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Selective sampling with Gromov–Hausdorff metric:Efficient dense-shape correspondence via Confidence-based sample consensus

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虚拟现实与智能硬件（中英文） 2024年第1期6卷 30-42页

作者： Dvir GINZBURG dan raviv Department of Engineering University of Tel AvivIsrael

Background Functional mapping, despite its proven efficiency, suffers from a “chicken or egg” scenario, in that, poor spatial features lead to inadequate spectral alignment and vice versa during training, often resulting in slow convergence, high computational costs, and learning failures, particularly when small datasets are used. Methods A novel method is presented for dense-shape correspondence, whereby the spatial information transformed by neural networks is combined with the projections onto spectral maps to overcome the “chicken or egg” challenge by selectively sampling only points with high confidence in their alignment. These points then contribute to the alignment and spectral loss terms, boosting training, and accelerating convergence by a factor of five. To ensure full unsupervised learning, the Gromov–Hausdorff distance metric was used to select the points with the maximal alignment score displaying most confidence. Results The effectiveness of the proposed approach was demonstrated on several benchmark datasets, whereby results were reported as superior to those of spectral and spatial-based methods. Conclusions The proposed method provides a promising new approach to dense-shape correspondence, addressing the key challenges in the field and offering significant advantages over the current methods, including faster convergence, improved accuracy, and reduced computational costs.

关键词： Dense-shape correspondence Spatial information Neural networks Spectral maps Selective sampling

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Hierarchical Framework for Shape Correspondence

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Numerical Mathematics(Theory,Methods and Applications) 2013年第1期6卷 245-261页

作者： dan raviv Anastasia Dubrovina Ron Kimmel Technion Israel Institute of TechnologyTechnion CityHaifa 32000Israel

Detecting similarity between non-rigid shapes is one of the fundamental problems in computer *** order to measure the similarity the shapes must first be *** opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations,reflections and translations,non-rigid alignment is not easily *** of the methods addressing this problem boil down to a minimization of a certain distortion *** complexity of a matching process is exponential by nature,but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth *** we model the shapes using both local and global structures,employ these to construct a quadratic dissimilarity measure,and provide a hierarchical framework for minimizing it to obtain sparse set of corresponding *** correspondences may serve as an initialization for dense linear correspondence search.

关键词： Shape correspondence Laplace-Beltrami diffusion geometry local signatures

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Geometric and Photometric Data Fusion in Non-Rigid Shape Analysis

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Numerical Mathematics(Theory,Methods and Applications) 2013年第1期6卷 199-222页

作者： Artiom Kovnatsky dan raviv Michael M.Bronstein Alexander M.Bronstein Ron Kimmel Institute of Computational Science Faculty of InformaticsUniversitàdella Svizzera ItalianaLuganoSwitzerland School of Electrical Engineering Tel Aviv UniversityIsrael Technion–Israel Institute of Technology Computer Science DepartmentHaifaIsrael

In this paper,we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape *** construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric *** results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail.

关键词： Laplace-Beltrami operator diffusion equation heat kernel descriptors 3D shape retrieval deformation invariance

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