Gradient Estimation in Volume Data using 4D Linear Regression

Abstract

In this paper a new gradient estimation method is presented which is based on linear regression. Previous contextual shading techniques try to fit an approximate function to a set of surface points in the neighborhood of a given voxel. Therefore a system of linear equations has to be solved using the computationally expensive Gaussian elimination. In contrast, our method approximates the density function itself in a local neighborhood with a 3D regression hyperplane. This approach also leads to a system of linear equations but we will show that it can be solved with an efficient convolution. Our method provides at each voxel location the normal vector and the translation of the regression hyperplane which are considered as a gradient and a filtered density value respectively. Therefore this technique can be used for surface smoothing and gradient estimation at the same time.

Coarse-to-fine skeleton extraction for high resolution 3D meshes

“…Following [31], we compute the gradient by performing a 4D linear regression over all the neighbors of x. More formally, given a set of points…”

Volumetric ambient occlusion for volumetric models

“…As Ruiz et al [12] proposed, the gradient of the ambient occlusion indicates where the salient regions are, so it is worth modulating the opacity value by this gradient, which is estimated by a 4D regression filter [9]. The gradient calculation cannot be done using a separable filter, which increases the computational cost.…”

Neville interpolation-based normal estimation

“…In [11], a 4D linear regression-based gradient estimation is proposed. It uses a 26-connected neighborhood for regression and mean squared error for approximation.…”