Image Segmentation with Eigen-Subspace Projections

Abstract

In this chapter, object segmentation algorithms dependent on the characteristics of eigen-structure are proposed. The eigen-subspaces are obtained from eigen-decomposition of the covariance matrix, which is computed from the selected color samples. Hence, the color space can be transformed into the signal subspace and its orthogonal noise subspaces. After statistical analysis of eigen-structure of target color samples, the color eigen-structure segmentation algorithms are then designed to extract the desired objects, which are close to the color samples. The principal component transformation (PCT) techniques, which only use the signal subspace can be treated as a subset of color eigenspace algorithms. The eigenspaces discriminated as signal and noise subspaces related to original color samples should be effectively utilized. The adaptive eigen-subspace segmentation (AESS) algorithm, which can save the computation of eigen-decomposition, is applied to adaptively adjust the eigen-subspaces. Finally, the Eigen-based fuzzy C-means (FCM) clustering algorithm has been proposed to effective segment color object. By jointly consideration of signal and noise subspace projections of desired colors, the separate eigen-based FCM (SEFCM) and coupled eigen-based FCM (CEFCM) are used to achieve effective color object segmentation. With these proposed algorithms, the color objects can be successfully extracted by using eigen-subspace projections.