Sussner and Ritter: Rank-based Decompositions of Mor- Phological Templates Rank-based Decompositions of Morphological Templates
نویسندگان
چکیده
| Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for these investigations is the new theory of rank within minimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing community. In this paper we derive a heuristic algorithm for the decomposition of matrices having arbitrary rank.
منابع مشابه
Rank-based decompositions of morphological templates
Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for th...
متن کاملDecomposition of Gray-Scale Morphological Templates Using the Rank Method
Convolutions are a fundamental tool in image processing. Classical examples of two dimensional linear convolutions include image correlation, the mean filter, the discrete Fourier transform, and a multitude of edge mask filters. Nonlinear convolutions are used in such operations as the median filter, the medial axis transform, and erosion and dilation as defined in mathematical morphology. For ...
متن کاملOn Integer Programming Approaches for Morphological Template Decomposition Problems in Computer Vision
In morphological image processing and analysis, a template or structuring element is applied to an image. Often savings in computation time and a better fit to the given computer architecture can be achieved by using the technique of template decomposition. Researchers have written a multitude of papers on finding such decompositions for special classes of templates. Justifying recent integer p...
متن کاملRanks of modules relative to a torsion theory
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...
متن کاملSubspace-Based Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions: Survey and Analysis
We survey the definitions and use of rank-revealingmatrix decompositions in single-channel noise reduction algorithms for speech signals. Our algorithms are based on the rank-reduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both diagonal (eigenvalue and singular value) decompositions and rank-revealing triangular decompositio...
متن کامل