Orientation-Preserving Spectral Correspondence for 3D Shape Analysis

In this article, the authors present an orientation-preserving spectral correspondence for three-dimensional (3D) shape analysis, which is robust and efficient for topological and deformable changes, even for non-isometric shapes. Our technique introduces an optimal spectral representation by combining the eigendecomposition with principal components analysis (PCA) to the heat kernel Laplacian matrix, and we further propose an efficient symmetry detection method based on so-called dominant eigenfunctions. Finally, a 3D descriptor encoding intrinsic symmetry structure and local geometric feature is constructed which effectively reveals the consistent structure between the deformable shapes. Consequently, sufficient orientation-preserving correspondence can be established in our embedding space. Experimental results showed that our method produces stable matching results in comparison with state-of-the-art methods.

Consistent Correspondences for Shape and Image Problems

Establish consistent correspondences between different objects is a classic problem in computer science/vision. It helps to match highly similar objects in both 3D and 2D domain. Inthe 3D domain, finding consistent correspondences has been studying for more than 20 yearsand it is still a hot topic. In 2D domain, consistent correspondences can also help in puzzlesolving. However, only a few works are focused on this approach. In this thesis, we focuson finding consistent correspondences and extend to develop robust matching techniques inboth 3D shape segments and 2D puzzle solving. In the 3D domain, segment-wise matching isan important research problem that supports higher-level understanding of shapes in geometryprocessing. Many existing segment-wise matching techniques assume perfect input segmentation and would suffer from imperfect or over-segmented input. To handle this shortcoming,we propose multi-layer graphs (MLGs) to represent possible arrangements of partially mergedsegments of input shapes. We then adapt the diffusion pruning technique on the MLGs to findconsistent segment-wise matching. To obtain high-quality matching, we develop our own voting step which is able to remove inconsistent results, for finding hierarchically consistent correspondences as final output. We evaluate our technique with both quantitative and qualitativeexperiments on both man-made and deformable shapes. Experimental results demonstrate theeffectiveness of our technique when compared to two state-of-art methods. In the 2D domain,solving jigsaw puzzles is also a classic problem in computer vision with various applications.Over the past decades, many useful approaches have been introduced. Most existing worksuse edge-wise similarity measures for assembling puzzles with square pieces of the same size, and recent work innovates to use the loop constraint to improve efficiency and accuracy. Weobserve that most existing techniques cannot be easily extended to puzzles with rectangularpieces of arbitrary sizes, and no existing loop constraints can be used to model such challenging scenarios. We propose new matching approaches based on sub-edges/corners, modelledusing the MatchLift or diffusion framework to solve square puzzles with cycle consistency.We demonstrate the robustness of our approaches by comparing our methods with state-of-artmethods. We also show how puzzles with rectangular pieces of arbitrary sizes, or puzzles withtriangular and square pieces can be solved by our techniques.

Minimal multi-camera system for perception of deformable shapes

Within the context of autonomous manipulation of deformable objects, we propose a minimal multi-camera perception system that allows to cover a deforming 2D shape over time according to a specific visibility objective. Our method iteratively solves an optimization problem that includes collision avoidance and robust visibility constraints.