A Study of Two-Way Relaxation with Fuzzy Split-and-Merge Mechanism

[[abstract]]While many relaxation schemes concerning structural matching have claimed that they are invariant under geometrical transformations, they are actually invariant to rotation and translation only but not to scale change. Endowing a relaxation scheme with scale-invariance is itself not formidable. What is laborious is to simultaneously take into account both shape occlusion and spatial transformation. This paper tackles both the issues at a time. Relaxation processes often reach local suboptimalities rather than the global primes. For reducing the probability that a relaxation process is trapped at a local extremum, strategies such as simulated annealing, repeated perturbation, as well as global tracing may be introduced. However, these strategies are generally time expensive. A fuzzy split-and-merge mechanism analogous to the well known divide-and-conquer procedure is proposed for paring down computational complexities of relaxation processes. Furthermore, in order to enhance consistency and correctness of feature mapping, a two-way relaxation paradigm implementing the relation of marriage is imposed on the relaxation scheme. The applicability and effectiveness of the proposed scheme are demonstrated by successful applications to scenes containing multiple objects.