Matrix analysis
Curvature-based representation of objects from range data
Image and Vision Computing
Segmentation and Classification of Range Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Segmentation through Variable-Order Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct Computation of Qualitative 3-D Shape and Motion Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visualization and modeling contours of trivariate functions
Visualization and modeling contours of trivariate functions
Essential Maple: an introduction for scientific programmers
Essential Maple: an introduction for scientific programmers
Experiments in Curvature-Based Segmentation of Range Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing the differential characteristics of isointensity surface
Computer Vision and Image Understanding
An Experimental Comparison of Range Image Segmentation Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Role of Model-Based Segmentation in the Recovery of Volumetric Parts From Range Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matrix computations (3rd ed.)
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D digital cleansing using segmentation rays
Proceedings of the conference on Visualization '00
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curvature-Augmented Tensor Voting for Shape Inference from Noisy 3D Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automatic Isosurface Propagation Using an Extrema Graph and Sorted Boundary Cell Lists
IEEE Transactions on Visualization and Computer Graphics
Edge-Region-Based Segmentation of Range Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconstruction of Planar Surfaces Behind Occlusions in Range Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Numerical Methods
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Curvature-Based Transfer Functions for Direct Volume Rendering: Methods and Applications
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Automatic Detection of Fiducial Marker Center Based on Shape Index and Curvedness
MIAR '08 Proceedings of the 4th international workshop on Medical Imaging and Augmented Reality
Multiscale geometric modeling of macromolecules I: Cartesian representation
Journal of Computational Physics
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This paper presents a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. This scheme derives a new differential scalar field for a given volumetric scalar field, which could easily be adapted to other differential properties. Moreover, this scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.