16 September 1994 Multiscale filtering method for derivative computation
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Proceedings Volume 2308, Visual Communications and Image Processing '94; (1994) https://doi.org/10.1117/12.185887
Event: Visual Communications and Image Processing '94, 1994, Chicago, IL, United States
Abstract
In this paper, we propose a multiscale filtering method to compute derivatives with any orders. As a special case, we consider the computation of the second derivatives, and show that the difference of two smoothers with the same kernel, but different scales constructs a Laplacian operator and has a zero crossing at a step edge. Selecting a Gaussian function as the smoother, we show the DOG (difference of Gaussian) itself is a zero crossing edge extractor, and it needn't approximate to LoG (Laplacian of Gaussian). At the same time, we show that even though DOG for bandwidth ratio 0.625 (1:1.6) is the optimal approximation to LoG, it is not optimal for edge detection. Finally, selecting an exponential function as the smoothing kernel, we obtain a Laplacian of exponential (LoE) operator, and it is shown theoretically and experimentally that the LoE has a high edge detection performance, furthermore its computation is efficient and its computational complexity is independent of the filter kernel bandwidths.
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Bingcheng Li, Songde Ma, "Multiscale filtering method for derivative computation", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); doi: 10.1117/12.185887; https://doi.org/10.1117/12.185887
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