Pub Date : 2023-08-10DOI: 10.1007/s10851-023-01157-8
Gilles Bertrand, Nicolas Boutry, Laurent Najman
Any watershed, when defined on a stack on a normal pseudomanifold of dimension d, is a pure $$(d-1)$$ -subcomplex that satisfies a drop-of-water principle. In this paper, we introduce Morse stacks, a class of functions that are equivalent to discrete Morse functions. We show that the watershed of a Morse stack on a normal pseudomanifold is uniquely defined and can be obtained with a linear-time algorithm relying on a sequence of collapses. Last, we prove that such a watershed is the cut of the unique minimum spanning forest, rooted in the minima of the Morse stack, of the facet graph of the pseudomanifold.
{"title":"Discrete Morse Functions and Watersheds","authors":"Gilles Bertrand, Nicolas Boutry, Laurent Najman","doi":"10.1007/s10851-023-01157-8","DOIUrl":"https://doi.org/10.1007/s10851-023-01157-8","url":null,"abstract":"Any watershed, when defined on a stack on a normal pseudomanifold of dimension d, is a pure $$(d-1)$$ -subcomplex that satisfies a drop-of-water principle. In this paper, we introduce Morse stacks, a class of functions that are equivalent to discrete Morse functions. We show that the watershed of a Morse stack on a normal pseudomanifold is uniquely defined and can be obtained with a linear-time algorithm relying on a sequence of collapses. Last, we prove that such a watershed is the cut of the unique minimum spanning forest, rooted in the minima of the Morse stack, of the facet graph of the pseudomanifold.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135492959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-09DOI: 10.1007/s10851-023-01159-6
Nicolas Boutry
{"title":"Introducing Poset-Based Connected n-Manifolds and $$mathcal {P}$$-well-composedness in Partially Ordered Sets","authors":"Nicolas Boutry","doi":"10.1007/s10851-023-01159-6","DOIUrl":"https://doi.org/10.1007/s10851-023-01159-6","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42524921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-05DOI: 10.1007/s10851-023-01158-7
Marcos A. T. Condori, P. A. Miranda
{"title":"Differential Oriented Image Foresting Transform and Its Applications to Support High-level Priors for Object Segmentation","authors":"Marcos A. T. Condori, P. A. Miranda","doi":"10.1007/s10851-023-01158-7","DOIUrl":"https://doi.org/10.1007/s10851-023-01158-7","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46559029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-17DOI: 10.1007/s10851-023-01153-y
Lidija Comic, P. Magillo
{"title":"Surface-Based Computation of the Euler Characteristic in the BCC Grid","authors":"Lidija Comic, P. Magillo","doi":"10.1007/s10851-023-01153-y","DOIUrl":"https://doi.org/10.1007/s10851-023-01153-y","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48086282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-17DOI: 10.1007/s10851-023-01155-w
F. Feschet, J. Lachaud
{"title":"An Envelope Operator for Full Convexity to Define Polyhedral Models in Digital Spaces","authors":"F. Feschet, J. Lachaud","doi":"10.1007/s10851-023-01155-w","DOIUrl":"https://doi.org/10.1007/s10851-023-01155-w","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46222709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-17DOI: 10.1007/s10851-023-01151-0
Shintaro Kondo, Masaki Mori, Takamichi Sushida
{"title":"Spatiotemporal Kernel of a Three-Component Differential Equation Model with Self-control Mechanism in Vision","authors":"Shintaro Kondo, Masaki Mori, Takamichi Sushida","doi":"10.1007/s10851-023-01151-0","DOIUrl":"https://doi.org/10.1007/s10851-023-01151-0","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42527559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-15DOI: 10.1007/s10851-023-01152-z
Tristan Roussillon
{"title":"Combinatorial Generation of Planar Sets","authors":"Tristan Roussillon","doi":"10.1007/s10851-023-01152-z","DOIUrl":"https://doi.org/10.1007/s10851-023-01152-z","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46618310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-12DOI: 10.1007/s10851-023-01149-8
Yuchen He, S. Kang, J. Morel
{"title":"Topology- and Perception-Aware Image Vectorization","authors":"Yuchen He, S. Kang, J. Morel","doi":"10.1007/s10851-023-01149-8","DOIUrl":"https://doi.org/10.1007/s10851-023-01149-8","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42672310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-12DOI: 10.1007/s10851-023-01150-1
Olga Anosova, Vitaliy Kurlin
Abstract Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are determined in a rigid form, but any minimal cells can discontinuously change due to small noise in measurements. For any integer $$kge 0$$ k≥0 , the density function of a periodic set S was previously defined as the fractional volume of all k -fold intersections (within a minimal cell) of balls that have a variable radius t and centers at all points of S . This paper introduces the density functions for periodic sets of points with different initial radii motivated by atomic radii of chemical elements and by continuous events occupying disjoint intervals in time series. The contributions are explicit descriptions of the densities for periodic sequences of intervals. The new densities are strictly stronger and distinguish periodic sequences that have identical densities in the case of zero radii.
{"title":"Density Functions of Periodic Sequences of Continuous Events","authors":"Olga Anosova, Vitaliy Kurlin","doi":"10.1007/s10851-023-01150-1","DOIUrl":"https://doi.org/10.1007/s10851-023-01150-1","url":null,"abstract":"Abstract Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are determined in a rigid form, but any minimal cells can discontinuously change due to small noise in measurements. For any integer $$kge 0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , the density function of a periodic set S was previously defined as the fractional volume of all k -fold intersections (within a minimal cell) of balls that have a variable radius t and centers at all points of S . This paper introduces the density functions for periodic sets of points with different initial radii motivated by atomic radii of chemical elements and by continuous events occupying disjoint intervals in time series. The contributions are explicit descriptions of the densities for periodic sequences of intervals. The new densities are strictly stronger and distinguish periodic sequences that have identical densities in the case of zero radii.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136222918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-02DOI: 10.1007/s10851-023-01148-9
Kehan Shi, Zhichang Guo
{"title":"Non-Gaussian Noise Removal via Gaussian Denoisers with the Gray Level Indicator","authors":"Kehan Shi, Zhichang Guo","doi":"10.1007/s10851-023-01148-9","DOIUrl":"https://doi.org/10.1007/s10851-023-01148-9","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45182844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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