Multiscale geometric feature extraction and object recognition

This thesis describes a new adaptive approximation technique called high resolution pursuit (HRP), and demonstrates how HRP can be used to extract features that are suitable for object recognition. Recently, adaptive approximation techniques have become popular for obtaining representations of large classes of signals. These techniques include method of frames, matching pursuit, and basis pursuit. In this work, HRP is developed as an alternative to existing function approximation techniques. Existing techniques do not always efficiently yield representations that are sparse and physically interpretable. HRP is an enhanced version of the matching pursuit algorithm that overcomes its shortcomings by emphasizing local fit over global fit at each stage. Furthermore, the HRP algorithm has the same order of computational complexity as matching pursuit. To demonstrate the utility of HRP for feature extraction, we develop a technique based on HRP features for the recognition of airplanes from silhouettes. Features extracted by HRP are shown to be robust to boundary perturbations, scale variations, small orientation variations, and variations due to occlusion. Furthermore, the HRPbased technique is shown to surpass the traditional Fourier descriptor techniques in the presence of occlusion. Thesis Supervisor: Alan S. Willsky Title: Professor of Electrical Engineering and Computer Science Thesis Supervisor: W. Clement 1\'.'arl Title: Assistant Professor of Electrical, Computer, and Systems Engineering Boston University