Project Polygonal meshes based on papers in
CTIC 2019 EMMCVPR 2017 JEI 2017 ISVC 2016
Paper: A persistencebased approach to automatic detection of line segments in images.
@article{KM19CTIC, author = {Kurlin, V. and Muszynski, G.}, booktitle = {Lecture Notes in Computer Science}, title = {A persistencebased approach to automatic detection of line segments in images}, 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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Paper: Superpixels Optimized by Color and Shape (SOCS).

@article{KH17EMM, author = {Kurlin, V. and Harvey, D.}, booktitle = {Lecture Notes in Computer Science}, title = {Superpixels Optimized by Color and Shape}, publisher = {Springer}, volume = {10746}, pages = {297311}, year = {2018} }
 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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Paper: Convex Constrained Meshes for superpixel segmentations of images.
vs 

@article{FK17JEI, 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}, url = {http://dx.doi.org/10.1117/1.JEI.26.6.061609} year = {2017} }
 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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Paper: Resolutionindependent superpixels based on convex constrained meshes without small angles.

@inproceedings{FKF16ISVC, 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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