Multiscale filtering method for derivative computation

Bingcheng Li; Songde Ma

doi:10.1117/12.185887

16 September 1994 Multiscale filtering method for derivative computation

Bingcheng Li, Songde Ma

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.

Citation Download Citation

Bingcheng Li and Songde Ma "Multiscale filtering method for derivative computation", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); https://doi.org/10.1117/12.185887

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