the refractive index of air”, Metrologica, vol.30 pp.155-162, 1993.

dhdt.preprocessing.atmospheric_geometry.update_list_with_corr_zenith_pd(dh, file_dir, file_name='conn.txt')¶

Parameters

dh (pandas.DataFrame) – array with photohypsometric information
file_dir (string) – directory where the file should be situated
file_name (string, default='conn.txt') – name of the file to export the data columns to

Notes

The nomenclature is as follows:

 * sun
              \ <-- sun trace
                 |\ <-- caster
    |              |  \                    ^ Z
    |   \                   |
----┴----+  <-- casted      └-> {X,Y}

The angles related to the sun are as follows:

surface normal              * sun
^                     ^    /
|                     |   /
|-- zenith angle      |  /
| /                   | /|
|/                    |/ | elevation angle
└----                 └------ {X,Y}

The azimuth angle declared in the following coordinate frame:

     ^ North & Y
     |
- <--|--> +
     |
     +----> East & X

The text file has at least the following columns:

* conn.txt
├ caster_X      <- map location of the start of the shadow trace
├ caster_Y
├ casted_X
├ casted_Y      <- map location of the end of the shadow trace
├ azimuth       <- argument of the illumination direction
├ zenith        <- off-normal angle of the sun without atmosphere
└ zenith_refrac <- off-normal angle of the sun with atmosphere

See also

get_refraction_angle

dhdt.preprocessing.atmospheric_geometry.water_vapor_frac(p, T, fH)¶

Parameters

p (float, unit=Pascal) – total pressure
T (float, unit=Kelvin) – temperature
fH (float, range=0...1) – fractional humidity

Returns

x_w – molar fraction of water vapor in moist air

Return type

float

Notes

The following parameters are used in this function:

T : unit=Kelvin, temperature svp : unit=Pascal, saturation vapor pressure t : unit=Celcius, temperature

References

Ci96: Ciddor, “Refractive index of air: new equations for the visible and near infrared”, Applied optics, vol.35(9) pp.1566-1573, 1996.
MM93: Marti & Mauersberger, “A survey and new measurements of ice vapor pressure at temperatures between 170 and 250K” Geophysical research letters, vol.20(5) pp.363-366, 1993.
Gi82: Giacomo, “Equation for the determination of the density of moist air” Metrologica, vol.18, pp.33-40, 1982.