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Analyzed about 10 hours ago. based on code collected 1 day ago.
Nov 05, 2025 — Nov 05, 2026
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Section 1189 updated
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
Section 1189 updated
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
1189. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological and Graph Theoretic Face Recognition - Voronoi FaceG raph Isomorphism Similarity - Percentage similarity and arbitrary visuals analyzed - related to 159,660,714,715,720,1185,1186,1187,1188 and al l sections on Topological Face and Handwriting recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformation s, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth mover distance, Graph Isomorphism (Ex act, Approximate and Subgraph),Graph matching,Graph similarity,Image Search - 29 December 2021
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1189. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological and Graph Theoretic Face Recognition - Voronoi FaceGraph Isomorphism Similarity - Percentage similarity and arbitrary visuals analyzed - related to 159,660,714,715,720,1185,1186,1187,1188 and all sections on Topological Face and Handwriting recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth mover distance, Graph Isomorphism (Exact, Approximate and Subgraph),Graph matching,Graph similarity,Image Search - 29 December 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1189.1 DeepLearning_ConvolutionNetwork_BackPropagation.py has been updated to analyze more visuals for unique person identification across arbitrary images. 1189.2 facegraph_similarity_metrics() has been changed to increase number of default isomorphism iterations to 25. ISMAGS symmetry and Graph Edit Distance have been made function parameters set to default False and their respective clauses have been uncommented. 1189.3 Subgraph Isomorphism Percentage similarity between two facial visuals are computed for VF2 and ISMAGS clauses by ratio of number of vertices in the isomorphic Voronoi subgraphs and total nuumber of vertices in Voronoi Facegraphs. If two visuals are Fully Isomorphic percentage similarity is set to 100. Both directions of the percentage ratio (denominator changes for size of image Facegraphs of image1 and image2 while numerator - size of isomorphic subgraph - stays same) are printed and the minimum of the two is considered as subgraph similarity. 1189.4 Two more visuals have been compared - testlogs/IMG_20171112_180837.jpg and testlogs/ExamplePortrait1.jpg - former a visual of author (2017) and the latter being a portrait drawn by author (1990). Following are pairwise similarity computations by facegraph_similarity_metrics(): facegraph_similarity_metrics("testlogs/IMG_20160610_071455.jpg","testlogs/IMG_20160610_071603.jpg",image1,image2) facegraph_similarity_metrics("testlogs/IMG_20160610_071455.jpg","testlogs/KSrinivasan_2003.jpg",image1,image3) facegraph_similarity_metrics("testlogs/IMG_20160610_071603.jpg","testlogs/KSrinivasan_2003.jpg",image2,image3) facegraph_similarity_metrics("testlogs/IMG_20160610_071455.jpg","testlogs/IMG_20171112_180837.jpg",image1,image4) facegraph_similarity_metrics("testlogs/IMG_20160610_071603.jpg","testlogs/IMG_20171112_180837.jpg",image2,image4) facegraph_similarity_metrics("testlogs/IMG_20171112_180837.jpg","testlogs/ExamplePortrait1.jpg",image4,image5) 1189.5 Excerpts of the logs at testlogs/DeepLearning_ConvolutionNetwork_BackPropagation.log.29December2021 reveal an important finding - Visuals of a person separated by small time durations are Fully Isomorphic. Three facial images testlogs/IMG_20160610_071455.jpg, testlogs/IMG_20160610_071603.jpg and testlogs/IMG_20171112_180837.jpg of the author separated by 1.5 years are fully isomorphic while all these three images are only subgraph isomorphic to 13 years older image testlogs/KSrinivasan_2003.jpg. This points to change in facial features over a period of 14+ years affecting Voronoi facegraph and isomorphism: ('Voronoi FaceGraphs of two facial images are isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - percentage similarity - ', 'testlogs/IMG_20160610_071455.jpg', ' and ', 'testlogs/IMG_20160610_071603.jpg', ': 100.0') ('Voronoi FaceGraphs of two facial images are subgraph isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - (True or False):', False) ('Voronoi FaceGraphs of two facial images are subgraph isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - (True or False):', False) ('Voronoi FaceGraphs of two facial images are subgraph isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - percentage similarity - ', 'testlogs/IMG_20160610_071455.jpg', ' and ', 'testlogs/IMG_20171112_180837.jpg', ': 100.0') ('Voronoi FaceGraphs of two facial images are subgraph isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - percentage similarity - ', 'testlogs/IMG_20160610_071603.jpg', ' and ', 'testlogs/IMG_20171112_180837.jpg', ': 100.0') ('Voronoi FaceGraphs of two facial images are subgraph isomorphic - (True or False):', True) ('Voronoi FaceGraphs of two facial images are isomorphic - (True or False):', False) ('Voronoi FaceGraphs of two facial images are subgraph isomorphic - (True or False):', True) 1189.6 Following could be a thumbrule decision tree for face recognition by isomorphism (Earth mover distance between Voronoi Facegraphs of the images is attached high priority in the tree) where leaves are graded by probabilities - extremely likely,highly likely and likely: If Voronoi facegraphs of two images are Fully isomorphic: { /* There are less chances of False positives and False negatives - Face recognition is almost certain.