import rastereasy
Dempster-Shafer fusion for 2 hypotheses
It is possible to fuse belief masses issued from images for two hypotheses A and B. For this, we assume that each image is composed of 3 spectral bands :
1st band : belief mass $m(A)$ for hypothesis $A$
2nd band : belief mass $m(B)$ for hypothesis $B$
3rd band : belief mass $m(A \cup B)$ for hypothesis $A \cup B$ (uncertainty)
For consistent mass functions, the sum along bands must be $1$ for each pixel of each source
1) Create 5 toy images
# 1. Read image (just to have meta informations)
name_im='./data/demo/sentinel.tif'
image=rastereasy.Geoimage(name_im)
# 2. Create a 3 band image consistent with mass functions (i.e. positive and sum to 1)
import numpy as np
raw = np.random.rand(image.shape[0], image.shape[1], 3)
# 3. Normalize mass functions such that m(A) + m(B) + m(A∪B) = 1 in each pixel
mass_functions = raw / np.sum(raw, axis=2, keepdims=True)
print(mass_functions.shape)
# 4. Upload the table
mass_function1 = image.upload_image(mass_functions,channel_first=False)
# 5 verify that the sum is 1 along bands
print(mass_function1.sum(axis='band'))
## Repeat this operation 5 times to create 5 sources
raw = np.random.rand(image.shape[0], image.shape[1], 3)
mass_functions = raw / np.sum(raw, axis=2, keepdims=True)
mass_function2 = image.upload_image(mass_functions,channel_first=False)
raw = np.random.rand(image.shape[0], image.shape[1], 3)
mass_functions = raw / np.sum(raw, axis=2, keepdims=True)
mass_function3 = image.upload_image(mass_functions,channel_first=False)
raw = np.random.rand(image.shape[0], image.shape[1], 3)
mass_functions = raw / np.sum(raw, axis=2, keepdims=True)
mass_function4 = image.upload_image(mass_functions,channel_first=False)
raw = np.random.rand(image.shape[0], image.shape[1], 3)
mass_functions = raw / np.sum(raw, axis=2, keepdims=True)
mass_function5 = image.upload_image(mass_functions,channel_first=False)
(1000, 1000, 3)
[[1. 1. 1. ... 1. 1. 1.]
[1. 1. 1. ... 1. 1. 1.]
[1. 1. 1. ... 1. 1. 1.]
...
[1. 1. 1. ... 1. 1. 1.]
[1. 1. 1. ... 1. 1. 1.]
[1. 1. 1. ... 1. 1. 1.]]
mass_function1.image
array([[[0.12571802, 0.25086056, 0.18328983, ..., 0.09160784,
0.16420958, 0.22534334],
[0.22449783, 0.05369949, 0.13427468, ..., 0.48883442,
0.55197949, 0.61125815],
[0.41689285, 0.04157854, 0.50268653, ..., 0.07765427,
0.41123555, 0.33504538],
...,
[0.05546719, 0.75829898, 0.50423343, ..., 0.38172759,
0.25669968, 0.37609214],
[0.64042402, 0.29924155, 0.1708952 , ..., 0.2388334 ,
0.48679624, 0.20806528],
[0.23922514, 0.53796906, 0.44941302, ..., 0.35755458,
0.25504246, 0.446345 ]],
[[0.4546271 , 0.10578535, 0.49255176, ..., 0.472167 ,
0.59570854, 0.38831502],
[0.27936 , 0.69792962, 0.194582 , ..., 0.18611645,
0.36901982, 0.23794597],
[0.27687108, 0.46032741, 0.0916974 , ..., 0.60872449,
0.07072767, 0.32069137],
...,
[0.44288423, 0.12847884, 0.15907349, ..., 0.12155445,
0.46674052, 0.56966528],
[0.34087475, 0.69525966, 0.70591245, ..., 0.30560047,
0.32621901, 0.73158923],
[0.71419186, 0.05437057, 0.1414912 , ..., 0.61960515,
0.35577265, 0.40328638]],
[[0.41965488, 0.64335409, 0.32415841, ..., 0.43622516,
0.24008188, 0.38634163],
[0.49614217, 0.24837089, 0.67114331, ..., 0.32504913,
0.07900069, 0.15079588],
[0.30623606, 0.49809405, 0.40561608, ..., 0.31362124,
0.51803679, 0.34426325],
...,
[0.50164858, 0.11322218, 0.33669308, ..., 0.49671796,
0.27655981, 0.05424259],
[0.01870123, 0.00549879, 0.12319235, ..., 0.45556613,
0.18698475, 0.06034549],
[0.046583 , 0.40766037, 0.40909578, ..., 0.02284027,
0.38918489, 0.15036862]]], shape=(3, 1000, 1000))
2) Perform the fusion
1) With function fuse_dempster_shafer_2 of class Geoimage
help(mass_function1.fuse_dempster_shafer_2)
Help on method fuse_dempster_shafer_2 in module rastereasy.rastereasy:
fuse_dempster_shafer_2(*images) method of rastereasy.rastereasy.Geoimage instance
Fuse the 3 band image (associated with mass functions) from multiple
sources using Dempster-Shafer theory with two hypotheses: A and B.
Parameters
----------
*images : Geoimage
Each input is a 3-band Geoimage.
- Band 1: mass function m(A)
- Band 2: mass function m(B)
- Band 3: mass function m(A ∪ B)
Returns
-------
Geoimage
A new Geoimage with 3 bands containing the fused mass functions:
m(A), m(B), and m(A ∪ B).
Geoimage
A new Geoimage with 1 band containing the conflict values.
Examples
--------
>>> fused, conflict = im1.fuse_dempster_shafer_2(im2)
>>> fused, conflict = im1.fuse_dempster_shafer_2(im1, im2, im3, im4)
fusion, conflict = mass_function2.fuse_dempster_shafer_2(mass_function5,mass_function4,mass_function1,mass_function3)
2) With function fuse_dempster_shafer_2hypotheses of class InferenceTools
help(rastereasy.InferenceTools.fuse_dempster_shafer_2hypotheses)
Help on function fuse_dempster_shafer_2hypotheses in module rastereasy.rastereasy:
fuse_dempster_shafer_2hypotheses(*images)
Fuse mass functions from multiple sources using Dempster-Shafer theory
with two hypotheses: A and B.
Parameters
----------
*images : Geoimage
Each input is a 3-band Geoimage.
- Band 1: mass function m(A)
- Band 2: mass function m(B)
- Band 3: mass function m(A ∪ B)
Returns
-------
Geoimage
A new Geoimage with 3 bands containing the fused mass functions:
m(A), m(B), and m(A ∪ B).
Geoimage
A new Geoimage with 1 band containing the conflict values.
Examples
--------
>>> fused, conflict = fuse_dempster_shafer_2hypotheses(im1, im2, im3)
>>> fused, conflict = fuse_dempster_shafer_2hypotheses(im1, im2, im3, im4)
>>> fused, conflict = fuse_dempster_shafer_2hypotheses(im1, im2)
fusion, conflict = rastereasy.InferenceTools.fuse_dempster_shafer_2hypotheses(
mass_function5,
mass_function4,
mass_function3,
mass_function2,
mass_function1)
Verify that the fused masses sum to $1$
fusion.sum(axis='band')
array([[1., 1., 1., ..., 1., 1., 1.],
[1., 1., 1., ..., 1., 1., 1.],
[1., 1., 1., ..., 1., 1., 1.],
...,
[1., 1., 1., ..., 1., 1., 1.],
[1., 1., 1., ..., 1., 1., 1.],
[1., 1., 1., ..., 1., 1., 1.]], shape=(1000, 1000))