EQUIVALENT SEQUENTIAL AND PARALLEL REDUCTIONS IN ARBITRARY BINARY PICTURES

作者：Palagyi Kalman^*

来源：International Journal of Pattern Recognition and Artificial Intelligence, 2014, 28(7): 1460009.

DOI：10.1142/SO21800141460009X

• Discrete geometry
• digital topology
• topology-preserving reductions
• order-independency
• thinning algorithms

A reduction transforms a binary picture only by changing some black points to white ones, which is referred to as deletion. Sequential reductions traverse the black points of a picture, and consider a single point for possible deletion, while parallel reductions can delete a set of black points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. A deletion rule is said to be equivalent if it yields a pair of equivalent parallel and sequential reductions. This paper introduces a class of equivalent deletion rules that allows us to establish a new sufficient condition for topology-preserving parallel reductions in arbitrary binary pictures. In addition we present a method of verifying that a deletion rule given by matching templates is equivalent, a necessary and sufficient condition for order-independent deletion rules, and a sufficient criterion for order-independent and translation-invariant parallel subfield-based algorithms.

• 出版日期2014-11