We propose a new segmentation or clustering model that combines Markov Random Field (MRF) and Normalized Cut (NC) objectives. Both NC and MRF models are widely used in machine learning and computer vision, but they were not combined before due to significant differences in the corresponding optimization, e.g. spectral relaxation and combinatorial max-flow techniques. On the one hand, we show th...

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of minimizing normalized cut. However, unlike spectral approaches, the proposed algorithm scales to graphs with millions of nodes and edges. The algorithm consists o...

The main objective of this paper is to solve the problem of finding graphs on which the spectral clustering method and the normalized cut produce different partitions. To this end, we derive formulae for minimum normalized cut for graphs in some classes such as paths, cycles, complete graphs, double-trees, lollipop graphs LPn,m, roach type graphs Rn,k and weighted paths Pn,k.

Partitioning of a graph representation, defined over low-level image features based on Gestalt inspired relations, is an effective strategy for forming coherent perceptual groups in an image. The usual practice, mainly motivated by efficiency considerations, is to approximate the general K-way partitioning solution by recursive bi-partitioning, where at each step the graph is broken into two pa...

In this research paper, we use a normalized graph cut measure as a thresholding principle to separate an object from the background based on the standard S membership function. The implementation of the proposed algorithm known as fuzzy normalized graph cut method. This proposed algorithm compared with the fuzzy entropy method [25], Kittler [11], Rosin [21], Sauvola [23] and Wolf [33] method. M...

Many spectral clustering algorithms have been proposed and successfully applied to many highdimensional applications. However, there are still two problems that need to be solved: 1) existing methods for obtaining the final clustering assignments may deviate from the true discrete solution, and 2) most of these methods usually have very high computational complexity. In this paper, we propose a...