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.

It has been shown that employing multiple atlas images improves segmentation accuracy in atlas-based medical image segmentation. Each atlas image is registered to the target image independently and the calculated transformation is applied to the segmentation of the atlas image to obtain a segmented version of the target image. Several independent candidate segmentations result from the process, which must be somehow combined into a single final segmentation. Majority voting is the generally used rule to fuse the segmentations, but more sophisticated methods have also been proposed. In this paper, we show that the use of global weights to ponderate candidate segmentations has a major limitation. As a means to improve segmentation accuracy, we propose the generalized local weighting voting method. Namely, the fusion weights adapt voxel-by-voxel according to a local estimation of segmentation performance. Using digital phantoms and MR images of the human brain, we demonstrate that the performance of each combination technique depends on the gray level contrast characteristics of the segmented region, and that no fusion method yields better results than the others for all the regions. In particular, we show that local combination strategies outperform global methods in segmenting high-contrast structures, while global techniques are less sensitive to noise when contrast between neighboring structures is low. We conclude that, in order to achieve the highest overall segmentation accuracy, the best combination method for each particular structure must be selected.

In this paper we present an adaptive B-spline smoothing algorithm to reduce noise in biomedical images. The filter consists of a convolution between the input image and an adaptive B-spline kernel that varies its size according to the local image characteristics. We show that this filter can be efficiently implemented by taking advantage of the convolution and factorization properties of B-splines. We tested our filter on phantoms and real images, obtaining very high noise reduction in homogeneous areas with little degradation of the edges.