Improving Angular Error by Near Circular Operator Design

In image filtering, the circularity of an operator is an important factor affecting its accuracy. When step edge orientation is estimated in a square neighbourhood, the use of standard methods can result in a detected orientation error of up to 6.6% [2]. Circular differential edge operators are effective in minimising this angular error and may in fact reduce it to zero for all orientations [2]. The principles of circularity [2] and scale (see, for example, [4]) are amongst the principal considerations when designing low-level image processing operators. When coupled with the task of designing optimal discrete Gaussian operators [1], such considerations become both particularly relevant and challenging. In this paper, we show how the adoption of a finite-element-based approach allows us to formulate a design procedure that can embrace all three aspects: circularity, scale and Gaussian approximation. Via the use of edge sensitivity analysis, we show that such a design procedure can significantly improve detected edge orientation over a full range of orientations and displacements compared with standard operators.