Using Kernel Principal Components for Color Image Segmentation

Abstract

Distinguishing objects on the basis of color is fundamental to humans. In this paper, a clustering approach is used to segment color images. Clustering is usually done using a single point or vector as a cluster prototype. The data can be clustered in the input or feature space where the feature space is some nonlinear transformation of the input space. The idea of kernel principal component analysis (KPCA) was introduced to align data along principal components in the kernel or feature space. KPCA is a nonlinear transformation of the input data that finds the eigenvectors along which this data has maximum information content (or variation). The principal components resulting from KPCA are nonlinear in the input space and represent principal curves. This is a necessary step as colors in RGB are not linearly correlated especially considering illumination effects such as shading or highlights. The performance of the k-means (Euclidean distance-based) and Mixture of Principal Components (vector angle-based) algorithms are analyzed in the context of the input space and the feature space obtained using KPCA. Results are presented on a color image segmentation task. The results are discussed and further extensions are suggested.