Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts

Abstract

Formulations of the Image Decomposition Problem [8] as a Multicut Problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are hard to solve in practice, and, secondly, due to the lack of long-range terms in the objective function of the MP. We propose a generalization of the MP with longrange terms (LMP). We design and implement two efficient algorithms (primal feasible heuristics) for the MP and LMP which allow us to study instances of both problems w.r.t. the pixel grid graphs of the images in the BSDS-500 benchmark [8]. The decompositions we obtain do not differ significantly from the state of the art, suggesting that the LMP is a competitive formulation of the Image Decomposition Problem. To demonstrate the generality of the LMP, we apply it also to the Mesh Decomposition Problem posed by the Princeton benchmark [16], obtaining state-of-the-art decompositions.

Feature-aligned segmentation using correlation clustering

“…For image segmentation, impressive results have been obtained by weights defined by the local image intensity and learned from a database of ground truth annotations [44]. Keuper et al [10] formulated part-based mesh segmentation in terms of CC. Their weights are built upon primarily part-aware shape descriptors, such as the shape diameter function and dihedral angles.…”

“…Drawing inspirations from applications of CC in image segmentation [10,[40][41][42], our method solves CC on a much smaller, precomputed graph that still captures the essence of the input mesh and features.…”

“…Approximate solvers either solve a sequence of linear programs [9,45] or make greedy changes to an initial clustering [10,[46][47][48]. The latter seems to have the best efficiency at present for large and sparse graphs [10].…”

“…This prevents the result from degenerating to a single cluster (as such a cut uses no negative edges) or |V | clusters (as such a cut includes all positive edges). CC has found uses in problems involving unknown and possibly large number of clusters, such as entity deduplication [37], community detection in social networks [38], gene clustering [39], and image segmentation [10,[40][41][42][43].…”

“…Although CC has been used for related problems including image segmentation and part-based mesh segmentation [10], it has not been used for featurealigned mesh segmentation. We make the following three technical contributions:…”