Robust multi-scale orientation estimation: Directional filter bank based approach

Orientation estimation is considered as an important task in many subsequent pattern recognition and image enhancement systems. In a noisy environment, the gradient-based estimator provides poor results. A pre-smoothing Gaussian function with an appropriate scale is conventionally used to get improved gradients. Later on, a family of pre-smoothing Gaussian functions with a range of scales is employed for estimation, this is referred to as multi-scale orientation estimator. To provide groundwork for comparison, a more formal framework of multi-scale orientation estimation, based on scale-space axioms, in spatial domain is presented. Then for improvement purposes a Fourier domain approach, where directional filter bank (DFB) structure is embedded in multi-scale orientation estimation framework, is proposed. This is referred to as multi-scale DFB approach. The paper presents the comparison work for estimation of local orientations using multi-scale approaches both in spatial and Fourier domain. In the Fourier-domain approach, two linear combinations are deployed, one across the directional image, and the other across the scales. This is opposed to only one linear combination across the scales, used in simple spatial domain techniques. Further more, the DFB-based Fourier domain approach extracts the best local orientation by comparing and contrasting all possible orientations with their respective strength measures. The strength measure used in Fourier method is based on local variance, free from inaccurate gradient calculation. Simulations are conducted over noisy test images as well as real fingerprints. 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 approaches. The improvements made by Fourier domain estimate can largely be attributed to the use of double linear combination both across the directional bands and across the scales.