This paper describes an optimal method of inserting new frames or recovering missing frames in a video sequence. The method is based on an optimization scheme using graph-cuts that finds the ‘optimal’ frames to be inserted in between two given frames. The core problem is a typical visual correspondence problem between pixels in two or more frames and having formulated the appropriate energy, gr...

An edge cut of a connected graph is 5-restricted if its removal leaves every component having order at least five. Graphs that contain 5-restricted edge cuts are characterized in this paper. As a result, it is shown that a connected graph G of order at least 13 contains 5-restricted edge cuts if and only if G \ v contains a component of order at least five for every vertex v of graph G.

A 4-restricted edge cut is an edge cut of a connected graph which disconnects the graph, where each component has order at least 4. Graphs that contain 4-restricted edge cuts are characterized in this paper. As a result, it is proved that a connected graph G of order at least 10 contains 4-restricted edge cuts if and only if it contains no cut-vertex u where every component of G \ u has order a...

Finding sparse cuts is an important tool for analyzing large graphs that arise in practice, such as the web graph, online social communities, and VLSI circuits. When dealing with such graphs having billions of nodes, it is often hard to visualize global partitions. While studies on sparse cuts have traditionally looked at cuts with respect to all the nodes in the graph, some recent works analyz...

In previous lectures, we discussed various topics on graph: sparsest cut, clustering which finds small k-cuts, max flow, multicommodity flow, etc. For very large graphs, we’d like to ask “instead of regular approximation algorithms which run in polynomial time, can we find any near-linear time algorithm for minimum cut or maximum flow problems?”. A simple idea is for a given graph G, to solve t...

This is a survey of the method of graph cuts and its applications to graph clustering of weighted unsigned and signed graphs. I provide a fairly thorough treatment of the method of normalized graph cuts, a deeply original method due to Shi and Malik, including complete proofs. I also cover briefly the method of ratio cuts, and show how it can be viewed as a special case of normalized cuts. I in...