Multivariate interpolation of arbitrarily spaced data by moving least squares methods
Journal of Computational and Applied Mathematics
A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Zippered polygon meshes from range images
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast level set method for propagating interfaces
Journal of Computational Physics
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A Level-Set Approach to 3D Reconstruction from Range Data
International Journal of Computer Vision
Creating generative models from range images
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A PDE-based fast local level set method
Journal of Computational Physics
Directional 3D edge detection in anisotropic data: detector design and performance assessment
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Shape constraints in deformable models
Handbook of medical imaging
Level set methods: an overview and some recent results
Journal of Computational Physics
Computer and Robot Vision
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Level Set Based Segmentation with Intensity and Curvature Priors
MMBIA '00 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Fusion of Short-Axis and Long-Axis Cardiac MR Images
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Segmentation of biological volume datasets using a level-set framework
VG'01 Proceedings of the 2001 Eurographics conference on Volume Graphics
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
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Typically 3-D MR and CT scans have a relatively high resolution in the scanning X - Y plane, but much lower resolution in the axial Z direction. This non-uniform sampling of an object can miss small or thin structures. One way to address this problem is to scan the same object from multiple directions. In this paper we describe a method for deforming a level set model using velocity information derived from multiple volume datasets with non-uniform resolution in order to produce a single high-resolution 3D model. The method locally approximates the values of the multiple datasets by fitting a distance-weighted polynomial using moving least-squares. The proposed method has several advantageous properties: its computational cost is proportional to the object surface area, it is stable with respect to noise, imperfect registrations and abrupt changes in the data, it provides gain-correction, and it employs a distance-based weighting to ensures that the contributions from each scan are properly merged into the final result. We have demonstrated the effectiveness of our approach on four multi-scan datasets, a griffin laser scan reconstruction, a CT scan of a teapot and MR scans of a mouse embryo and a zucchini.