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On the discrete representation of the Laplacian of Gaussian

On the discrete representation of the Laplacian of Gaussian
On the discrete representation of the Laplacian of Gaussian
The Laplacian of Gaussian (LoG) is commonly employed as a second-order edge detector in image processing, and it is popular because of its attractive scaling properties. However, its application within a finite sampled domain is non-trivial due to its infinite extent. Heuristics are often employed to determine the required mask size and they may lead to poor edge detection and location. We derive an explicit relationship between the size of the LoG mask and the probability of edge detection error introduced by its approximation, providing a strong basis for its stable implementation. In addition, we demonstrate the need for bias correction, to correct the offset error introduced by truncation, and derive strict bounds on the scales that may be employed by consideration of the aliasing error introduced by sampling. To characterise edges, a zero-crossing detector is proposed which uses a bilinear surface to guarantee detection and closure of edges. These issues are confirmed by experimental results, which particularly emphasise the importance of bias correction. As such, we give a new basis for implementation of the LoG edge detector and show the advantages that such analysis can confer.
0031-3203
1463-1472
Gunn, S.R.
306af9b3-a7fa-4381-baf9-5d6a6ec89868
Gunn, S.R.
306af9b3-a7fa-4381-baf9-5d6a6ec89868

Gunn, S.R. (1999) On the discrete representation of the Laplacian of Gaussian. Pattern Recognition, 32 (8), 1463-1472. (doi:10.1016/S0031-3203(98)00163-0).

Record type: Article

Abstract

The Laplacian of Gaussian (LoG) is commonly employed as a second-order edge detector in image processing, and it is popular because of its attractive scaling properties. However, its application within a finite sampled domain is non-trivial due to its infinite extent. Heuristics are often employed to determine the required mask size and they may lead to poor edge detection and location. We derive an explicit relationship between the size of the LoG mask and the probability of edge detection error introduced by its approximation, providing a strong basis for its stable implementation. In addition, we demonstrate the need for bias correction, to correct the offset error introduced by truncation, and derive strict bounds on the scales that may be employed by consideration of the aliasing error introduced by sampling. To characterise edges, a zero-crossing detector is proposed which uses a bilinear surface to guarantee detection and closure of edges. These issues are confirmed by experimental results, which particularly emphasise the importance of bias correction. As such, we give a new basis for implementation of the LoG edge detector and show the advantages that such analysis can confer.

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Published date: August 1999
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 250631
URI: https://eprints.soton.ac.uk/id/eprint/250631
ISSN: 0031-3203
PURE UUID: 2616abc7-9550-45b8-a643-dea532825c5a

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Date deposited: 25 Jun 1999
Last modified: 21 Dec 2018 16:31

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Author: S.R. Gunn

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