*/ Images are "extremely likely to be similar" and might belong to same person. } else if Voronoi facegraphs of two images are not Fully isomorphic but less stringent subgraph isomorphic: { /* high chances of false positives and false negatives depending on decision tree branch */ /* and percentage probability for "likely" and "highly likely" */ if Wasserstein EMD between Voronoi facet areas of the images are high: { if subgraph isomorphism percentage similarity is low: Images are "highly likely to be dissimilar" and might belong to different persons if subgraph isomorphism percentage similarity is high: Images are "likely to be similar" and might belong to same person } else if Wasserstain EMD between Voronoi facet areas of the images are low: { if subgraph isomorphism percentage similarity is low: Images are "likely to be similar" and might belong to same person if subgraph isomorphism percentage similarity is high: Images are "highly likely to be similar" and might belong to same person } } else if Voronoi facegraphs of two images are neither fully isomorphic not subgraph isomorphic: { Images are "extremely likely to be dissimilar" and might belong to different persons } 1189.7 In the examples earlier testlogs/ExamplePortrait1.jpg and testlogs/IMG_20171112_180837.jpg are subgraph isomorphic (and percentage similarity is high and EMD of Voronoi Facet areas is also high which are mutually in conflict) though former is a faminine watercolor art and thus a False positive. 1189.8 Previous Graph theoretic and topological face recognition is an unsupervised classifier while conventional face recognizers are mostly supervised depending on training data. Rather, Machine learning training models could be formulated from Voronoi facet areas of face images as training priors.
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
1188. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Voronoi FaceGraph Isomorphism-Subgraph Isomorphism Similarity - VF2 and ISMAGS Isomorphic Subgraphs iteration - related to 159,660,714,715,720,1185,1186,1187 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth Mover Distance, Graph Isomorphism (Exact, Approximate and Subgraph),Graph Matching,Graph similarity,Image Search - 24 December 2021
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1188. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Voronoi FaceGraph Isomorphism-Subgraph Isomorphism Similarity - VF2 and ISMAGS Isomorphic Subgraphs iteration - related to 159,660,714,715,720,1185,1186,1187 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth Mover Distance, Graph Isomorphism (Exact, Approximate and Subgraph),Graph Matching,Graph similarity,Image Search - 24 December 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1188.1 DeepLearning_ConvolutionNetwork_BackPropagation.py has been updated (facegraph_similarity_metrics()) to compute isomorphic subgraphs of Voronoi Diagram Facegraphs obtained from 2 facial images by two algorithms - VF2 and ISMAGS 1188.2 Number of iterations of isomorphic subgraphs has been set to 15 as default which is configurable function parameter. ISMAGS algorithm prints different subgraphs for symmetry=False and symmetry=True. 1188.3 ISMAGS symmetry=True clause has been commented due to slowdown. Percentage similarity between two images could be derived from the number and size of isomorphic subgraphs. Example function for image similarity between two images = number of isomorphic Voronoi subgraphs of size > constant 1188.4 Contour segmented and Facegraph images of the 3 JPG files have been added to repository: testlogs/DeepLearning_ConvolutionNetwork_BackPropagation.log.24December2021 testlogs/IMG_20160610_071455_FaceGraph.jpg testlogs/IMG_20160610_071455_contour_segmented.jpg testlogs/IMG_20160610_071603_FaceGraph.jpg testlogs/IMG_20160610_071603_contour_segmented.jpg testlogs/KSrinivasan_2003_FaceGraph.jpg testlogs/KSrinivasan_2003_contour_segmented.jpg and logs are at testlogs/DeepLearning_ConvolutionNetwork_BackPropagation.log.24December2021 1188.5 It is obvious to note that contours of facial images themselves are landmark detectors to some extent as contours mostly straddle facial features. Accuracy of contour based face landmark detection could be increased by changing pixel color contrast of the binary inverted images.
