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.
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Early work, e.g., Davies (Image Vision Computing, 1984 and 1987), established the importance of circularity in designing feature extraction operators, but implementation typically has been restricted to small neighbourhood operators. This paper addresses the key issue of scalability by developing a general, but practical, framework to enable fully scalable circular operators to be designed and implemented efficiently. Highly accurate angular orientation results are demonstrated. The work is currently being developed in collaboration between our Information & Software Engineering and Intelligent Systems research groups for application to range image data in an EPSRC-funded project on Direct Range Image Processing (EP/C006283/1).
- Angular error
- Feature extraction