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Visual space geometry derived from occlusion axioms

机译:从遮挡公理派生的视觉空间几何

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Abstract: In our previous work the occlusion phenomena were considered as a base for development of geometrical structures in the visual field. Laws of occlusion were formulated and converted thereafter into axiomatic system. Occlusion is formalized as a ternary relation and among the laws of occlusion we find a requirement of symmetry of the relation (Gibson's law), a transitivity axiom and others. This leads us to a notion of abstract visual space (AVS). The geometry of AVS is the subject of this research. Typical examples of AVS are convex open subsets of an n-dimensional real affine space for n $GREQ 2, or more generally speaking, convex open subsets of any n-dimensional affine space over some totally ordered field F, commutative or noncommutative one. !12
机译:摘要:在我们以前的工作中,闭塞现象被认为是视野中几何结构发展的基础。制定了咬合定律并将其转化为公理体系。遮挡被正式化为三元关系,并且在遮挡定律中,我们发现关系的对称性(吉布森定律),及物公理和其他要求。这使我们想到了抽象视觉空间(AVS)的概念。 AVS的几何结构是本研究的主题。 AVS的典型示例是n $ GREQ 2的n维实数仿射空间的凸开子集,或更一般地说,是在某些可交换或非交换的完全有序场F上任何n维仿射空间的凸开子集。 !12

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