Krishna iResearch - NeuronRain - K.Srinivasan
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Updated Requirements.txt
Krishna iResearch - NeuronRain - K.Srinivasan
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1187. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Voronoi diagram and Delaunay Triangulation of Facial images from centroids computed by Dlib face landmarks detection and Voronoi FaceGraph Isomorphism-Subgraph Isomorphism Similarity - related to 159,660,714,715,720,1185,1186 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth Mover Distance, Graph Isomorphism (Exact, Approximate and Subgraph),Graph Matching,Graph similarity,Image Search - 23 December 2021
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1187. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Voronoi diagram and Delaunay Triangulation of Facial images from centroids computed by Dlib face landmarks detection and Voronoi FaceGraph Isomorphism-Subgraph Isomorphism Similarity - related to 159,660,714,715,720,1185,1186 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth Mover Distance, Graph Isomorphism (Exact, Approximate and Subgraph),Graph Matching,Graph similarity,Image Search - 23 December 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1187.1 DeepLearning_ConvolutionNetwork_BackPropagation.py has been updated to import dlib face landmarks detection and draw Voronoi and Delaunay triangulation facegraphs from face landmark centroids instead of contour centroids which aligns the Voronoi faces symmetrically centered around face landmarks. Dlib face landmarks detection finds standard of 68 points of five features of Human face Shape Grammar - Ear, Nose, 2 Eyes, Mouth. 1187.2 DeepLearning_ConvolutionNetwork_BackPropagation.py has been updated to import netrd Graph Distance and NetworkX Graph Isomorphism implementations. Netrd implements extensive distance similarity measures for comparing two Graphs. Image FaceGraph Voronoi Planar Subdivision is populated either from contour centroids or face landmark centroids depending on boolean flag fromlandmarks which defaults to True. 1187.3 Image Voronoi FaceGraph similarity computations between 2 images have been segregated to a new function facegraph_similarity_metrics() which computes Voronoi FaceGraph Facet areas EMD, Hausdorff distance between facial image contour polynomials, Whether 2 facegraphs are isomorphic or not, Whether 2 facegraphs are subgraph isomorphic or not, Netrd Jaccard distance between 2 facegraphs, Netrd Jensen-Shannon Degree Divergence between 2 facegraphs and Graph Edit Distance between 2 facegraphs (commented). 1187.4 Three facial images testlogs/IMG_20160610_071455.jpg,testlogs/IMG_20160610_071603.jpg and testlogs/KSrinivasan_2003.jpg of author are compared pairwise for similarity. While first two images dated 2016 are heavily similar, last image dated 2003 has noticeable differences separated by 13 years. 1186.5 Histogram partition distance and Voronoi FaceGraph similarities are computed pairwise for 3 images earlier. While two heavily resembling images testlogs/IMG_20160610_071455.jpg and testlogs/IMG_20160610_071603.jpg are Voronoi FaceGraph Isomorphic and Subgraph Isomorphic, image pairs (testlogs/IMG_20160610_071603.jpg and testlogs/KSrinivasan_2003.jpg) and (testlogs/IMG_20160610_071455.jpg and testlogs/KSrinivasan_2003.jpg) are less similar and are not Voronoi FaceGraph isomorphic but Subgraph isomorphic. Thus Graph Isomorphism and Subgraph Isomorphism of Voronoi FaceGraphs act as distinguishers of facial features - Percentage of Voronoi FaceGraph Isomorphism-Subgraph Isomorphism wanes as images become increasingly dissimilar (Voronoi facegraphs of images are more likely to be subgraph-isomorphic than isomorphic for same person). Graph Isomorphism similarity earlier is an unusual application in Topological Face Recognition for measuring homeomorphic facial deformations (or conjecturally, Voronoi Graph-Subgraph Isomorphism implies Topological Homeomorphism). 1187.6 Dlib uses iBUG 300W training dataset /tmp/shape_predictor_68_face_landmarks.dat for learning face landmarks which can be downloaded from https://github.com/italojs/facial-landmarks-recognition/blob/master/shape_predictor_68_face_landmarks.dat. Earlier implementation of Face recognition is Graph theoretic differing from usual computer vision algorithms focussing on machine learning models for face recognition. Graph similarity, Graph matching and Exact-Subgraph-Approximate Graph Isomorphism are related concepts for mining patterns in graphs. Percentage of isomorphism between image Voronoi facegraphs could be an intrinsic merit ranking metric for an image search engine. 