Point pattern matching and its application in GCxGC

Point pattern matching is the process of aligning a point template with a target point pattern. The objective is to find a transformation that minimizes the distance between the two patterns. Point pattern matching has applications in many diverse domains, such as computer vision, remote sensing, medical image analysis, etc. The first part of this dissertation presents various techniques for general point pattern matching problems. A progressive matching scheme is proposed for interactive applications. Compared to the “batch mode” matching algorithms, the progressive matching algorithms are easier to use and typically are more efficient. With the constrained polynomial transformation models that have no more than two parameters on each coordinate, transformation spaces and constraint sets can be represented as Cartesian products of 2D polygons. Two algorithms are proposed based on polygon clipping and polygon scan-conversion. The first algorithm searches for optimal matchings by sequentially subdividing transformation spaces. The second algorithm starts by rasterizing transformation spaces into discrete canvases, and then scan-converts constraint sets and searches the canvases for optimal matchings. A framework is proposed for hierarchically matching large point patterns in two phases. The global matching phase matches a small set of marker points. The local matching phase refines the matching over each region of the domain subdivision generated from the matching marker points. The second part of this dissertation describes the motivating problem of chemical identification in GCxGC (comprehensive two-dimensional gas chromatography) analysis. The chemical identification problem is then formulated as a peak pattern matching problem and further as a point pattern matching problem. In addition, an edge pattern matching technique is developed based on the ordering constraint imposed by the GCxGC data acquisition process. All the proposed algorithms are comparatively evaluated based on both GCxGC data and synthetic data. The results show that the algorithms are efficient under practical settings