| Summary: | This thesis investigates the use of phase information from the Dual-Tree Complex Wavelet Transform (DT CWT) for the purpose of image matching. We review methods for image matching with a particular emphasis on matching with local features. We review the meaning and current uses of local phase, and introduce the DT CWT. We highlight the shortcomings of decimated wavelets for typical local phase analysis, and introduce two new functions that can extract useful information from the phases of decimated complex wavelets. The first, the InterLevel Product (ILP), is a pyramidal representation where the phases are equal to the phase difference between co-located, same-direction DT CWT coefficients at different scales. The second function, the Same-Level Product (SLP), has phases proportional to the phase differences between adjacent coefficients in the same level; these SLP phases are parallel to the gradient of dominant local features. We seek to represent dominant local features sparsely by clustering areas where the ILP phase is large and same-phase. Three novel clustering techniques are introduced and discussed, with the Line-Growing technique shown to be the best. Line-Growing is a technique similar to the Canny edge detector, operating upon decimated coefficients and sensitive to phase symmetry changes. We call the resulting clusters Edge-Profile Clusters (EPC’s). We explore three different matching techniques based upon local phase information. The first technique shows how ILP information can be combined with the normalized cross correlation (template matching) to accelerate traditional matching. We also show a hybrid ILP/SLP format, where the target is abstracted into EPC cluster constellations that may be rotated quickly to test different match hypotheses. Finally, we show a method where EPC parameters are used to represent both images in the comparison, and a geometric hashing algorithm is combined with a cluster overlap metric to evaluated matches in a fully affine-invariant manner. We highlight the compatibility of our EPC and ILP representations and current physiological/psychovisual observations regarding the mammalian visual cortex, including an ILP phase-based explanation of the “pop-out” effect and perceptual grouping regarding “Glass patterns”.
|
|---|
