Fast Euclidean morphological operators using local distance transformation by propagation

We propose a new method to compute the morphological dilation of a binary image with a circular structuring element of any given size, on a discrete lattice. The algorithm is equivalent to applying a threshold on an exact Euclidean distance map, but computations are restricted to a minimum number of pixels. The complexity of this dilation algorithm is compared to the complexity of the commonly used approximation of circular structuring elements and found to have a similar cost, while providing better results.

[1]  P. Danielsson.  Euclidean distance mapping , 1980 .

[2]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[3]  Gunilla Borgefors,et al.  Distance transformations in digital images , 1986, Comput. Vis. Graph. Image Process..

[4]  Jim Piper,et al.  Computing distance transformations in convex and non-convex domains , 1987, Pattern Recognit..

[5]  Lucas J. van Vliet,et al.  A contour processing method for fast binary neighbourhood operations , 1988, Pattern Recognit. Lett..

[6]  Piet W. Verbeek,et al.  An Efficient Uniform Cost Algorithm Applied to Distance Transforms , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Luc Vincent,et al.  Morphological transformations of binary images with arbitrary structuring elements , 1991, Signal Process..

[8]  Ingemar Ragnemalm,et al.  Fast erosion and dilation by contour processing and thresholding of distance maps , 1992, Pattern Recognit. Lett..

[9]  Ingemar Ragnemalm.  Neighborhoods for distance transformations using ordered propagation , 1992, CVGIP Image Underst..

[10]  Hinnik Eggers,et al.  Two Fast Euclidean Distance Transformations in Z2Based on Sufficient Propagation , 1998, Comput. Vis. Image Underst..

[11]  Benoit M. Macq,et al.  Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods , 1999, Comput. Vis. Image Underst..

[12]  Benoit M. Macq,et al.  Fast and exact signed Euclidean distance transformation with linear complexity , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).