Cortically Based Optimal Transport

被引：0
作者：
Mattia Galeotti
Giovanna Citti
Alessandro Sarti
机构：
[1] Università di Bologna,Mathematics Department
[2] CNRS,undefined
[3] CAMS - EHESS,undefined
来源：
Journal of Mathematical Imaging and Vision | 2022年 / 64卷
关键词：
Optimal transport; PDEs; Visual cortex; Metric geometry; Image deformation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We introduce a model for image morphing in the primary visual cortex V1 to perform completion of missing images in time. We model the output of simple cells through a family of Gabor filters and the propagation of the neural signal accordingly to the functional geometry induced by horizontal connectivity. Then we model the deformation between two images as a path relying two different outputs. This path is obtained by optimal transport considering the Wasserstein distance geodesics associated to some probability measures naturally induced by the outputs on V1. The frame of Gabor filters allows to project back the output path, therefore obtaining an associated image stimulus deformation. We perform a numerical implementation of our cortical model, assessing its ability in reconstructing rigid motions of simple shapes.
引用
收藏
页码：1040 / 1057
页数：17
相关论文
共 48 条
[11]  
Sarti A(1977)Ferrier lecture-functional architecture of macaque monkey visual cortex Proc. R. Soc. Lond. Ser. B. Biol. Sci. 198 1-59
[12]  
Daubechies I(2008)Identifying natural images from human brain activity Nature 452 352-355
[13]  
Daugman JG(1996)Image representation using 2d gabor wavelets IEEE Trans. Pattern Anal. Mach. Intell. 18 959-971
[14]  
Favali M(1985)Balls and metrics defined by vector fields i: basic properties Acta Math. 155 103-147
[15]  
Abbasi-Sureshjani S(1999)Vers une neurogéométrie. fibrations corticales, structures de contact et contours subjectifs modaux Mathématiques et sciences humaines 145 5-101
[16]  
ter Haar Romeny B(2018)Entropic optimal transport is maximum-likelihood deconvolution Comptes Rendus Mathematique 356 1228-1235
[17]  
Sarti A(2010)A model of natural image edge co-occurrence in the rototranslation group J. Vis. 10 37-37
[18]  
Gangbo W(2008)The symplectic structure of the primary visual cortex Biol. Cybern. 98 33-48
[19]  
McCann RJ(2019)Differential heterogenesis and the emergence of semiotic function Semiotica 2019 1-34
[20]  
Hoffman WC(2007)An image morphing technique based on optimal mass preserving mapping IEEE Trans. Image Process. 16 1481-1495
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