Level Lines Selection with Variational Models for Segmentation and Encoding

Abstract. This paper discusses the interest of the Tree of Shapes of an image as a region oriented image representation. The Tree of Shapes offers a compact and structured representation of the family of level lines of an image. This representation has been used for many processing tasks such as filtering, registration, or shape analysis. In this paper we show how this representation can be used for segmentation, rate distortion optimization, and encoding. We address the problem of segmentation and rate distortion optimization using Guigues algorithm on a hierarchy of partitions constructed using the simplified Mumford-Shah multiscale energy. To segment an image, we minimize the simplified Mumford-Shah energy functional on the set of partitions represented in this hierarchy. The rate distortion problem is also solved in this hierarchy of partitions. In the case of encoding, we propose a variational model to select a family of level lines of a gray level image in order to obtain a mi...

• Type: Journal
• Year: 2007
• Where: JMIV
• Authors: Coloma Ballester, Vicent Caselles, Laura Igual, Lluís Garrido
• Keywords: Image, JMIV 2007, Level Lines, Rate Distortion Optimization