1,267 research outputs found
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
Distance, granulometry, skeleton
In this chapter, we present a series of concepts and operators based on the notion of distance. As often with mathematical morphology, there exists more than one way to present ideas, that are simultaneously equivalent and complementary. Here, our problem is to present methods to characterize sets of points based on metric, geometry and topology considerations. An important concept is that of the skeleton, which is of fundamental importance in pattern recognition, and has many practical application
A 3D Sequential Thinning Scheme Based on Critical Kernels
International audienceWe propose a new generic sequential thinning scheme based on the critical kernels framework. From this scheme, we derive sequential algorithms for obtaining ultimate skeletons and curve skeletons. We prove some properties of these algorithms, and we provide the results of a quantitative evaluation that compares our algorithm for curve skeletons with both sequential and parallel ones
Fractional maximal functions in metric measure spaces
We study the mapping properties of fractional maximal operators in Sobolev
and Campanato spaces in metric measure spaces. We show that, under certain
restrictions on the underlying metric measure space, fractional maximal
operators improve the Sobolev regularity of functions and map functions in
Campanato spaces to H\"older continuous functions. We also give an example of a
space where fractional maximal function of a Lipschitz function fails to be
continuous
Nucleation-free rigidity
When all non-edge distances of a graph realized in as a {\em
bar-and-joint framework} are generically {\em implied} by the bar (edge)
lengths, the graph is said to be {\em rigid} in . For ,
characterizing rigid graphs, determining implied non-edges and {\em dependent}
edge sets remains an elusive, long-standing open problem.
One obstacle is to determine when implied non-edges can exist without
non-trivial rigid induced subgraphs, i.e., {\em nucleations}, and how to deal
with them.
In this paper, we give general inductive construction schemes and proof
techniques to generate {\em nucleation-free graphs} (i.e., graphs without any
nucleation) with implied non-edges. As a consequence, we obtain (a) dependent
graphs in that have no nucleation; and (b) nucleation-free {\em
rigidity circuits}, i.e., minimally dependent edge sets in . It
additionally follows that true rigidity is strictly stronger than a tractable
approximation to rigidity given by Sitharam and Zhou
\cite{sitharam:zhou:tractableADG:2004}, based on an inductive combinatorial
characterization.
As an independently interesting byproduct, we obtain a new inductive
construction for independent graphs in . Currently, very few such inductive
constructions are known, in contrast to
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