Ravi, D and Venkatesh, YV (2000) A new framework for reconstruction of images from boundaries. In: SIAM Journal of Applied Mathmatics, 60 (6). pp. 1841-1866.
The problem of reconstructing images from boundaries has been studied in the literature chie y as one based on the information from zero crossings. In contrast, we formulate the problem within the framework of approximation theory, and we propose a representation scheme involving (i) the point arbitrarily near the boundarie and (ii) the gradient information at these point . We show that the representation scheme is complete and stable under rea onable conditions. Further, we develop an efficient reconstruction mechanism, using the concept of a regularized solution, in which we penalize a candidate solution in proportion to its departure from a model which resembles the original in shape but is simple to construct. Finally, we demonstrate the effectiveness of the cost functional with the help of experimental results, using a representation in which the number of data points is much less than the number of pixels in the original image.
|Item Type:||Journal Article|
|Additional Information:||Copyright for this article belongs to Society for Industrial and Applied Mathematics (SIAM)|
|Keywords:||computer vision;boundary detection;image gradient;regularization;stable image reconstruction;inverse problems;zero crossings|
|Department/Centre:||Division of Electrical Sciences > Electrical Engineering|
|Date Deposited:||02 Jun 2004|
|Last Modified:||19 Sep 2010 04:12|
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