Exploiting Eigenvalues of the Hessian Matrix for Volume Decimation.
Jiřı́ Hladůvka, Andreas König, Eduard M. Groller · Digital Library (University of West Bohemia) · 2001
In recent years the Hessian matrix and its eigenvalues became important in pattern recognition. Several algorithms based on the information they provide have been introduced. We recall the relationship between the eigenvalues of Hessian matrix and the 2nd order edge detection lter, show the usefulness of treating them separately and exploit these facts to design a combined threshold operation to generate sparse data sets. Keywords: Volume Rendering, Sparse data, Hessian matrix, Eigenvalues, Laplacian lter. 1 INTRODUCTION A common approach to analyze the local behaviour of a 2D/3D image I is to consider its Taylor expansion in the neighborhood of a point x 0 I(x 0 +x) I(x 0 )+x T rI(x 0 )+x T H(x 0 )x (1) where rI is the gradient vector and H denotes the Hessian matrix { a matrix built of the second partial derivatives of I . H = 2 4 I xx I xy I xz I yx I yy I yz I zx I zy I zz 3 5 (2) with I ab = @ 2 I @a@b denes the Hessian matrix for the 3D image (vol...