Robust multi-scale orientation estimation: Spatial domain Vs Fourier domain

Orientation estimation is considered as an important and vital step towards many pattern recognition and image enhancement tasks. In a noisy environment, the gradient-based estimations provide poor results. A pre-smoothing Gaussian function with an appropriate scale is conventionally used to get better gradients. Later on, fixed-scale approach was extended to include multi-scale gradient estimates. More specifically, multi-scale orientation estimation, based on scale-space axioms, in spatial domain can be formulated. To further boost the performance of multi-scale orientation estimates, a Fourier domain foundation in the form of Directional Filter bank (DFB)is incorporated with multi scale spatial domain approach. This paper presents an approach for estimation of local orientations using multi-scale approach both in spatial and fourier domain. In fourier-domain approach, two linear combinations are deployed, one across the directional image, and the other across scales. This is opposed to only one linear combination across the scales, used in normal spatial domain technique. Simulations are conducted over noisy test images as well as real data. Our objective results indicate that multi-scale fourier domain approach always yields better estimates at variable level of noise as compared to stand alone multi-scale spatial domain. The improvements made by fourier domain estimate can largely be attributed to the use of double linear combination both across directional bands and across scales.