System and method for determining the presence of an object of interest in a target data set. Portions of a target data set may be located that match an object of interest, e.g., in a template data set, with respect to various information, e.g., edge or boundary information. The invention includes improved methods for mapping point sets or curves to new point sets or curves for curve matching. The method determines the presence of an object of interest in a target data set despite of or using various types of topological transformations of the object of interest in the target data set. One or more mapping operators are determined based on template curves and/or example target curves. Pattern matching is performed on one or more target data sets using the mapping operator(s) to generate pattern matching results, and the pattern matching results output.