Abstract: Based on the Riemannian geometry of multinomial manifold, a novel method designed in the framework of matrix manifold is presented to quantize the information divergences between Color Co-occurrence Matrices（CCMs） for object recognition. With the given color quantization levels and the neighbourhood mode of per pixel, the method models the co-occurring colors in any two color channels of a color image as a probabilistic realization of an underlying multinomial distribution. By the compactified co-occurrence frequency-based embedding, each image is identified with a point of a product matrix manifold where each factor manifold is endowed with the Fisher information distance metric that is induced from corresponding multinomial manifold. For a recognition task, the nearest neighbor matching between testing samples and training samples is first conducted by label prediction on every factor manifold, and then followed by majority voting on product manifold. The effectiveness of the proposed method is validated by the promising recognition results on the GT face database and the COIL-100 object database.

Key words: Color Co-occurrence Matrices（CCMs）, multinomial distribution, color co-occurrence matrix manifold, Fisher information distance

摘要： 基于多项流形的黎曼几何，提出一个在矩阵流形框架下度量颜色共生矩阵信息差异并将其应用于目标识别的新方法。对于给定的颜色量化水平和每个像素局部邻域，该方法将一幅彩色图像的任意两个颜色通道中共生的颜色建模为一个潜在的多项分布的概率实现。通过基于紧化的共生频率嵌入，可将每幅图像等同为一个积矩阵流形上的一点，其中每个因子流形被赋予了从对应的多项流形上诱导的Fisher信息距离度量。对于一个识别任务，测试样本与训练样本间的匹配通过先在每个因子流形上使用最近邻分类器进行标签预测然后在积流形上进行多数投票完成。在GT彩色人脸库和COIL-100目标库上获得的出色的识别效果验证了该方法的有效性。

关键词: 颜色共生矩阵, 多项分布, 颜色共生矩阵流形, Fisher信息度量