1187.7 Following are the log excerpts: ('EMD Histogram distance similarity between images - testlogs/IMG_20160610_071455.jpg and testlogs/IMG_20160610_071603.jpg :', (0.029700525104999542, None, array([[203., 0., 0., ..., 0., 0., 0.], [ 0., 222., 0., ..., 0., 0., 0.], [ 0., 0., 190., ..., 0., 0., 0.], ..., [ 0., 0., 0., ..., 242., 0., 0.], [ 0., 0., 0., ..., 0., 251., 0.], [ 0., 0., 0., ..., 0., 0., 232.]], dtype=float32))) ('EMD Histogram distance similarity between images - testlogs/IMG_20160610_071603.jpg and testlogs/KSrinivasan_2003.jpg :', (0.010611597448587418, None, array([[210., 0., 0., ..., 0., 0., 0.], [ 0., 229., 0., ..., 0., 0., 0.], [ 0., 0., 210., ..., 0., 0., 0.], ..., [ 0., 0., 0., ..., 244., 0., 0.], [ 0., 0., 0., ..., 3., 247., 0.], [ 0., 0., 0., ..., 0., 0., 235.]], dtype=float32))) ('EMD Histogram distance similarity between images - testlogs/IMG_20160610_071455.jpg and testlogs/KSrinivasan_2003.jpg :', (0.013819809071719646, None, array([[203., 0., 0., ..., 0., 0., 0.], [ 0., 222., 0., ..., 0., 0., 0.], [ 0., 0., 190., ..., 0., 0., 0.], ..., [ 0., 0., 0., ..., 242., 0., 0.], [ 0., 0., 0., ..., 1., 247., 3.], [ 0., 0., 0., ..., 0., 0., 232.]], dtype=float32))) ==================================================== EMD Similarity between Voronoi Facet Areas of the images: 51952.31409460765 ('Hausdorff Distance between DP polynomials approximating two facial image contours:', (99.36297097007517, 0, 0)) ('Voronoi FaceGraphs of two facial images are isomporphic - (True or False):', True) ('Jaccard distance between Voronoi Facegraphs of two facial images:', 1.0) ('Jensen-Shannon Degree Divergence distance between Voronoi Facegraphs of two facial images:', 0) ('Voronoi FaceGraphs of two facial images are subgraph isomporphic - (True or False):', True) ==================================================== EMD Similarity between Voronoi Facet Areas of the images: 566002.5197416454 ('Hausdorff Distance between DP polynomials approximating two facial image contours:', (1261.1621624517602, 0, 0)) ('Voronoi FaceGraphs of two facial images are isomporphic - (True or False):', False) ('Jaccard distance between Voronoi Facegraphs of two facial images:', 1.0) ('Jensen-Shannon Degree Divergence distance between Voronoi Facegraphs of two facial images:', 0) ('Voronoi FaceGraphs of two facial images are subgraph isomporphic - (True or False):', True) ==================================================== EMD Similarity between Voronoi Facet Areas of the images: 556108.7037362487 ('Hausdorff Distance between DP polynomials approximating two facial image contours:', (1336.449400463781, 0, 0)) ('Voronoi FaceGraphs of two facial images are isomporphic - (True or False):', False) ('Jaccard distance between Voronoi Facegraphs of two facial images:', 1.0) ('Jensen-Shannon Degree Divergence distance between Voronoi Facegraphs of two facial images:', 0) ('Voronoi FaceGraphs of two facial images are subgraph isomporphic - (True or False):', True)
Srinivasan Kannan
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1186. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Distance similarity between Facial Image Voronoi Tessellations of similar Faces and Facial Landmark Detection - related to 159,660,714,715,720,1185 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth Mover Distance - 22 December 2021
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1186. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Distance similarity between Facial Image Voronoi Tessellations of similar Faces and Facial Landmark Detection - related to 159,660,714,715,720,1185 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Merit of Large Scale Visuals, People Analytics, Computational Geometry, Graph Edit Distance and Earth Mover Distance - 22 December 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1186.1 DeepLearning_ConvolutionNetwork_BackPropagation.py has been changed to compute centroids of the contours from cv2.moments() and if there is an exception from minEnclosingCircle(). 1186.2 Areas of Voronoi polygons are computed from Shapely Polygon() and Wasserstein EMD similarity of Voronoi facet areas between 2 images is computed which measures the deformation of the facial features in 2 images. 