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, Bingcheng Li, Songde Ma, 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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