Edge Detection from Surface Fitting by Orthogonal Polynomial
采用正交多项式曲面拟合法的边缘检测

A method for image edge detection using facet model is presented. The surface fitting functional consists of the tensor product of one-dimensional orthogonal polynomial with order up to three. The edge point is defined as zero crossing of the second derivative taken in the direction of the largest gradient at the point. It is proved that: based on the orthogonal polynomial, the fitted image and its nth partial derivative can be obtained by two-dimensional convolution which can be realized as two successive one-dimensional convolutions, thus the amount of operations is largely reduced. Experiments show that, compared with traditional operators, this method reveals good properties of noise attenuation and edges location.