1186.3 Performing Voronoi tessellation around centroids computed from facial landmarks detection algorithm instead of cv2.moments() centroids might increase the alignment of the Voronoi facets along facial feature landmarks (<Eye>,<Nose>,<Mouth>,...) of the Shape Grammar. 1186.4 Hausdorff distance between Douglas-Peucker contour polynomials of the two images are computed which is another similarity metric. 1186.5 Histogram Partition Distance (EMD) similarity (cv2.EMD()) of the two images in toto is computed (histogram_partition_distance_similarity()). These three distance similarities help identify people more often if faces in two images are heavily similar (and not arbitrary images of same person) and could assist in landmark based facial recognition. OpenCV Voronoi Tessellation is done in 2D and 3D Voronoi Tessellation could be a better choice for modelling arbitrarily oriented images of same person - changes in facial features and emotional face orientations happen in 3D and not in 2D. 1186.6 Finally Approximate and Exact Graph Edit Distance similarity computation between Voronoi Facegraphs of the two images has been introduced but left commented because of NP-Hardness. 1187.7 Logs and tessellated images for this update are (compared images: testlogs/IMG_20160610_071455.jpg and testlogs/IMG_20160610_071603.jpg): testlogs/DeepLearning_ConvolutionNetwork_BackPropagation.log.22December2021 testlogs/IMG_20160610_071455-tessellated.jpg testlogs/IMG_20160610_071455_FaceRecognition_Segmentation_FaceGraph.dot testlogs/IMG_20160610_071603-tessellated.jpg testlogs/IMG_20160610_071603_FaceRecognition_Segmentation_FaceGraph.dot
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 1185 updated
Krishna iResearch - NeuronRain - K.Srinivasan
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1185. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Voronoi Tessellation and Delaunay Triangulation of Faces, their Morphology and Shape Grammar - related to 159,660,714,715,720 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Marit of Large Scale Visuals, People Analytics, Computational Geometry, Augmenting Graph Edit Distance by Facet Area - 20 December 2021
Krishna iResearch - NeuronRain - K.Srinivasan
More... almost 5 years ago
-------------------------------------------------------------------------------------------------------------------------------------------- 1185. (THEORY and FEATURE) People Analytics - Merit of Large Scale Visuals - Topological Face Recognition - Voronoi Tessellation and Delaunay Triangulation of Faces, their Morphology and Shape Grammar - related to 159,660,714,715,720 and all sections on Topological Face and Handwriting Recognition, Product Homotopy, Unique identification, Homeomorphism and Topological Deformations, Marit of Large Scale Visuals, People Analytics, Computational Geometry, Augmenting Graph Edit Distance by Facet Area - 20 December 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1185.1 Recognition of Shapes (Shape Grammar for Faces,Handwriting,...) by Topological Product Homotopy and Homeomorphic Deformations (their limitations) mentioned earlier has been implemented geometrically by Segmenting an image and plotting Voronoi tessellation and Delaunay triangulation spiderweb on it as overlay. Their morphology is analyzed. 1185.2 python-src/DeepLearning_ConvolutionNetwork_BackPropagation.py has been updated to define two functions face_recognition_image_segmentation() and face_recognition_image_segmentation_contours() which segment an imagefile of human face and draw Voronoi tessellations and Delaunay triangulations as overlay 1185.3 Two visuals of the author python-src/testlogs/IMG_20160610_071455.jpg and python-src/testlogs/IMG_20160610_071603.jpg having small differences have been Voronoi tessellated and Delaunay triangulated and mesh(s) have been written to python-src/testlogs/IMG_20160610_071455-tessellated.jpg and python-src/testlogs/IMG_20160610_071603-tessellated.jpg. 1185.4 Voronoi Facegraphs of the images have been written as DOT files to python-src/testlogs/IMG_20160610_071455_FaceRecognition_Segmentation_FaceGraph.dot and python-src/testlogs/IMG_20160610_071603_FaceRecognition_Segmentation_FaceGraph.dot 1185.5 Watershed segmentation for the images are written to python-src/testlogs/IMG_20160610_071455_segmented.jpg and python-src/testlogs/IMG_20160610_071603_segmented.jpg 