The vector distance transform in two and three dimensions

Abstract The application of the distance transform (DT) to three-dimensional image data, collected, for example, by a confocal scanning laser microscope, requires special modifications to account for the possible anisotropic nature of these images. If anisotropic sampling is not properly accounted for, large errors can occur when simple image processing and image analysis operations related to the DT, such as erosions, dilations, skeletonizations, and distance measurements, are performed. This paper presents a simple, relatively fast way to account for this problem that is suitable for the large sizes typically associated with 3-D images.

[1]  Q. Ye.  The signed Euclidean distance transform and its applications , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

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

[3]  A. ROSENFELD,et al.  Distance functions on digital pictures , 1968, Pattern Recognit..

[4]  Gunilla Borgefors,et al.  Distance transformations on hexagonal grids , 1989, Pattern Recognit. Lett..

[5]  H. T. M. 0 Voort,et al.  Three‐dimensional visualization methods for confocal microscopy , 1989, Journal of microscopy.

[6]  G. J. Brakenhoff,et al.  3‐D image formation in high‐aperture fluorescence confocal microscopy: a numerical analysis , 1990 .

[7]  Ben J. H. Verwer,et al.  Improved metrics in image processing applied to the Hilditch skeleton , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[8]  Azriel Rosenfeld,et al.  Sequential Operations in Digital Picture Processing , 1966, JACM.

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

[10]  Albert M. Vossepoel,et al.  A note on "distance transformations in digital images" , 1988, Comput. Vis. Graph. Image Process..

[11]  Arnold W. M. Smeulders,et al.  A comment on "a note on 'distance transformations in digital images'" , 1989, Comput. Vis. Graph. Image Process..

[12]  G. Borgefors.  Distance transformations in arbitrary dimensions , 1984 .