Pattern matching by scan-converting polygons

Pattern matching is one of the well-known pattern recognition techniques. When using points as matching features, a pattern matching problem becomes a point pattern matching problem. This paper proposes a novel point pattern matching algorithm that searches transformation space by transformation sampling. The algorithm defines a constraint set (a polygonal region in transformation space) for each possible pairing of a template point and a target point. Under constrained polynomial transformations that have no more than two parameters on each coordinate, the constraint sets and the transformation space can be represented as Cartesian products of 2D polygonal regions. The algorithm then rasterizes the transformation space into a discrete canvas and calculates the optimal matching at each sampled transformation efficiently by scan-converting polygons. Preliminary experiments on randomly generated point patterns show that the algorithm is effective and efficient. In addition, the running time of the algorithm is stable with respect to missing points.