1185.6 python-src/DeepLearning_BackPropagation.py , python-src/DeepLearning_ConvolutionNetwork_BackPropagation.py and python-src/image_pattern_mining/ImageToBitMatrix.py have been upgraded to Python 3.7.5 by autopep8 and 2to3 utilities. Python 2.7 versions of the files have been renamed to python-src/DeepLearning_BackPropagation.py.2.7, python-src/DeepLearning_ConvolutionNetwork_BackPropagation.py.2.7 and python-src/image_pattern_mining/ImageToBitMatrix.py.2.7 1185.7 Shape Grammar for Human face mentioned in 715 in terms of union of product homotopies as follows: <Hair> <Ear><Eye><Eye><Ear> <Nose> <Mouth> is easier to define in tessellated images as homeomorphic deformations (Typical example: Coffee mug is homeomorphic to Donut Torus, 'D' is product of 'I' and ')' by pasting lemma) of Voronoi facets (Graph edit distance as face similarity between 2 facegraphs could be costlier even for closely resembling images being NP-Hard and has been ignored. GED does not measure change in areas of facets between two graphs which is a drawback). Voronoi facets could be partitioned into components of the Shape grammar earlier - facets for <Hair>,<Ear>,<Eye>,<Nose>,<Mouth>. 1185.8 Facet areas of Voronoi and Delaunay spiderweb (and angles of facet edges) have changed notably between two images earlier in spite of minute variations in features while number of facets (vertices and edges) is almost the same. This requires a Facet Area Augmented Graph Edit Distance measure which counts in changed angles between the morphed facet edges. 1185.9 logs for this update are at testlogs/DeepLearning_ConvolutionNetwork_BackPropagation.log.20December2021
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Section 1184 - reference
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Reference - Section 1184
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References - OSGeo GRASS Voronoi
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Updated index.rst for https://astroinfer.readthedocs.io/en/latest/
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Updated Section 1184
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Reference - HITS algorithm
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Reference - Computing area of Voronoi polygons
Krishna iResearch - NeuronRain - K.Srinivasan
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Updated Requirements.txt
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184. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Computation of Urbanization Correlation from Voronoi Polygons and Urban Sprawl Contours - related to 1183 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Computational Geometry, Intrinsic Merit Rankings, R Ricker, NASA Suomi NPP VIIRS and SEDAC GPW4 imagery Convex Hull Population Estimations, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing (Sparse), Polygonal packing (Close), Computational Geometry, Four color theorem, Economic Merit, Computational Economics, Machine Learning models of Urban Extent, Approximation of functions by polynomials, Weirstrass Theorem, Jordan Curve Theorem, Cellular Automaton Graph model of diffusion of opinions/memes/cybercrimes/pandemics, Community Detection in Social Networks, Multiple Agent Resource Allocation, Earth Mover Distance, Graph Edit Distance - 17 December 2021
Krishna iResearch - NeuronRain - K.Srinivasan
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--------------------------------------------------------------------------------------------------------------------------------------------- 1184. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Computation of Urbanization Correlation from Voronoi Polygons and Urban Sprawl Contours - related to 1183 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Computational Geometry, Intrinsic Merit Rankings, R Ricker, NASA Suomi NPP VIIRS and SEDAC GPW4 imagery Convex Hull Population Estimations, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing (Sparse), Polygonal packing (Close), Computational Geometry, Four color theorem, Economic Merit, Computational Economics, Machine Learning models of Urban Extent, Approximation of functions by polynomials, Weirstrass Theorem, Jordan Curve Theorem, Cellular Automaton Graph model of diffusion of opinions/memes/cybercrimes/pandemics, Community Detection in Social Networks, Multiple Agent Resource Allocation, Earth Mover Distance, Graph Edit Distance - 17 December 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1184.1 Ratio of Voronoi Tessellation Polygon area to the Urban sprawl contour polynomial area contained in polygon is an estimate of Rural-Urban Land use and disparity. 