An Algorithm for a 3D Simplicity Test

Every thinning (or shrinking) algorithm can be stated as a list of deletion configurations. If a neighborhood of a given image point matches one of these configurations, the point will be deleted. In order to make design of a (3D) thinning (or shrinking) algorithm easy to handle, and therefore the list of configurations as short as possible, every configuration is described in three colors, black, white, and “don't-care,” where the don't-care “color” matches either a black or white point in a given image. A thinning algorithm is connectivity preserving if and only if every set deleted by this algorithm can be ordered in such a sequence that every point is simple after all previous points in the sequence are deleted. Therefore, it is very important to determine whether a deleted point is simple or not. We present the first 3D algorithm for determining the simplicity of any three-color deletion configuration. This algorithm is memory efficient and fast. Hence it can be a very useful tool for designing 3D connectivity preserving thinning (or shrinking) algorithms.

[1]  Richard W. Hall.  Connectivity-preserving parallel operators in 2D and 3D images , 1993, Other Conferences.

[2]  King-Sun Fu,et al.  A parallel thinning algorithm for 3-D pictures , 1981 .

[3]  Christian Ronse,et al.  Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images , 1988, Discret. Appl. Math..

[4]  Cherng Min Ma,et al.  On topology preservation in 3D thinning , 1994 .

[5]  Azriel Rosenfeld,et al.  A Characterization of Parallel Thinning Algorithms , 1975, Inf. Control..

[6]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[7]  T. Yung Kong,et al.  Problem of determining whether a parallel reduction operator for n-dimensional binary images always preserves topology , 1993, Other Conferences.

[8]  Grégoire Malandain,et al.  Fast characterization of 3D simple points , 1992, Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol. III. Conference C: Image, Speech and Signal Analysis,.

[9]  R. W. Hall.  Tests for connectivity preservation for parallel reduction operators , 1992 .

[10]  Gilles Bertrand,et al.  A simple parallel 3D thinning algorithm , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[11]  Partha Pratim Das,et al.  On connectivity issues of ESPTA , 1990, Pattern Recognit. Lett..