Axial Flip Invariance and Fast Exhaustive Searching with Wavelets. Matthew Bolitho. Outline. Goals Shape Descriptors Invariance to rigid transformation Wavelets The wavelet transform Haar basis functions Axial ambiguity with wavelets Axial ambiguity Invariance Fast Exhaustive Searching.
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Axial Flip Invariance and Fast Exhaustive Searching with Wavelets
Perform wavelet transform:Transform basis:
may hurt ability to discriminate
R is the set of all possible axial reflections
fast exhaustive searching
Recall gi , hi : sign according to axial reflection
Recall the mapping of R(gi) gi, thus:
Collect together terms to form:
Calculate gh+ and gh- from S(W(g)) and S(W(h)):
Gaussian smoothing can distribute votes better