We propose a new nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding attempts to recover a piecewise constant image representation with sparse region boundaries and sparse cluster value scattering. The resultant piecewise flat embedding exhibits interesting properties such as suppressing slowly varying signals, and offers an image representation with higher region identifiability which is desirable for image segmentation or high-level semantic analysis tasks. We formulate our embedding as a variant of the Laplacian Eigenmap embedding with an $L_{1,p} (0<p\leq1)$ regularization term to promote sparse solutions. First, we devise a two-stage numerical algorithm based on Bregman iterations to compute $L_{1,1}$-regularized piecewise flat embeddings. We further generalize this algorithm through iterative reweighting to solve the general $L_{1,p}$-regularized problem. To demonstrate its efficacy, we integrate PFE into two existing image segmentation frameworks, segmentation based on clustering and hierarchical segmentation based on contour detection. Experiments on three major benchmark datasets, BSDS500, MSRC, Stanford Background Dataset, and PASCAL Context, show that segmentation algorithms incorporating our embedding achieve significantly improved results.

本文提出了一种新的多维非线性嵌入——Piecewise Flat Embedding (PFE)，能够对图像进行分割，并且在四个主要基准数据集上的实验结果表明，采用该嵌入的分割算法显著提高了分割结果。

分段平面嵌入图像分割