Abstract

Image segmentation is a critical step in many computer vision tasks, including high-level visual recognition and scene understanding as well as low-level photo and video processing. In this paper, we propose a new nonlinear embedding, called piecewise flat embedding, for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding attempts to identify segment boundaries while significantly suppressing variations within segments. We adopt an $L_1$-regularized energy term in the formulation to promote sparse solutions. We further devise an effective two-stage numerical algorithm based on Bregman iterations to solve the proposed embedding. Piecewise flat embedding can be easily integrated into existing image segmentation frameworks, including segmentation based on spectral clustering and hierarchical segmentation based on contour detection. Experiments on BSDS500 indicate that segmentation algorithms incorporating this embedding can achieve significantly improved results in both frameworks.