282 research outputs found
Dimensional operators for mathematical morphology on simplicial complexes
International audienceIn this work we study the framework of mathematical morphology on simplicial complex spaces. Simplicial complexes are widely used to represent multidimensional data, such as meshes, that are two dimensional complexes, or graphs, that can be interpreted as one dimensional complexes. Mathematical morphology is one of the most powerful frameworks for image processing, including the processing of digital structures, and is heavily used for many applications. However, mathematical morphology operators on simplicial complex spaces is not a concept fully developed in the literature. Specifically, we explore properties of the dimensional operators, small, versatile operators that can be used to define new operators on simplicial complexes, while maintaining properties from mathematical morphology. These operators can also be used to recover many morphological operators from the literature. Matlab code and additional material, including the proofs of the original properties, are freely available at~\url{https://code.google.com/p/math-morpho-simplicial-complexes.
Morphological filtering on hypergraphs
The focus of this article is to develop computationally efficient
mathematical morphology operators on hypergraphs. To this aim we consider
lattice structures on hypergraphs on which we build morphological operators. We
develop a pair of dual adjunctions between the vertex set and the hyper edge
set of a hypergraph H, by defining a vertex-hyperedge correspondence. This
allows us to recover the classical notion of a dilation/erosion of a subset of
vertices and to extend it to subhypergraphs of H. Afterward, we propose several
new openings, closings, granulometries and alternate sequential filters acting
(i) on the subsets of the vertex and hyperedge set of H and (ii) on the
subhypergraphs of a hypergraph
Writing Reusable Digital Geometry Algorithms in a Generic Image Processing Framework
Digital Geometry software should reflect the generality of the underlying
mathe- matics: mapping the latter to the former requires genericity. By
designing generic solutions, one can effectively reuse digital geometry data
structures and algorithms. We propose an image processing framework focused on
the Generic Programming paradigm in which an algorithm on the paper can be
turned into a single code, written once and usable with various input types.
This approach enables users to design and implement new methods at a lower
cost, try cross-domain experiments and help generalize resultsComment: Workshop on Applications of Discrete Geometry and Mathematical
Morphology, Istanb : France (2010
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Metrics for Learning in Topological Persistence
Acknowledgments We gratefully acknowledge Roel Neggers for providing the DALES simulation data. JLS acknowledges support by the DFG-funded transregional research collaborative TR32 on Patterns in SoilâVegetationâAtmosphere Systems.Peer reviewedPublisher PD
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
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