MULTISCALE FEATURE DETECTION USING FILTER BANKS

Hazem M. HAJJ

 This thesis  presents a novel methodology for designing a multiscale feature detector, which consists of a filter bank and a maximum a posteriori (MAP) classifier. The framework assumes the availability of a one-scale filter with a particular indicator response to the desired feature. This filter is used to generate a multiscale set of discrete filters by proper sampling . One dimensional (ID) filters are sampled at a dyadic rate, With the highest resolution filter selected by examining the multiscale Fourier transform. Although other sampling lattices are possible for two dimensional (2D) filters, the rectangular lattice is chosen to preserve the indicator responses at all the scales.

The next step in the framework consists of the filter bank design by matching its structure to approximate the generated filters. The derivation is based on least square minimization across the scales. Non-separable 2D filters require efficient packing to satisfy symmetry constraints. Vector space representations of 2D convolution is employed to simplify the mathematical formulation of the 2D filter bank design.

Once the filter bank is developed, a MAP detector is designed to minimize the detection errors. The approach assumes additive white gaussian noise. With the assumption of known feature, the resulting detector depends only on the filter bank, and not on the noise. This assumption can be relaxed, which yields a detection algorithm that is noise dependent and computationally intensive. A closed form expression is derived for the misclassification errors.

The framework is applied to edge detection in a noisy environment, and the results indicate efficient detection without specific knowledge of the signal, the appropriate scale of detection and noise. Moreover in a high SNR case, the 2D MAP can find corners by direct processing of the image. This is unlike conventional methods where edges need to be first detected and then processed to locate the corners. Case studies show that multiscale detection is superior to single scale, indicator choice play little role in the performance, and detection is not highly affected by local interference.