Optical EngineeringForest representation of wavelet transform and feature detection
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A forest representation of 2-D wavelet transform is proposed to emphasize a local signal and coefficient propagation across multiscales. A multiresolution analysis involves a forest consisting of an approximate forest and three detail (horizontal, vertical, and diagonal) forests. An approximate tree is a collection of successive approximations at multiscales at a location, and a detail tree is a collection of detail coefficients along an orientation. In fine-to-coarse processing, local neighboring trees merge into a bulky tree recursively and thereby incur large uncertainty in signal location. The coefficient propagation across multiscales can be used for local signal detection.