Detecting and extracting complex patterns from images and realizations of spatial point processes

Abstract

A common goal in the field of Computer Vision is the detection and extraction of patterns (e.g. lines, object boundaries) from binary image data . These images routinely occur as the product of edge detection algorithms, mathematical morphological operations, or simple thresholds, applied to a gray-scale or color images. In certain cases, binary image data can resemble spatial point patterns. In the statistics literature the usual goal of analyzing a point pattern is to make inference about the underlying process that generated the data. Both of these problems could be broadly classified as pattern recognition tasks.In this dissertation, we investigate the following pattern recognition problems: (1) How to distinguish between mixtures of spatial point processes. (2) How to identify a subset of points in a spatial point pattern that displays a particular stochastic pattern. (3) How to efficiently identify parametric curves in binary edge images.Problems 1 and 2 are motivated by the task of detecting minefields from aerial images. We develop partial Bayes factors to approach problem 1 and investigate their effectiveness via a simulation study. The second problem is tackled by developing a stochastic model to describe the particular stochastic pattern we are seeking (in this case the location of the mines in a minefield). A Markov chain Monte Carlo algorithm is outlined to fit the model. Results from applying the model to several datasets are presented.In the third problem, we introduce the Hough transform as a method for detection of parametric curves in binary images. We re-examine this transform through the framework of importance sampling, which leads to a better understanding of its properties. An improved algorithm for parametric curve detection is given.