Connectivity Preservation of 3D 6-Subiteration Thinning Algorithms

✍ Scribed by C.Min Ma

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 241 KB
• Volume: 58
• Category: Article
• ISSN: 1077-3169
• DOI: 10.1006/gmip.1996.0030

✦ Synopsis

It seems straightforward that such tests can be computer-Thinning is a process which erodes an object layer by layer ized by checking the 2 8 test patterns (since each corner is until only a skeleton is left. A thinning algorithm should preeither an object point or a background point). Unfortuserve connectivity; i.e., any object and its skeleton should mainnately, this conclusion is incorrect. Consider a thinning tain the same connectivity structure. This paper concerns the algorithm with n different templates (every object point connectivity preservation of 3D 6-subiteration thinning algoin an image with a neighborhood that matches any template rithms. The first objective of this paper is to propose sufficient is deleted). To check whether Theorem 3.1.4 is satisfied, conditions so that any 3D 6-subiteration parallel thinning algoevery four templates should be merged (in particular ways);

rithm satisfying these conditions is guaranteed to preserve coni.e., the time complexity is O(n 4 ). The program is not feasinectivity. Even with these sufficient conditions, it is still not very ble when n is a large number. This paper emphasizes in easy to prove the connectivity soundness of a 3D 6-subiteration thinning algorithm. Thus, the second objective of this paper computerizing the sufficient conditions for 3D 6-subiterais to propose an approach to computerize the above suffition parallel thinning algorithms to preserve connectivity. cient conditions. Any 3D 6-subiteration thinning algorithm Our computerized tests reduce the associated time compassing the computerized tests is guaranteed to preserve plexity from O(n 4 ) to O(n). The sufficient conditions proconnectivity.