Abstract
Visual curve completion is a fundamental problem in understanding the principles of the human visual system. This problem is usually divided into two problems: a grouping problem and a shape problem. On one hand, though perception of the visually completed curve is clearly a global task (for example, a human perceives the Kanizsa triangle only when seeing all three black objects), conventional methods for solving the grouping problem are generally based on local Gestalt laws. On the other hand, the shape of the visually completed curve is usually recovered by minimizing shape energy in existing methods. However, not only do these methods lack mechanisms to adjust the shape of the recovered visual curve using perceptual, psychophysical, and neurophysiological knowledge, but it is also difficult to calculate an explicit representation of the visually completed curve. In this paper, we present a systematic computational model for generating a visually completed curve. Firstly, based on recent studies of perception, psychophysics, and neurophysiology, we formulate a grouping procedure based on the human visual system by seeking a minimum Hamiltonian cycle in a graph, solving the grouping problem in a global manner. Secondly, we employ a Bezier curve-based model to represent the visually completed curve. Not only is an explicit representation deduced, but we also present a means to integrate knowledge from related areas, such as perception, psychophysics, and neurophysiology, and so on. The proposed computational model has been validated using many modal and amodal completion examples, and desirable results were obtained.
Highlights
When a human sees an object with boundary fragments, such as the Kanizsa triangle in Fig. 1(a), the human visual system fills in the missing parts between boundary fragments, making observer perceive a complete object
The cubic Bezier curve P (t), with the constraint that P (t) is tangent to the two boundary segments at their end points, is generated by minimizing an energy function, which is designed by taking knowledge from perception, psychophysics, and neurophysiology into account
Our Bezier curve-based model provides an extensible model into which new knowledge from perception, psychophysics, and neurophysiology can be integrated by improving the functions f (α) in Eq (3) and β(L) in Eq (4)
Summary
When a human sees an object with boundary fragments, such as the Kanizsa triangle in Fig. 1(a), the human visual system fills in the missing parts between boundary fragments, making observer perceive a complete object. [4] introduces a factor to adjust the shape of the visually completed curve, the visual curve is produced by a numerical method, and its closed form representation is hard to generate. This makes the computation complicated, and analysis of the visually completed curve inconvenient. The cubic Bezier curve P (t), with the constraint that P (t) is tangent to the two boundary segments at their end points, is generated by minimizing an energy function, which is designed by taking knowledge from perception, psychophysics, and neurophysiology into account.
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