1184.2 Area of Voronoi Facet Polygon combines Rural and Urban sprawls (Close polygonal packing - as Voronoi Tessellation is a partition of total surface area) while Area of Contour is specific to more populous urban sprawl subset (Sparse polynomial packing) of the outer Voronoi polygon. 1184.3 GISUrbanSprawlAnalytics.py has been updated to compute area of each of the Voronoi Tessellation Facet polygon by Shapely Polygon() and Correlation-PValue of the sorted arrays of Voronoi polygon areas and Contour polynomial areas of urban sprawls is found by Kendall-Tau Correlation Coefficient and there are some striking facts emerging from it. 1184.4 Following are excepts of logs from testlogs/GISUrbanSprawlAnalytics.log.17December2021 Correlation-PValues of sorted arrays of Areas for VoronoiFacets-Contours of NASA VIIRS India Urban Sprawls from NightLights 2012 and 2016: 1184.4.1 VIIRS NightLights 2012 - (Correlation,PValue) between Contour areas and Voronoi polygon areas of Urban sprawls: (0.9089575693287888, 4.4992471056554334e-294) implying 90% correlation between areas of Voronoi polygons (Rural+Urban) and Contours (Urban) 1184.4.2 VIIRS NightLights 2016 - (Correlation,PValue) between Contour areas and Voronoi polygon areas of Urban sprawls: (0.8049119202576946, 0.0) implying 80% correlation between areas of Voronoi polygons (Rural+Urban) and Contours (Urban) 1184.5 Downward trend of correlation from 90% to 80% (2012 to 2016) perhaps is an indicator of rising disparity between areas of Voronoi polygons (Rural + Urban) and Contours (Urban) contained in them or there is a growing mismatch between Urban sprawls and Rural areas. Previous deduction is just an one angle of interpreting the anamoly while there could be many. 1184.6 Following are contour-convexhull segmented images and logs affected: testlogs/RemoteSensingGIS/NightLights_13nasa-india-2012_FaceGraph.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2012_contour_segmented.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2016_FaceGraph.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2016_contour_segmented.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2016_convex_hull_segmented.jpg testlogs/GISUrbanSprawlAnalytics.log.17December2021
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 1183 updated
Krishna iResearch - NeuronRain - K.Srinivasan
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Centroidal Voronoi Tessellation and Climate models
Krishna iResearch - NeuronRain - K.Srinivasan
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1183. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Distance similarity of Voronoi Tessellations and Measuring Urban Expansion - related to 1182 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Computational Geometry, Intrinsic Merit Rankings, R Ricker and SEDAC GPW4 Convex Hull Population Estimations, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing, Computational Geometry, Four color theorem, Economic Merit, Computational Economics, Machine Learning models of Urban Extent, Approximation of functions by polynomials, Weirstrass Theorem, Jordan Curve Theorem, Cellular Automaton Graph model of diffusion of opinions/memes/cybercrimes/pandemics, Community Detection in Social Networks, Multiple Agent Resource Allocation, Earth Mover Distance, Graph Edit Distance - 16 December 2021
Krishna iResearch - NeuronRain - K.Srinivasan
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--------------------------------------------------------------------------------------------------------------------------------------------- 1183. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Distance similarity of Voronoi Tessellations and Measuring Urban Expansion - related to 1182 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Computational Geometry, Intrinsic Merit Rankings, R Ricker and SEDAC GPW4 Convex Hull Population Estimations, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing, Computational Geometry, Four color theorem, Economic Merit, Computational Economics, Machine Learning models of Urban Extent, Approximation of functions by polynomials, Weirstrass Theorem, Jordan Curve Theorem, Cellular Automaton Graph model of diffusion of opinions/memes/cybercrimes/pandemics, Community Detection in Social Networks, Multiple Agent Resource Allocation, Earth Mover Distance, Graph Edit Distance - 16 December 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1183.1 Average Degree of Transportation graph vertices or its approximation by Delaunay triangulation increases with the economic importance and urban expanse of a city sprawl contour - Centroids of Large urban area contours have high transport connectivity and high degree. 