This paper proposes a new object representation, called connected segmentation tree (CST), which captures canonical characteristics of the object in terms of the photometric, geometric, and spatial adjacency and containment properties of its constituent image regions. CST is obtained by augmenting the objectpsilas segmentation tree (ST) with inter-region neighbor links, in addition to their recursive embedding structure already present in ST. This makes CST a hierarchy of region adjacency graphs. A regionpsilas neighbors are computed using an extension to regions of the Voronoi diagram for point patterns. Unsupervised learning of the CST model of a category is formulated as matching the CST graph representations of unlabeled training images, and fusing their maximally matching subgraphs. A new learning algorithm is proposed that optimizes the model structure by simultaneously searching for both the most salient nodes (regions) and the most salient edges (containment and neighbor relationships of regions) across the image graphs. Matching of the category model to the CST of a new image results in simultaneous detection, segmentation and recognition of all occurrences of the category, and a semantic explanation of these results.