Fuzzy Eigenvalues and Fuzzy Eigenvectors of Fuzzy Markov Chain Transition Matrix under Max-min Composition
The study of the stability of many stochastic processes as Markov chains needs sometimes to use eigenvalues and eigenvectors of the transition matrix. This paper is an investigation on a methodology which computes fuzzy eigenvalues and fuzzy eigenvectors within the context of a fuzzy Markov chain transition matrix, under max-min composition.
In this paper, we show how linear, but not necessarily shift-invariant, filters can be used to propagate sparse labels throughout an image. We propose a new propagation method based on the domain transform filter, a linear, shift-varying filter whose kernel width varies based on local edge information. We contrast this against the more well-known energy minimization approach and show that it can produce significantly better results when the input labels contain errors. Finally, we show how minimization-based methods are better suited for purely user-guided applications.