Reducing graphs in graph cut segmentation

Abstract

In few years, graph cuts have become a leading method for solving a wide range of problems in computer vision. However, graph cuts involve the construction of huge graphs which sometimes do not fit in memory. Currently, most of the maxflow algorithms are impracticable to solve such large scale problems. In the image segmentation context, some authors have proposed heuristics [1, 2, 3, 4] to get round this problem. In this paper, we introduce a new strategy for reducing graphs. During the creation of the graph, before creating a new node, we test if the node is really useful to the max-flow computation. The nodes of the reduced graph are typically located in a narrow band surrounding the object edges. Empirically, solutions obtained on the reduced graphs are identical to the solutions on the complete graphs. A parameter of the algorithm can be tuned to obtain smaller graphs when an exact solution is not needed. The test is quickly computed and the time required by the test is often compensated by the time that would be needed to create the removed nodes and the additional time required by the computation of the cut on the larger graph. As a consequence, we sometimes even save time on small scale problems.

Simultaneous Segmentation and Filtering via Reduced Graph Cuts

“…In the manner of [12,5], the graph nodes are typically located in a narrow band surrounding the object edges to segment. Empirically, the authors show in [8] that the solutions obtained with and without reduction are identical and the time for reducing the graph is even compensated by the time for computing the min-cut in the reduced graph when the regularization is of moderate level.…”

“…For a fixed amount of RAM, one clearly see that the maximum image size quickly decreases as the dimensionality d of P increases. As shown in [8], most of the nodes in the graph are however useless during the max-flow computation since they are not traversed by any flow. Ideally, one would like to extract the smallest possible graph G = (V , E ) from G = (V, E) while keeping the max-flow value f * in G identical or very close to the max-flow value f * in G. This corresponds to an ideal optimization problem which we will not try to solve since the method for determining G also needs to be (very) fast.…”

“…Ideally, one would like to extract the smallest possible graph G = (V , E ) from G = (V, E) while keeping the max-flow value f * in G identical or very close to the max-flow value f * in G. This corresponds to an ideal optimization problem which we will not try to solve since the method for determining G also needs to be (very) fast. Let us first introduce some terminology before reviewing the method of [8] for building G . For the sake of clarity, the same notations are used as in [8].…”

“…Finally, another band-based method called Reduced Graph Cuts (RGC) was proposed for reducing graphs in binary image segmentation [8]. The graph is progressively built by only adding nodes which locally satisfy a condition.…”

“…We first briefly review the graph cuts framework in Section 2 as well as the band-based strategy of [8] in Section 3 for reducing graphs. Afterwards, a new parameter is introduced in Section 4 for further reducing the graphs and removing small undesired segments in the segmentation due to noise.…”