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 Bézier 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.
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Hongwei Lin received his B.S. degree from the Department of Applied Mathematics at Zhejiang University, China, in 1996, and Ph.D. degree from the Department of Mathematics at Zhejiang University in 2004. He is currently an associate professor in the School of Mathematical Science, State Key Laboratory of CAD&CG, Zhejiang University. His research interests include geometric design, computer graphics, and computer vision.
Zihao Wang received his B.S. degree from Zhejiang University, China, in 2013. He is currently a graduate student in the School of Mathematical Science, Zhejiang University. His research interests include visual curve completion and computer vision.
Panpan Feng received his B.S. degree from Jiangsu University of Science and Technology in 2011, and M.S. degree from the State Key Laboratory of CAD&CG, Zhejiang University, in 2014. He is currently working in iQiyi as a software engineer. His research interests include computer vision and geometric design.
Xingjiang Lu received his B.S. degree from the Department of Applied Mathematics at Zhejiang University, China, in 1985, and Ph.D. degree from the Department of Mathematics at Zhejiang University in 1999. He is currently a professor in the School of Mathematical Science, Zhejiang University. His research interests include geometric computation, computer graphics, and computer vision.
Jinhui Yu received his B.S. and M.S. degrees in electronics engineering from Harbin Shipbuilding Engineering Institute, Harbin Engineering University, China, in 1982 and 1987, respectively. He received his Ph.D. degree in computer graphics from the University of Glasgow in 1999. He is a professor of computer science at the State Key Laboratory of CAD&CG, Zhejiang University, China. His research interests include image-based modeling, nonphotorealistic rendering, computer animation, and computer graphics art.
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Lin, H., Wang, Z., Feng, P. et al. A computational model of topological and geometric recovery for visual curve completion. Comp. Visual Media 2, 329–342 (2016). https://doi.org/10.1007/s41095-016-0055-3
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DOI: https://doi.org/10.1007/s41095-016-0055-3