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We present an efficient algorithm to compute multidimensional spatially variant convolutions--or inner products-between N-dimensional signals and B-splines--or their derivatives--of any order and arbitrary sizes. The multidimensional B-splines are computed as tensor products of 1-D B-splines, and the input signal is expressed in a B-spline basis. The convolution is then computed by using an adequate combination integration and scaled finite differences as to have, for moderate and large scale values, a computational complexity that does depend on the scaling factor. To show in practice the benefit using our spatially variant convolution approach, we present adaptive noise filter that adjusts the kernel size to the local image characteristics and a high sensitivity local ridge detector. [ABSTRACT FROM AUTHOR]