Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Sun, 26 Jan 2020 11:03:52 GMT2020-01-26T11:03:52Z10571A Global Method for Reducing Multidimensional Size Graphshttp://hdl.handle.net/11380/695093Titolo: A Global Method for Reducing Multidimensional Size Graphs
Abstract: This paper introduces the concept of discrete multidimensionalsize function, a mathematical tool studying the so-called sizegraphs. These graphs constitutes an ingredient of Size Theory, a geometrical/topological approach to shape analysis and comparison. A globalmethod for reducing size graphs is presented, together with a theoremstating that size graphs reduced in such a way preserve all the informationin terms of multidimensional size functions. This approach can leadto simplify the effective computation of discrete multidimensional sizefunctions, as shown by examples.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11380/6950932011-01-01T00:00:00ZRecognition of Occluded Shapes Using Size Functionshttp://hdl.handle.net/11380/695095Titolo: Recognition of Occluded Shapes Using Size Functions
Abstract: The robustness against occlusions and the ability to performnot only global matching, but also partial matching are investigated incomputer vision in order to evaluate the performance of shape descriptors.In this paper we consider the size function shape descriptor, andwe illustrate some results about size functions of occluded shapes. Theoreticalresults indicate that size functions are able to detect a partialmatching between shapes by showing a common subset of cornerpoints.Experiments are presented which outline the potential of the proposedapproach in recognition tasks in the presence of occlusions.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6950952009-01-01T00:00:00ZNew pseudo-distances for the size function spacehttp://hdl.handle.net/11380/587538Titolo: New pseudo-distances for the size function space
Abstract: A method to construct new pseudo-distances for the size function space based on the formal series representation of size functions is introduced. These new pseudo-distances allow to measure quantitatively the differences in shapes by comparing size functions. Some experiments on digital images are shown.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11380/5875381997-01-01T00:00:00ZApplied and Computational Algebraic Topology Advanced School 2012 (ACAT 2012)http://hdl.handle.net/11380/735247Titolo: Applied and Computational Algebraic Topology Advanced School 2012 (ACAT 2012)
Abstract: The Bologna ACAT Advanced School focuses on the area of Computational Topology applied to Computer Image and Vision. It is mainly aimed at PhD students and young researchers in Mathematics, Applied Mathematics, and Computer Science interested in Computational Topology and Computer Vision and the interaction between these areas.In the Bologna ACAT Advanced School, experts in the fields of - Computational Homology - Persistent Topology - Discrete Morse Theory - Computer Vision will give introductory talks on the respective topics in which they are specialists.The Bologna ACAT Advanced School will be followed by the 4th International Workshop on Computational Topology in Image Context (CTIC2012), held in Bertinoro (Italy), May 28-30, 2012.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11380/7352472012-01-01T00:00:00ZUniqueness of models in persistent homology: the case of curveshttp://hdl.handle.net/11380/686661Titolo: Uniqueness of models in persistent homology: the case of curves
Abstract: We consider generic curves in R^2, i.e. generic C^1 functions f : S^1 → R^2. We analyze these curves through the persistent homology groups of a filtration induced on S^1 by f . In particular, we consider the question whether these persistent homology groups uniquely characterize f , at least up to reparameterizationsof S^1. We give a partially positive answer to this question.More precisely, we prove that f = g ◦ h, where h : S^1 → S^1 is a C^1-diffeomorphism, if and only if the persistent homology groups of s ◦ f and s ◦g coincide, for every s belonging to the group S generated by reflections in the coordinate axes. Moreover, for a smaller set of generic functions, we show that f and g are close to each other in themax-norm (up to re-parameterizations)if and only if, for every s in S, the persistent Betti number functions of s ◦ f and s ◦ g are close to each other, with respect to a suitable distance.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11380/6866612011-01-01T00:00:00ZReeb Graphs of Piecewise Linear Functionshttp://hdl.handle.net/11380/1135448Titolo: Reeb Graphs of Piecewise Linear Functions
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11380/11354482017-01-01T00:00:00ZDeformation energy for size functionshttp://hdl.handle.net/11380/589969Titolo: Deformation energy for size functions
Abstract: Size functions are functions from the real plane to thenatural numbers useful for describing shapes of objects. Theyallow to translate the problem of comparing shapes to the problemof comparing functions, that is a much simpler task. In order toperform the comparison between size functions we present a methodto measure the energy necessary to deform size functions into eachother. Minimizing such an energy allows for a measure of thesimilarity between shapes. Some experimental results concerningthe comparison of free hand-drawn sketches are shown.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/11380/5899691999-01-01T00:00:00ZComputational Topology in Image Contexthttp://hdl.handle.net/11380/735249Titolo: Computational Topology in Image Context
Abstract: Organizing the 4th International Workshop on Computational Topology in ImageContext (CTIC 2012) has been an interesting experience indeed, going farbeyond Mathematics and Computer Science. This collection documents the presentations accepted at CTIC 2012. Theresearch made by the authors of these papers has been the core of the workshop,and we thank all the contributors for their commitment and dedication. Theireort has allowed us to continue the tradition of CTIC in providing a forum forscientic exchange in Topology and Computation in Image Context at a highquality level.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11380/7352492012-01-01T00:00:00ZAlgebraic representation of size functionshttp://hdl.handle.net/11380/587537Titolo: Algebraic representation of size functions
Abstract: In this paper we show that size functions, a class of shape descriptors, can be represented as countable collections of points and lines of the real plane with multiplicities, i.e. as particular formal series. This algebraic approach allows to reduce the information storage necessary to work with size functions. Some further applications are discussed. Namely, the possibility ofdefining new pseudo-distances between size functions and the possibility of emphasizing the part of information considered more important from the shape recognition viewpoint in order to make recognition more efficient.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/11380/5875371999-01-01T00:00:00ZPersistence Modules, Shape Description, and Completenesshttp://hdl.handle.net/11380/735250Titolo: Persistence Modules, Shape Description, and Completeness
Abstract: Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorialstructure, the H0-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11380/7352502012-01-01T00:00:00Z