TY - CHAP A1 - Mukhopadhyay, Anirban A1 - Porikli, Fatih A1 - Bhandarkar, Suchendra T1 - Detection and Characterization of Intrinsic Symmetry of 3D Shapes T2 - Proceedings of IEEE International Conference on Pattern Recognition N2 - A comprehensive framework for detection and characterization of partial intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled into a Correspondence Space Voting (CSV) procedure followed by a Transformation Space Mapping (TSM) procedure. In the CSV procedure, significant symmetries are first detected by identifying surface point pairs on the input shape that exhibit local similarity in terms of their intrinsic geometry while simultaneously maintaining an intrinsic distance structure at a global level. To allow detection of potentially overlapping symmetric shape regions, a global intrinsic distance-based voting scheme is employed to ensure the inclusion of only those point pairs that exhibit significant intrinsic symmetry. In the TSM procedure, the Functional Map framework is employed to generate the final map of symmetries between point pairs. The TSM procedure ensures the retrieval of the underlying dense correspondence map throughout the 3D shape that follows a particular symmetry. The TSM procedure is also shown to result in the formulation of a metric symmetry space where each point in the space represents a specific symmetry transformation and the distance between points represents the complexity between the corresponding transformations. Experimental results show that the proposed framework can successfully analyze complex 3D shapes that possess rich symmetries. Y1 - 2016 ER - TY - JOUR A1 - Mukhopadhyay, Anirban A1 - Bhandarkar, Suchendra T1 - Biharmonic Density Estimate - a scale space descriptor for 3D deformable surfaces JF - Pattern Analysis and Application Y1 - 2017 U6 - https://doi.org/10.1007/s10044-017-0610-2 SP - 1 EP - 13 ER - TY - GEN A1 - Mukhopadhyay, Anirban A1 - Kumar, Arun A1 - Bhandarkar, Suchendra T1 - Joint Geometric Graph Embedding for Partial Shape Matching in Images T2 - IEEE Winter Conference on Applications of Computer Vision N2 - A novel multi-criteria optimization framework for matching of partially visible shapes in multiple images using joint geometric graph embedding is proposed. The proposed framework achieves matching of partial shapes in images that exhibit extreme variations in scale, orientation, viewpoint and illumination and also instances of occlusion; conditions which render impractical the use of global contour-based descriptors or local pixel-level features for shape matching. The proposed technique is based on optimization of the embedding distances of geometric features obtained from the eigenspectrum of the joint image graph, coupled with regularization over values of the mean pixel intensity or histogram of oriented gradients. It is shown to obtain successfully the correspondences denoting partial shape similarities as well as correspondences between feature points in the images. A new benchmark dataset is proposed which contains disparate image pairs with extremely challenging variations in viewing conditions when compared to an existing dataset [18]. The proposed technique is shown to significantly outperform several state-of-the-art partial shape matching techniques on both datasets. Y1 - 2016 SP - 1 EP - 9 PB - IEEE ET - IEEE Winter Conference on Applications of Computer Vision (WACV) ER -