The truncated variational model for image labeling and graph partitioning

Abstract

Image labeling and graph partitioning aim to divide a set of pixels or vertices into a specific number of meaningful groups. In this paper, we propose effective truncated regularization methods for both image labeling and graph partitioning problems. More specifically, we present optimization models for piecewise constant and piecewise smooth image labeling that minimize the truncation of different potential functions. The efficient alternating direction method of multipliers based algorithm is put forward for solving these models, where all subproblems can be solved by the closed-form solution or fast Fourier transform. Moreover, we propose a semi-supervised graph partitioning model based on truncated regularization under the definition of the graph, which is solved by the proximal gradient method. The efficiency of the proposed methods is demonstrated through labeling results on synthetic and real images and semi-supervised partitioning results on graph data.