In this paper, we propose a new method to construct an edge-preserving filter which has very similar response to the bilateral filter. The bilateral filter is a normalized convolution in which the weighting for each pixel is determined by the spatial distance from the center pixel and its relative difference in intensity range. The spatial and range weighting functions are typically Gaussian in the literature. In this paper, we cast the filtering problem as a vector-mapping approximation and solve it using a support vector machine (SVM). Each pixel will be represented as a feature vector comprising of the exponentiation of the pixel intensity, the corresponding spatial filtered response, and their products. The mapping function is learned via -SVM regression using the feature vectors and the corresponding bilateral filtered values from the training image. The major computation involved is the computation of the spatial filtered responses of the exponentiation of the original image whi...