Filtering with a normalized Laplacian of a Gaussian kernel

David H. Eberly; Daniel S. Fritsch; Charles Kurak

doi:10.1117/12.130889

9 December 1992 Filtering with a normalized Laplacian of a Gaussian kernel

David H. Eberly, Daniel S. Fritsch, Charles Kurak

Proceedings Volume 1768, Mathematical Methods in Medical Imaging; (1992) https://doi.org/10.1117/12.130889
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

Our approach to segmenting images involves object definition via multiscale methods. Typically, at small scales an object consists of many details. At larger scales these details are less noticeable, and other more global features are prominent. In either case we want to characterize those scales at which features of interest occur. The dominant trend in object definition has been to describe object boundaries via edge detection processes [1]. For binary objects, an alternate approach is to describe object shape with medial axes [2] or with skeletons using the methods of mathematical morphology [3]. Extensions of these ideas to objects described by gray scale images can be found in the literature, for example [4,5]. Such results are based on geometric properties of the graph of the intensity function. We may also apply filters to the intensity function which measure medialness of points. At a given point, the filter should have a strong response when the point is approximately midway between two boundaries. The response of the filter should be proportional to distance from the point to the boundary. We analyze a particular filter which has these properties, called the normalized Laplacian of Gaussian filter. Section 2 gives motivation and a mathematical description of the filter. The filter is described in a continuous variable setting. For discrete images viewed continuously as piecewise constant functions, an exact formula for the response of the filter is given. Section 3 gives the algorithm for construction of medial axes. In section 4 we discuss the numerical implementation of the filter. The appendix contains C code for an implementation of the filter using fast convolutions.

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David H. Eberly, Daniel S. Fritsch, and Charles Kurak "Filtering with a normalized Laplacian of a Gaussian kernel", Proc. SPIE 1768, Mathematical Methods in Medical Imaging, (9 December 1992); https://doi.org/10.1117/12.130889

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KEYWORDS

Convolution

Gaussian filters

Medical imaging

Computer science

Edge detection

Image filtering

Image segmentation

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