Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page1for the source code2and the datasets.

Convolutional Neural Networks (CNNs) are widely used for handwritten character recognition tasks. The task of handwritten Chinese character recognition is especially outlined by a large number of target classes. The total number of Chinese characters exceeds 40,000, the average Chinese uses several thousand characters in his speech. In this article, we will work with about 4,000 Chinese characters. Dealing with a large number of classes might be problematic for a single-network approach in terms of both speed and accuracy, especially when running on a CPU. In this paper, we suggest an approach to meet this challenge to do separate handwritten Chinese characters recognition. We propose that a hierarchy of multiple neural networks should be used wherein a first-level network chooses a second-level network that performs the final recognition. Further, as every second-level network is only trained for a subset of classes, it can be simpler and more accurate than the whole classification network. In our approach, we combine several classes of Chinese characters with similar external features in one group (cluster) and work with these clusters further. Experimental results on CASIA 200-class and 3755-class handwritten datasets are presented, which compare the proposed hierarchical approach with the classical single-network approach.