Article

Completion Energies and Scale.

Dept. of Comput. Sci. & Appl. Math., Weizmann Inst. of Sci., Rehovot, Israel
IEEE Transactions on Pattern Analysis and Machine Intelligence (Impact Factor: 4.8). 01/2000; 22:1117-1131. DOI: 10.1109/34.879792
Source: DBLP

ABSTRACT Abstract The detection of smooth curves in images and their completion over gaps are two important problems,in perceptual grouping. In this paper we examine,the notion of completion energy and introduce a fast method,to compute,the most likely completions in images. Specifically, we develop two novel analytic approximations,to the curve of least energy. In addition, we introduce a fast numerical method to compute the curve of least energy, and show that our approximations are obtained at early stages of this numerical computation. We then use our newly developed energies to find the most likely completions in images through a generalized summation,of induction fields. Since in practice edge elements are obtained by applying filters of certain widths and lengths to the image, we adjust our computation to take these parameters into account. Finally, we show that, due to the smoothness of the kernel of summation, the process of summing,induction fields can be run in time that is linear in the number of different edge elements in the image, or in log where is the number of pixels in the image, using multigrid methods.

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    [Show abstract] [Hide abstract]
    ABSTRACT: Abstract The detection of smooth curves in images and their completion over gaps are two important problems,in perceptual grouping. In this paper we examine,the notion of completion energy and introduce a fast method,to compute,the most likely completions in images. Specifically, we develop two novel analytic approximations,to the curve of least energy. In addition, we introduce a fast numerical method to compute the curve of least energy, and show that our approximations are obtained at early stages of this numerical computation. We then use our newly developed energies to find the most likely completions in images through a generalized summation,of induction fields. Since in practice edge elements are obtained by applying filters of certain widths and lengths to the image, we adjust our computation to take these parameters into account. Finally, we show that, due to the smoothness of the kernel of summation, the process of summing,induction fields can be run in time that is linear in the number of different edge elements in the image, or in log where is the number of pixels in the image, using multigrid methods.
    IEEE Transactions on Pattern Analysis and Machine Intelligence 01/2000; 22:1117-1131. · 4.80 Impact Factor
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May 22, 2014