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":"65 1","pages":"802 - 817"},"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":" ","pages":""},"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":"65 1","pages":"754 - 769"},"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":" ","pages":""},"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":"65 1","pages":"702 - 717"},"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":" ","pages":""},"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":"1 1","pages":"0"},"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":"1 1","pages":"1-17"},"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}
Pub Date : 2023-04-16DOI: 10.1007/s10851-023-01147-w
Gijs Bellaard, Daan L. J. Bon, Gautam Pai, Bart M. N. Smets, Remco Duits
Abstract Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs have the advantage over CNNs that they do not waste network capacity on training symmetries that should have been hard-coded in the network. The recently introduced framework of PDE-based G-CNNs (PDE-G-CNNs) generalizes G-CNNs. PDE-G-CNNs have the core advantages that they simultaneously (1) reduce network complexity, (2) increase classification performance, and (3) provide geometric interpretability. Their implementations primarily consist of linear and morphological convolutions with kernels. In this paper, we show that the previously suggested approximative morphological kernels do not always accurately approximate the exact kernels accurately. More specifically, depending on the spatial anisotropy of the Riemannian metric, we argue that one must resort to sub-Riemannian approximations. We solve this problem by providing a new approximative kernel that works regardless of the anisotropy. We provide new theorems with better error estimates of the approximative kernels, and prove that they all carry the same reflectional symmetries as the exact ones. We test the effectiveness of multiple approximative kernels within the PDE-G-CNN framework on two datasets, and observe an improvement with the new approximative kernels. We report that the PDE-G-CNNs again allow for a considerable reduction of network complexity while having comparable or better performance than G-CNNs and CNNs on the two datasets. Moreover, PDE-G-CNNs have the advantage of better geometric interpretability over G-CNNs, as the morphological kernels are related to association fields from neurogeometry.
群等变卷积神经网络(g - cnn)已成功应用于几何深度学习。通常，g - cnn比cnn有一个优势，即它们不会浪费网络容量来训练应该在网络中硬编码的对称性。最近引入的基于pde的g - cnn框架(pde - g - cnn)是对g - cnn的推广。pde - g - cnn的核心优势是同时(1)降低网络复杂度，(2)提高分类性能，(3)提供几何可解释性。它们的实现主要由带核的线性和形态卷积组成。在本文中，我们证明了先前提出的近似形态学核并不总是准确地接近精确核。更具体地说，根据黎曼度量的空间各向异性，我们认为必须采用次黎曼近似。我们通过提供一个新的近似核来解决这个问题，该核不受各向异性的影响。我们提供了新的定理，对近似核具有更好的误差估计，并证明它们都具有与精确核相同的反射对称性。我们在两个数据集上测试了PDE-G-CNN框架内多个近似核的有效性，并观察到了新的近似核的改进。我们报告说，pde - g - cnn再次允许大大降低网络复杂性，同时在两个数据集上具有与g - cnn和cnn相当或更好的性能。此外，pde - g - cnn具有比g - cnn更好的几何可解释性，因为形态学核与神经几何学的关联场相关。
{"title":"Analysis of (sub-)Riemannian PDE-G-CNNs","authors":"Gijs Bellaard, Daan L. J. Bon, Gautam Pai, Bart M. N. Smets, Remco Duits","doi":"10.1007/s10851-023-01147-w","DOIUrl":"https://doi.org/10.1007/s10851-023-01147-w","url":null,"abstract":"Abstract Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs have the advantage over CNNs that they do not waste network capacity on training symmetries that should have been hard-coded in the network. The recently introduced framework of PDE-based G-CNNs (PDE-G-CNNs) generalizes G-CNNs. PDE-G-CNNs have the core advantages that they simultaneously (1) reduce network complexity, (2) increase classification performance, and (3) provide geometric interpretability. Their implementations primarily consist of linear and morphological convolutions with kernels. In this paper, we show that the previously suggested approximative morphological kernels do not always accurately approximate the exact kernels accurately. More specifically, depending on the spatial anisotropy of the Riemannian metric, we argue that one must resort to sub-Riemannian approximations. We solve this problem by providing a new approximative kernel that works regardless of the anisotropy. We provide new theorems with better error estimates of the approximative kernels, and prove that they all carry the same reflectional symmetries as the exact ones. We test the effectiveness of multiple approximative kernels within the PDE-G-CNN framework on two datasets, and observe an improvement with the new approximative kernels. We report that the PDE-G-CNNs again allow for a considerable reduction of network complexity while having comparable or better performance than G-CNNs and CNNs on the two datasets. Moreover, PDE-G-CNNs have the advantage of better geometric interpretability over G-CNNs, as the morphological kernels are related to association fields from neurogeometry.","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136243274","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 : 2023-04-01DOI: 10.1007/s10851-023-01141-2
{"title":"Appreciation to Journal of Mathematical Imaging and Vision Reviewers","authors":"","doi":"10.1007/s10851-023-01141-2","DOIUrl":"https://doi.org/10.1007/s10851-023-01141-2","url":null,"abstract":"","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":"65 1","pages":"371-372"},"PeriodicalIF":2.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52392130","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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