Project Polygonal meshes based on papers in
PRL 2020 VISAPP 2020 ISVC 2019 CTIC 2019 EMMCVPR 2017 JEI 2017 ISVC 2016
This project has developed methods for extracting polygonal meshes from various images with theoretical guarantees.
PRL 2020 paper : Persistencebased resolutionindependent meshes of superpixels.

@article{kurlin2020persistence, author = {Kurlin, V. and Muszynski, G.}, journal = {Pattern Recognition Letters}, title = {Persistencebased resolutionindependent meshes of superpixels}, volume = {131}, pages = {300306}, year = {2020} }
 DOI : 10.1016/j.patrec.2020.01.014
 Abstract.
The oversegmentation problem is to split a pixelbased image into a smaller number of superpixels that can be treated as indecomposable regions to speed up higher level image processing such as segmentation or object detection.
A traditional superpixel is a potentially disconnected union of square pixels, which can have complicated topology (with holes) and geometry (highly zigzag boundaries).
This paper contributes to new resolutionindependent superpixels modeled as convex polygons with straightline edges and vertices with real coordinates not restricted to a fixed pixel grid.
Any such convex polygon can be rendered at any resolution higher than in original images, hence superpixels are resolutionindependent.
The key difficulty in obtaining resolutionindependent superpixels is to find continuous straightline edges, while classical edge detection focuses on extracting only discrete edge pixels. The recent Persistent Line Segment Detector (PLSD) avoids intersections and small angles between line segments, which are hard to fix before a proper polygonal mesh can be constructed. The key novelty is an automatic selection of strongest straightline segments by using the concept of persistence from Topological Data Analysis, which allows to rank segments by their strength. The PLSD performed well in comparison with the only past Line Segment Detector Algorithm (LSDA) on the Berkeley Segmentation Database of 500 reallife images. The PLSD is now extended to the Persistent ResolutionIndependent Mesh (PRIM).
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VISAPP 2020 paper : Polygonal Meshes of Images based on a new Thinning Algorithm with Guarantees.

@inproceedings{siddiqui2020polygonal, author = {Siddiqui, A. and Kurlin, V.}, booktile = {Proceedings of the International Conference on Computer Vision Theory and Applications}, title = {Polygonal Meshes of Noisy Images based on a new Thinning Algorithm with Theoretical Guarantees}, pages = {137146}, year = {2020} }
 Abstract. Microscopic images of vortex fields are important for understanding phase transitions in superconductors. These optical images include noise with high and variable intensity, hence are manually processed to extract numerical data from underlying meshes. The current thinning and skeletonization algorithms struggle to find connected meshes in these noisy images and often output edge pixels with numerous gaps and superfluous branching point. We have developed a new symmetric thinning algorithms to extract from such highly noisy images 1pixel wide skeletons with theoretical guarantees. The resulting skeleton is converted into a polygonal mesh that has only polygonal edges at subpixel resolution. The experiments on over 100 real and 6250 synthetic images establish the stateoftheart in extracting optimal meshes from highly noisy images.
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ISVC 2019 paper : ResolutionIndependent Meshes of Superpixels

@inproceedings{kurlin2019resolution, title={ResolutionIndependent Meshes of Superpixels}, author={Kurlin, Vitaliy and Smith, Philip}, booktitle={International Symposium on Visual Computing}, url = {https://doi.org/10.1007/9783030337209_15}, pages={194205}, year={2019} }
 Abstract. The oversegmentation problem for images is studied in the new resolutionindependent formulation when a large image is approximated by a small number of convex polygons with straight edges at subpixel precision. These polygonal superpixels are obtained by refining and extending subpixel edge segments to a full mesh of convex polygons without small angles and with approximation guarantees. Another novelty is the objective error difference between an original pixelbased image and the reconstructed image with a best constant color over each superpixel, which does not need human segmentations. The experiments on images from the Berkeley Segmentation Database show that new meshes are smaller and provide better approximations than the stateoftheart.
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CTIC 2019 paper : A persistencebased approach to automatic detection of line segments in images.

