A graph is superconnected, for short super-κ, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g that if D ≤ g − 2, then the graph is super-κ when g ≥ 5 and a complete graph otherwise.

Meaningful notions of distance between planar shapes typically involve the computation of a correspondence between points on one shape and points on the other. To determine an optimal correspondence is a computationally challenging combinatorial problem. Traditionally it has been formulated as a shortest path problem which can be solved efficiently by Dynamic Time Warping. In this paper, we sho...

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can exploit the intrinsic smoothness of these datasets in order to represent them in a both compact and accurate manner. However, how to discover wavelet bases that...

An N-dimensional image is divided into “object” and “background” segments using a graph cut approach. A graph is formed by connecting all pairs of neighboring image pixels (voxels) by weighted edges. Certain pixels (voxels) have to be a priori identified as object or background seeds providing necessary clues about the image content. Our objective is to find the cheapest way to cut the edges in...

Image stitching is commonly used in many different applications. One such application could be creating panoramas or high resolution images. To create seamless images is often very computationally demanding. On the other hand, the technological evolution of the latest years has created a customer demand for these algorithms to be used in handheld devices, such as cameras and cell phones. The me...

Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimum-cut using the maximum flow algorithm. This paper presents a third major approach by generalizing the Swendsen-Wang method– a well celebrated algorithm in statistical mech...

Graph cuts have become very popular in many areas of computer vision including segmentation, energy minimization, and 3D reconstruction. Their ability to find optimal results efficiently and the convenience of usage are some of the factors of this popularity. However, there are a few issues with graph cuts, such as inherent sequential nature of popular algorithms and the memory bloat in large s...

We study the minimum cut problem in the presence of uncertainty and show how to apply a novel robust optimization approach, which aims to exploit the similarity in subsequent graph measurements or similar graph instances, without posing any assumptions on the way they have been obtained. With experiments we show that the approach works well when compared to other approaches that are also oblivi...

While there are many algorithms which address the reconstruction of partial surfaces from single-view normal fields, to the best of our knowledge, there is only one method [Chang et al., ’Multiview Normal Field Integration using Level Sets’, CVPR 2007] which focuses on the reconstruction of the full shape of an object from multiple normal fields captured from multiple viewpoints. In this paper,...

Computer vision is a rich source of important yet intractable optimization problems. Over the past decade, researchers have shown that many such problems can be efficiently solved by graph cuts. Graph cut algorithms combine elegant theoretical properties with compelling experimental results. I will focus on the difficult but important challenge of solving rank-deficient linear inverse systems. ...