title: Spatially variant convolution with scaled B-splines.
abstract: 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 of integration and scaled finite differences as to have, for moderate and large scale values, a computational complexity that does not depend on the scaling factor. To show in practice the benefit of using our spatially variant convolution approach, we present an adaptive noise filter that adjusts the kernel size to the local image characteristics and a high sensitivity local ridge detector.
authors.affiliation: Cancer Imaging Laboratory, Oncology Division, Center for Applied Medical Research, University of Navarra, 31008-Pamplona, Navarra, Spain. arrmunoz@unav.es
authors.forename: Arrate
authors.initials: A
authors.lastname: Muñoz-Barrutia
authors.forename: Xabier
authors.initials: X
authors.lastname: Artaechevarria
authors.forename: Carlos
authors.initials: C
authors.lastname: Ortiz-de-Solorzano
mesh_terms: D000465:Algorithms; D000818:Animals; D003599:Cytoskeleton / Q000648:ultrastructure; D006257:Head / Q000033:anatomy & histology; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008168:Lung / Q000000981:diagnostic imaging; D008279:Magnetic Resonance Imaging / Q000379:methods*; D051379:Mice; D016011:Normal Distribution; D019047:Phantoms, Imaging; D055114:X-Ray Microtomography / Q000379:methods*