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.
[1]
E. R. Davies,et al.
Circularity - a new principle underlying the design of accurate edge orientation operators
,
1984,
Image Vis. Comput..
[2]
Tony Lindeberg,et al.
Scale-Space Theory in Computer Vision
,
1993,
Lecture Notes in Computer Science.
[3]
Andrew P. Witkin,et al.
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
,
1986,
IEEE Transactions on Pattern Analysis and Machine Intelligence.
[4]
L. J. Kitchen,et al.
The effect of spatial discretization on the magnitude and direction response of simple differential edge operators on a step edge
,
1987,
Comput. Vis. Graph. Image Process..