Improving angular error via systematically designed near-circular Gaussian-based feature extraction operators

Authors:
Bryan W. Scotney;Sonya A. Coleman
Affiliations:
School of Computing and Information Engineering, University of Ulster, Cromore Road, Coleraine BT52 1SA, Northern Ireland;School of Computing and Intelligent Systems, University of Ulster, Magee College, Northland Road, Londonderry BT48 7JL, Northern Ireland
Venue:
Pattern Recognition
Year:
2007

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Abstract

In image filtering, the 'circularity' of an operator is an important factor affecting its accuracy. For example, circular differential edge operators are effective in minimising the angular error in the estimation of image gradient direction. We present a general approach to the computation of scalable circular low-level image processing operators that is based on the finite element method. We show that the use of Gaussian basis functions within the finite element method provides a framework for a systematic and efficient design procedure for operators that are scalable to near-circular neighbourhoods through the use of an explicit scale parameter. The general design technique may be applied to a range of operators. Here we evaluate the approach for the design of the image gradient operator. We illustrate that this design procedure significantly reduces angular error in comparison to other well-known gradient approximation methods.