Abstract. There is a huge diversity of definitions of "visually meaningful" image segments, ranging from simple uniformly colored segments, textured segments, through symmetric patterns, and up to complex semantically meaningful objects. This diversity has led to a wide range of different approaches for image segmentation. In this paper we present a single unified framework for addressing this problem -"Segmentation by Composition". We define a good image segment as one which can be easily composed using its own pieces, but is difficult to compose using pieces from other parts of the image. This non-parametric approach captures a large diversity of segment types, yet requires no pre-definition or modelling of segment types, nor prior training. Based on this definition, we develop a segment extraction algorithm -i.e., given a single point-ofinterest, provide the "best" image segment containing that point. This induces a figure-ground image segmentation, which applies to a range of different segmentation tasks: single image segmentation, simultaneous co-segmentation of several images, and class-based segmentations.