Illusory Shapes via Corner Fusion

We propose a novel method for constructing illusory foreground and background shapes from convex corners. We first introduce a new class of visual cues called corner bases, which expands 0-dimensional corner points to 2-dimensional micro structures. These corner bases are then fused together by the functionalized elastica energy imposed upon an admissible phase field. The optimal phase field segments the visual field into disjoint connected components, which are further fused via a simple connectivity principle to construct both foreground illusory shapes and background occluded shapes. Robust and efficient numerical schemes are developed, and several generic examples are presented. Cognitive implications are highlighted.