Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Tensor product generalized ADI methods for separable elliptic problems
SIAM Journal on Numerical Analysis
Good vibrations: modal dynamics for graphics and animation
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiresolution stochastic hybrid shape models with fractal priors
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Auxiliary variables and two-step iterative algorithms in computer vision problems
Journal of Mathematical Imaging and Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deformable B-solids and implicit snakes for 3D localization and tracking of SPAMM MRI data
Computer Vision and Image Understanding
Automated 3D Segmentation Using Deformable Models and Fuzzy Affinity
IPMI '97 Proceedings of the 15th International Conference on Information Processing in Medical Imaging
Global Models with Parametric Offsets as Applied to Cardiac Motion Recovery
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Three-Dimensional Model-Based Segmentation of Brain MRI
WBIA '98 Proceedings of the IEEE Workshop on Biomedical Image Analysis
Topologically adaptable snakes
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Deformable Pedal Curves and Surfaces: Hybrid Geometric Active Models for Shape Recovery
International Journal of Computer Vision
Kernel Fisher for Shape Based Classification in Epilepsy
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part II
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Deformable pedal curves with application to face contour extraction
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
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In this paper, we introduce a novel geometric shape modeling scheme which allows for representation of global and local shape characteristics of an object. Geometric models are traditionally well-suited for representing global shapes without local detail. However, we propose a powerful geometric shape modeling scheme which allows for the representation of global shapes with local detail and permits model shaping as well as topological changes via physics-based control. The proposed modeling scheme consists of representing shapes by pedal curves and surfaces驴pedal curves/surfaces are the loci of the foot of perpendiculars to the tangents of a fixed curve/surface from a fixed point called the pedal point. By varying the location of the pedal point, one can synthesize a large class of shapes which exhibit both local and global deformations. We introduce physics-based control for shaping these geometric models by letting the pedal point vary and use a snake to represent the position of this varying pedal point. The model dubbed as a 驴snake pedal驴 allows for interactive manipulation via forces applied to the snake. We develop a fast numerical iterative algorithm for shape recovery from image data using this geometric shape modeling scheme. The algorithm involves the Levenberg-Marquardt (LM) method in the outer loop for solving the global parameters and the Alternating Direction Implicit (ADI) method in the inner loop for solving the local parameters of the model. The combination of the global and local scheme leads to an efficient numerical solution to the model fitting problem. We demonstrate the applicability of this modeling scheme via examples of shape synthesis and shape estimation from real image data.