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 resu...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.展开更多
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 descriptors.Our construction is based on the definition of a diffu...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 descriptors.Our 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 information.Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail.展开更多
Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision.In order to measure the similarity the shapes must first be aligned.As opposite to rigid alignment that can be parame...Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision.In order to measure the similarity the shapes must first be aligned.As 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 parameterized.Majority of the methods addressing this problem boil down to a minimization of a certain distortion measure.The 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 two-manifolds.Here 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 points.These correspondences may serve as an initialization for dense linear correspondence search.展开更多
基金Supported by the Zimin Institute for Engineering Solutions Advancing Better Lives。
文摘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.
基金The author would like to thank the referees for the helpful suggestionsThis work has been supported in part by the Israeli Science Foundation grant 615/11,the German-Israeli Foundation grant 2269/2010the Swiss High Performance and High Productivity Computing(HP2C)grant and grant agreement No.267414 of European Community’s FP7-ERC program.
文摘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 descriptors.Our 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 information.Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail.
基金This research was supported by European Community’s FP7-ERC program,grant agreement no.267414.
文摘Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision.In order to measure the similarity the shapes must first be aligned.As 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 parameterized.Majority of the methods addressing this problem boil down to a minimization of a certain distortion measure.The 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 two-manifolds.Here 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 points.These correspondences may serve as an initialization for dense linear correspondence search.
