Distance metric learning is an important topic in visual classification tasks. Learning an appropriate distance measure can greatly improve the performance of image recognitions. In this paper, we model an image set as a regularized convex hull and propose a distance metric learning method for image classification based on regularized convex hulls. In particular, a regularized point-to-convex hull distance metric (RPCHD) and a regularized convex hull-to-convex hull distance metric (RCHCHD) are introduced to measure the distance between the query image object and the existing image sets for image classification tasks. The coefficients in distance metric are solved by an approximate optimization strategy. Two SVM-like distance metric learning models are constructed and transformed into the standard support vector machines to learn distance metric matrix in RPCHD and RCHCHD. Positive and negative sample pairs are proposed to represent distance metric matrix. Experiments on three image databases show that our proposed RPCHD and RCHCHD can effectively improve the performance of image classification.

距离度量学习是视觉分类任务中的重要主题。学习适当的距离度量可以极大地提高图像识别的性能。在本文中，我们将图像集建模为正则化凸包，并提出了一种基于正则化凸包的距离度量学习方法。特别是，引入了正则化的点到凸的壳距离度量（RPCHD）和正则化的凸出的壳到凸的壳距离度量（RCHCHD），以测量查询图像对象与现有图像集之间的距离以进行图像分类任务。距离度量中的系​​数通过近似优化策略求解。构建了两个类似SVM的距离度量学习模型，并将其转换为标准支持向量机，以学习RPCHD和RCHCHD中的距离度量矩阵。提出了正负样本对来表示距离度量矩阵。在三个图像数据库上的实验表明，我们提出的RPCHD和RCHCHD可以有效地提高图像分类的性能。