1183.2 Urban sprawl expansion is quantifiable by distance between two Voronoi tessellations of geospatial imagery at two time points separated by some duration. 1183.3 Voronoi tessellations at two time points differ when new urban area contours (and Voronoi polygons containing them) emerge and existing urban area contours (and Voronoi polygons containing them) expand. 1183.4 Voronoi tessellation is a visual clustering algorithm (each polygon is a cluster) and Earth mover distance (EMD) can measure distance between Voronoi tessellation clusters of two GIS images separated by time interval which is directly proportional to expansion of urban sprawls. 1183.5 While EMD between two Voronoi tessellation clustering would consider the area of each Voronoi polygon, Graph edit distance between two Voronoi facegraphs would estimate newly added edges and vertices and cannot account for change in area of each face. 1183.6 As against Square and Hexagonal tessellated cellular automata grids which respectively are of 8 and 6 neighbours, Voronoi facegraph allows faces of arbitrary number of neighbours. 1183.7 Spread of memes/fads/opinions/pandemic in a social network of urban sprawls could be better simulated on their Voronoi facegraphs than Cellular automaton graph which is of average degree 8 or multiples of it. 1183.8 GISUrbanSprawlAnalytics.py has been updated to compute Approximate Graph Edit Distance (NetworkX implementation) between Voronoi facegraphs of two NASA VIIRS Nighttime Lights images of India (2012 and 2016) separated by 4 years but commented because of slow approximation of GED. Exact Graph Edit Distance wrapper in NeuronRain (GraphEditDistance() - GraphMining_GSpan.py) is NP-Hard and slower for huge graphs which is as well commented. Both Voronoi Facegraph and its dual Delaunay triangulation graph have been overlaid and plotted to NightLights_13nasa-india-2012-contourlabelled.jpg and NightLights_13nasa-india-2016-contourlabelled.jpg 1183.9 As a stopgap and timesaving alternative to costly Graph Edit Distance similarity of facegraphs, community structure of 2 facegraphs (how clustered urban sprawls are) is detected by modularity matrix of all vertices and Wasserstein Earth mover distance of modularity between two urban sprawl facegraphs is computed as distance similarity or growth of urban sprawl communities over a period of time. Infact, Modularity captures the notion of communities better than Graph Edit Distance. 1183.10 Community structure distance - increase in modularity between 2012 and 2016 NASA VIIRS imagery is printed to logs testlogs/GISUrbanSprawlAnalytics.log.15December2021 - excerpts: Increase in Community structure - Wasserstein EMD of modularity: 0.0006727360452344568 1183.11 Following are the affected logs and contour-convexhull segmented images for NASA VIIRS 2012 and 2016 images: testlogs/NightLights_13nasa-india-2012-contourlabelled.jpg testlogs/NightLights_13nasa-india-2016-contourlabelled.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2012_FaceGraph.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2012_ImageNet_Keras_Theano_Segmentation_FaceGraph.dot testlogs/RemoteSensingGIS/NightLights_13nasa-india-2016_FaceGraph.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2016_ImageNet_Keras_Theano_Segmentation_FaceGraph.dot testlogs/GISUrbanSprawlAnalytics.log.15December2021 testlogs/RemoteSensingGIS/NightLights_13nasa-india-2012_contour_segmented.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2012_convex_hull_segmented.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2016_contour_segmented.jpg testlogs/RemoteSensingGIS/NightLights_13nasa-india-2016_convex_hull_segmented.jpg
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 1182 - references
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 1181 updated to remove references to Voronoi diagram
Krishna iResearch - NeuronRain - K.Srinivasan
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