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Fast edge detection with subpixel precision by use of orthogonal function integration

Edges are important features in image analysis and edge detection by use of Gaussian filters is widely used in image processing and computer vision. After analyzing the problems of the classical edge detection methods using Gaussian filters, we propose in the present paper a fast Gaussian-filter-based edge detection method, called Hermite integration method, by use of Hermite polynomial theory. One-dimensional Gaussian filtering is at first analyzed and the fast algorithm by use of the input signal samples corresponding to the Hermite polynomial roots is proposed. To use this new algorithm for edge detection in noisy 2-D images, we generalize then this method to Gaussian-filtered derivatives calculation and to multi-dimensional cases, such as 2-D image processing. We show as well that with the proposed method, one can detect the edges with a subpixel precision and calculate the image characteristics for any subpixel positions, which is difficult for classical methods. Our algorithm gives a better algebraic precision and a less important complexity than the classical mask convolution method. Experimental results for artificial data and real images are reported, which confirm the theoretical analysis.