Direct Estimation and Error Analysis for Oriented Patterns

This paper presents an estimation algorithm and error analysis for single linear oriented pattern in images. The estimation is formulated in terms of minimizing an objective function, using the Lagrange multiplier rule. No specific noise model is assumed. The estimation algorithm uses the intensity image of a flow pattern and directly determines a symbolic description of the pattern. No preprocessing or enhancement is needed on the intensity image or any intermediate data. This results in an efficient computational algorithm. We show that it is feasible to directly compute relative divergence, curl, and deformation from the intensity image of an oriented flow pattern. These relative properties are further used for identification of the type of pattern in the intensity image. Since an oriented pattern is corrupted by noise and is distorted to some degree from a linear flow pattern, quality measures of the estimation are proposed. The sampling mean, sampling variance, and energy of noise are computed to characterize its distribution. A closed-form condition number is used to measure the vulnerability of an estimated critical point position to noise perturbation. We show results for several experiments on fluid flow images and wafer defect patterns.