Ray tracing voxel data via biquadratic local surface interpolation
The Visual Computer: International Journal of Computer Graphics
The Visual Computer: International Journal of Computer Graphics
On active contour models and balloons
CVGIP: Image Understanding
A comparison of normal estimation schemes
VIS '97 Proceedings of the 8th conference on Visualization '97
Using distance maps for accurate surface representation in sampled volumes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Object voxeliztion by filtering
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Generalized gradient vector flow external forces for active contours
Signal Processing - Special issue on deformable models and techniques for image and signal processing
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Reducing aliasing artifacts in iso-surfaces of binary volumes
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
Frequency Analysis of Gradient Estimators in Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Construction of Simplified Boundary Surfaces from Serial-sectioned Metal Micrographs
IEEE Transactions on Visualization and Computer Graphics
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In this paper a feature-preserving volume filtering method is presented. The basic idea is to minimize a three-component global error function penalizing the density and gradient errors and the curvature of the unknown filtered function. The optimization problem leads to a large linear equation system defined by a sparse coefficient matrix. We will show that such an equation system can be efficiently solved in frequency domain using fast Fourier transformation (FFT). For the sake of clarity, first we illustrate our method on a 2D example which is a dedithering problem. Afterwards the 3D extension is discussed in detail since we propose our method mainly for volume filtering. We will show that the 3D version can be efficiently used for elimination of the typical staircase artifacts of direct volume rendering without losing fine details. Unlike local filtering techniques, our novel approach ensures a⋅global smoothing effect. Previous global 3D methods are restricted to binary volumes or segmented iso-surfaces and they are based on area minimization of one single reconstructed surface. In contrast, our method is a general volume-filtering technique, implicitly smoothing all the iso-surfaces at the same time. Although the strength of the presented algorithm is demonstrated on a specific 2D and a specific 3D application, it is considered as a general mathematical tool for processing images and volumes.