Wavelet frame-based singularity detection for image analysis

Singularities are one of the most important structural features of signals. They are widely used for characterization of certain imagery features, such as edges, boundaries, contours, etc. They form the basis of numerous algorithms for signal analysis, pattern recognition, and image processing. The focus of this research is to develop singularity based image analysis algorithms using the wavelet frame transform. Our primary interests are (1) accurate location of singularities, and (2) efficient quantification of singularities. Three classes of singularities, namely (1) sharp variation points, (2) edge points, and (3) contours are discussed in this proposal. Unlike Fourier transform based approaches, we take the discrete wavelet frame transform (DWFT) approach to determine the precise positions of singular events. It is obviously difficult to see the merits of different approaches on a broad basis, because of the complexity of different types of imagery, and because of the diverse constraints of different applications. For example, an algorithm designed for detection of microcalcification (of mammography X-ray) may not be suitable for detection of edge points, even though they both can use singularity as the primary feature for analysis, screening, and classification. In another example, singularity of image pixels can be used as a key feature for extraction of a contour from its background, but additional steps will be necessary to make the algorithm robust and adaptive. Using the multi-resolution property of discrete wavelet frame transforms, we design singularity analysis algorithms to detect different sizes of sharp variation points, edge points and contours.