Linear filters are widely used in remote sensing image processing, such as smoothing, edge detection, feature extraction and wavelet analysis. In the present paper, we present a new method based on orthogonal polynomial integration theory to realize linear filters with a reduced and constant complexity and with a good precision. We at first introduce the orthogonal polynomial integration theory and generalize it for convolution calculation. We then present the construction of the orthogonal functions for a given filter, which is a key problem for the generalization of our method. To apply the method proposed to edge detection, we present, in particular, Laguerre integration method to implement the symmetrical exponential filter, an optimal filter for edge detection. Generalization to M-D cases and to derivative calculation is presented as well. Edge detection with subpixel precision by use of Laguerre integration is addressed. Experimental results for real images are reported.