We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic O(m log n log log n) time algorithm. This improves both on the best previously known deterministic running time of O(m log n) (Kawarabayashi and Thorup [12]) and the best previously known randomized running time of O(m log n) (Karger [11]) for this problem, though Karger’s algorithm can be fur...

Graph cuts optimization permits to minimize some Markov Random Fields (MRF) by computing a minimum cut (min-cut) in a relevant graph. Graph-cuts are very efficient and are now a well established field of research. However, due to the large amount of memory required for storing the graph, there application remains limited to the minimization of MRF involving a relatively small number of variable...

The max-cut problem asks for partitioning the nodes V of a graph G = (V,E) into two sets (one of which might be empty), such that the sum of weights of edges joining nodes in different partitions is maximum. Whereas for general instances the max-cut problem is NPhard, it is polynomially solvable for certain classes of graphs. For planar graphs, there exist several polynomial-time methods determ...

Multi-Resolution Graph Cuts for Stereo-Motion Estimation Joshua A. Worby Master of Applied Science Graduate Department of The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 2007 This thesis presents the design and implementation of a multi-resolution graph cuts (MRGC) for stereo-motion framework that produces dense disparity maps. Both stereo and mo...

In recent years the use of graph-cuts has become quite popular in computer vision. However, researchers have repeatedly asked the question whether it might be possible to compute a measure of uncertainty associated with the graphcut solutions. In this paper we answer this particular question by showing how the min-marginals associated with the label assignments in a MRF can be efficiently compu...

An algorithm for the calculation of the hyper-Wiener index (WW) of benzenoid hydrocarbons (both cata- and pericondensed) is described, based on the consideration of pairs of elementary cuts of the corresponding benzenoid graph B. A pair of elementary cuts partitions the vertices of B into four classes. WW is expressed as a sum of terms of the form n11n22 + n12n21, each associated with a pair of...

Being able to find the silhouette of an object is a very important front-end processing step for many high-level computer vision techniques, such as Shape-from-Silhouette 3D reconstruction methods, object shape tracking, and pose estimation. Graph cuts have been proposed as a method for finding very accurate silhouettes which can be used as input to such high level techniques, but graph cuts ar...

Graph cut algorithms are very popular in image segmentation approaches. However, the detailed parts of the foreground are not segmented well in graph cut minimization.There are basically two reasons of inadequate segmentations: (i) Data smoothness relationship of graph energy. (ii) Shrinking bias which is the bias towards shorter paths. This paper improves the foreground segmentation by integra...

The tracking of moving objects in a video sequence is an important task in different domains such as video compression, video surveillance and object recognition. In this paper, we propose an approach for integrated tracking and segmentation of moving objects from image sequences where the camera is in movement. This approach is based on the calculation of minimal cost of a cut in a graph “Grap...

Graph cuts has emerged as a preferred method to solve a class of energy minimization problems in computer vision. It has been shown that graph cut algorithms designed keeping the structure of vision based flow graphs in mind are more efficient than known strongly polynomial time max-flow algorithms based on preflow push or shortest augmenting path paradigms [1]. We present here a new algorithm ...