Abstract
The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used. In this paper, we tackle the classification tasks with limited training data on SPD manifolds. Our proposed framework, named Manifold Convex Class Model, represents each class on SPD manifolds using a convex model, and classification can be performed by computing distances to the convex models. We provide three methods based on different metrics to address the optimization problem of the smallest distance of a point to the convex model on SPD manifold. The efficacy of our proposed framework is demonstrated both on synthetic data and several computer vision tasks including object recognition, texture classification, person re-identification and traffic scene classification.
Abstract (translated)
对称正定流形特征的有效性已经在各种计算机视觉任务中得到验证。然而，由于这些特征的非欧几里德几何，现有的欧几里德机械不能直接使用。本文针对SPD流形训练数据有限的分类问题进行了研究。我们提出的框架称为流形凸类模型，用凸模型表示SPD流形上的每个类，并通过计算到凸模型的距离进行分类。针对SPD流形上的凸模型，提出了三种基于不同度量的点到凸模型最小距离优化问题。我们提出的框架在合成数据和几个计算机视觉任务（包括目标识别、纹理分类、人的重新识别和交通场景分类）上的效果都得到了证明。
URL
https://arxiv.org/abs/1806.05343