@article{kurlin2019persistence, author = {Kurlin, V. and Muszynski, G.}, booktitle = {Lecture Notes in Computer Science}, title = {A persistencebased approach to automatic detection of line segments in images}, volume = {11382}, pages = {137150}, url = {http://dx.doi.org/10.1007/9783030108281_11} publisher = {Springer}, year = {2019} }
 Abstract.
Edge detection algorithms usually produce a discrete set of edgels (edge pixels) in a given image on a fixed pixel grid.
We consider the harder problem of detecting continuous straight line segments at subpixel resolution.
The stateofthe art Line Segment Detection Algorithm (LSDA) outputs unordered line segments whose total number cannot be easily controlled.
Another motivation to improve the LSDA is to avoid intersections and small angles between line segments, hence difficulties in higher level tasks such as segmentation or contour extraction.
The new Persistent Line Segment Detector (PLSD) outputs only nonintersecting line segments and ranks them by a strength, hence the user can choose a number of segments. The main novelty is an automatic selection of strongest segments along any straight line by using the persistence from Topological Data Analysis. The experiments on the Berkeley Segmentation Database of 500 reallife images show that the new algorithm outperforms the LSDA on the important measure of Boundary Recall.
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EMMCVPR 2017 paper : Superpixels Optimized by Color and Shape (SOCS).

@article{kurlin2017superpixels, author = {Kurlin, V. and Harvey, D.}, title = {Superpixels Optimized by Color and Shape}, booktitle = {Lecture Notes in Computer Science (Proceedings of EMMCVPR 2017)}, publisher = {Springer}, volume = {10746}, pages = {297311}, year = {2018} }
 DOI : 10.1007/9783319781990_20
 Abstract. Image oversegmentation is formalized as the approximation problem when a large image is segmented into a small number of connected superpixels with best fitting colors. The approximation quality is measured by the energy whose main term is the sum of squared color deviations over all pixels and a regularizer encourages round shapes. The first novelty is the coarse initialization of a nonuniform superpixel mesh based on selecting most persistent edge segments. The second novelty is the scaleinvariant regularizer based on the isoperimetric quotient. The third novelty is the improved coarsetofine optimization where local moves are organized according to their energy improvements. The algorithm beats the stateoftheart on the objective reconstruction error and performs similarly to other superpixels on the benchmarks of BSD500. The only parameters are the number of superpixels and the shape coefficient for a tradeoff between accuracy and shape of superpixels.
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JEI 2017 paper: Convex Constrained Meshes for superpixel segmentations of images.
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@article{forsythe2017convex, author = {Forsythe, J. and Kurlin, V.}, title = {Convex Constrained Meshes for superpixel segmentations of images}, journal = {Journal of Electronic Imaging}, volume = {26(6)}, number = {061609}, year = {2017} }
 DOI : 10.1117/1.JEI.26.6.061609
 Abstract. We consider the problem of splitting a pixelbased image into convex polygons with vertices at subpixel resolution. Edges of resulting polygonal superpixels can have any direction and should adhere well to object boundaries. We introduce a Convex Constrained Mesh that accepts any straight line segments and outputs a complete mesh of convex polygons without small angles and with approximation guarantees for the given lines. Experiments on the Berkeley Segmentation Dataset BSD500 show that the resulting meshes of polygonal superpixels outperform other polygonal meshes on boundary recall and pixelbased SLIC and SEEDS superpixels on undersegmentation errors.
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ISVC 2016 : Resolutionindependent superpixels based on convex constrained meshes without small angles.

@inproceedings{forsythe2016resolution, author = {Forsythe, J. and Kurlin, V. and Fitzgibbon, A.}, title = {Resolutionindependent superpixels based on convex constrained meshes without small angles}, booktitle = {Lecture Notes in Computer Science (Proceedings of ISVC 2016)}, volume = {10072}, pages = {223233}, year = {2016} }
 Abstract. The oversegmentation problem for images is studied in the new resolutionindependent formulation when a large image is approximated by a small number of convex polygons with straight edges at subpixel precision. These polygonal superpixels are obtained by refining and extending subpixel edge segments to a full mesh of convex polygons without small angles and with approximation guarantees. Another novelty is the objective error difference between an original pixelbased image and the reconstructed image with a best constant color over each superpixel, which does not need human segmentations. The experiments on images from the Berkeley Segmentation Database show that new meshes are smaller and provide better approximations than the stateoftheart.
 Benchmarks of CCM superpixels: (average number of superpixels, average benchmark in percentages)
 BR (Boundary Recall with the 2pixel offset) : (349.1, 63.95), (376.6, 65.15),(386.6, 65.58), (446.7, 67.1), (528.0, 68.0)
 CUE (Corrected Undersegmentation Error) : (349.1, 4.87), (376.6, 4.67), (386.6, 4.57), (446.7, 4.33), (528.0, 4.24)
 USE (Undersegmentation Symmetric Error) : (349.1, 9.64), (376.6, 9.34), (386.6, 9.14), (446.7, 8.66), (528.0, 8.48)
 If you use these benchmarks for comparison over 500 BSD images, please cite the paper above.
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