This paper describes an extension of the Minimum Sobolev Norm interpolation scheme to an approximation
scheme. A fast implementation of the MSN interpolation method using the methods for Hierarchical Semiseparable
(HSS) matrices is described and experimental results are provided. The approximation scheme is
introduced along with a numerically stable solver. Several numerical results are provided comparing the interpolation
scheme, the approximation scheme and Thin Plate Splines. A method to decompose images into smooth
and rough components is presented. A metric that could be used to distinguish edges and textures in the rough
component is also introduced. Suitable examples are provided for both the above.
In this paper, we present an approach for classification and indexing of embryonic gene expression pattern images using shape descriptors for retrieval of data in the biological domain. For this purpose, the image is first subjected to a registration process that involves edge fitting and size-standardization. It is followed by segmentation in order to delineate the expression pattern from the cellular background. The moment invariants for the segmented pattern are computed. Image dissimilarity between images is computed based on these moment invariants for each image pair. Area and Centroids of the segmented expression shapes are used to neutralize the invariant behavior of moment invariants during image retrieval. Details of the proposed approach along with analysis of a pilot dataset are presented in this paper.