The long-tailed data distribution poses an enormous challenge for training neural networks in classification. A classification network can be decoupled into a feature extractor and a classifier. This paper takes a semi-discrete optimal transport (OT) perspective to analyze the long-tailed classification problem, where the feature space is viewed as a continuous source domain, and the classifier weights are viewed as a discrete target domain. The classifier is indeed to find a cell decomposition of the feature space with each cell corresponding to one class. An imbalanced training set causes the more frequent classes to have larger volume cells, which means that the classifier’s decision boundary is biased towards less frequent classes, resulting in reduced classification performance in the inference phase. Therefore, we propose a novel OT-dynamic softmax loss, which dynamically adjusts the decision boundary in the training phase to avoid overfitting in the tail classes. In addition, our method incorporates the supervised contrastive loss so that the feature space can satisfy the uniform distribution condition. Extensive and comprehensive experiments demonstrate that our method achieves state-of-the-art performance on multiple long-tailed recognition benchmarks, including CIFAR-LT, ImageNet-LT, iNaturalist 2018, and Places-LT.

Polycube construction and deformation are essential problems in computer graphics. In this paper, we present a robust, simple, efficient, and automatic algorithm to deform the meshes of arbitrary shapes into polycube form. We derive a clear relationship between a mesh and its corresponding polycube shape. Our algorithm is edge-preserving, and works on surface meshes with or without boundaries. Our algorithm outperforms previous ones with respect to speed, robustness, and efficiency. Our method is simple to implement. To demonstrate the robustness and effectivity of our method, we have applied it to hundreds of models of varying complexity and topology. We demonstrate that our method compares favorably to other state-of-the-art polycube deformation methods.