[论文解读] Visual Perception, Quantity of Information Function and the Concept of the Quantity of Information Continuous Splines

Rushan Ziatdinov|ArXiv.org|Feb 3, 2025

Advanced Image Fusion Techniques参考文献 15被引用 4

一句话总结

论文定义了从离散数据到视觉形状的信息量连续样条，并探讨在何种条件下平面曲线可以具有恒定的信息量函数，将视觉感知与信息理论联系起来。

ABSTRACT

The geometric shapes of the outside world objects hide an undisclosed emotional, psychological, artistic, aesthetic and shape-generating potential; they may attract or cause fear as well as a variety of other emotions. This suggests that living beings with vision perceive geometric objects within an information-handling process. However, not many studies have been performed for a better understanding of visual perception from the view of information theory and mathematical modelling, but the evidence first found by Attneave (1954) suggests that the concepts and techniques of information theory may shed light on a better and deeper understanding of visual perception. The quantity of information function can theoretically explain the concentration of information on the visual contours, and, based on this, we first propose the concept of the quantity of information continuous splines for visualization of shapes from a given set of discrete data without adding any in-between points with curvature extreme. Additionally, we first discover planar curve with a constant quantity of information function and demonstrate one of the conditions when a monotonic curvature curve has a constant quantity of information function.

研究动机与目标

• 通过信息理论和数学建模来激发对视觉感知的研究。
• 引入用于视觉轮廓的信息量函数。
• 提出用于从离散数据可视化形状的数量信息连续样条的概念。
• 研究在何种条件下平面曲线具有恒定的信息量函数。

提出的方法

• 借鉴自Attneave（1954）的信息理论概念来建模视觉轮廓。
• 在不引入中间点的情况下定义并构造用于形状可视化的信息量连续样条。
• 识别并分析具有恒定信息量函数的平面曲线。
• 给出一个单调曲率曲线可产生恒定信息量函数的条件。

实验结果

研究问题

• RQ1 信息量函数是否能解释视觉轮廓上信息的集中？
• RQ2 如何在不增加插值点的情况下，使用连续样条从离散数据表示形状？
• RQ3 在何种条件下平面曲线具有恒定的信息量函数？
• RQ4 曲率单调性与曲线中的信息恒定性之间的关系是什么？

主要发现

• 提出从离散数据可视化而不增加额外点的信息量连续样条的概念。
• 识别出具有恒定信息量函数的平面曲线。
• 证明了单调曲率曲线在某条件下具有恒定信息量函数。
• 将信息理论量度与几何形状的视觉感知联系起来。