Widely employed in cognitive psychology, Gestalt theory elucidates basic principles in visual perception, but meanwhile presents significant challenges for computation. The advancement of artificial intelligence requires the emulation of human cognitive behavior, for which Gestalt theory serves as a fundamental framework describing human visual cognitive behavior. In this paper, we utilize persistent homology, a mathematical tool in computational topology, to develop a computational model for Gestalt theory, addressing the challenges of quantification and computation. The Gestalt computational model not only holds promise for applications in artificial intelligence and computer vision, but also opens a new research direction of computational visual perception.

翻译：格式塔理论在认知心理学中被广泛运用，用以阐明视觉感知的基本原理，但同时也为计算带来了重大挑战。人工智能的发展要求对人类认知行为进行模拟，而格式塔理论正是描述人类视觉认知行为的基础框架。本文利用计算拓扑学中的数学工具——持续同调，为格式塔理论构建了一个计算模型，以解决其量化与计算的难题。该格式塔计算模型不仅在人工智能和计算机视觉领域具有应用前景，也为计算视觉感知开辟了新的研究方向。