作为异质泊松问题的皮层 V1 变换

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-02-21 DOI:10.1137/23m1555958

Alessandro Sarti, Mattia Galeotti, Giovanna Citti

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引用次数: 0

摘要

SIAM 影像科学杂志》第 17 卷第 1 期第 389-414 页，2024 年 3 月。摘要初级视觉皮层（V1）皮层细胞的感受轮廓是非常异质的，其作用是将刺激图像区分为从一个点到另一个点不断变化的操作者。本文旨在说明 V1 中的细胞分布虽然不能完整地重建原始图像，但足以重建具有主观恒定性的感知图像。我们证明，色彩恒定图像可以作为相关逆问题的解来重建，而逆问题是一个带有异质微分算子的泊松方程。在神经层面，短程连接的权重构成了逐点调整的泊松问题的基本解。通过同质化技术，首次证明了结果向同质重构的收敛性。

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The Cortical V1 Transform as a Heterogeneous Poisson Problem

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 389-414, March 2024.
Abstract. Receptive profiles of the primary visual cortex (V1) cortical cells are very heterogeneous and act by differentiating the stimulus image as operators changing from point to point. In this paper we aim to show that the distribution of cells in V1, although not complete to reconstruct the original image, is sufficient to reconstruct the perceived image with subjective constancy. We show that a color constancy image can be reconstructed as the solution of the associated inverse problem, which is a Poisson equation with heterogeneous differential operators. At the neural level the weights of short-range connectivity constitute the fundamental solution of the Poisson problem adapted point by point. A first demonstration of convergence of the result towards homogeneous reconstructions is proposed by means of homogenization techniques.

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来源期刊

SIAM Journal on Imaging Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

3.80

自引率

4.80%

发文量

审稿时长

>12 weeks

期刊介绍： SIAM Journal on Imaging Sciences (SIIMS) covers all areas of imaging sciences, broadly interpreted. It includes image formation, image processing, image analysis, image interpretation and understanding, imaging-related machine learning, and inverse problems in imaging; leading to applications to diverse areas in science, medicine, engineering, and other fields. The journal’s scope is meant to be broad enough to include areas now organized under the terms image processing, image analysis, computer graphics, computer vision, visual machine learning, and visualization. Formal approaches, at the level of mathematics and/or computations, as well as state-of-the-art practical results, are expected from manuscripts published in SIIMS. SIIMS is mathematically and computationally based, and offers a unique forum to highlight the commonality of methodology, models, and algorithms among diverse application areas of imaging sciences. SIIMS provides a broad authoritative source for fundamental results in imaging sciences, with a unique combination of mathematics and applications. SIIMS covers a broad range of areas, including but not limited to image formation, image processing, image analysis, computer graphics, computer vision, visualization, image understanding, pattern analysis, machine intelligence, remote sensing, geoscience, signal processing, medical and biomedical imaging, and seismic imaging. The fundamental mathematical theories addressing imaging problems covered by SIIMS include, but are not limited to, harmonic analysis, partial differential equations, differential geometry, numerical analysis, information theory, learning, optimization, statistics, and probability. Research papers that innovate both in the fundamentals and in the applications are especially welcome. SIIMS focuses on conceptually new ideas, methods, and fundamentals as applied to all aspects of imaging sciences.