1.
Registration & Modeling of Shapes with Uncertainties: Contributions and Applications to Knowledge Based Segmentation. PhD Thesis Defense, Presented on November the 15 th of 2007 by Maxime TARON Thesis advisors : Nikos Paragios Marie-Pierre Jolly
(Pennec Thirion 1995) have introduced uncertainty estimates on the registration of corresponding points sets with rigid motion.
(Simoncelli 1999) has introduced uncertainty within estimation of dense optical flow. Based on a probabilistic model for the error on the derivative estimates (temporal & spatial)
(Rohr 2003) has used uncertainty on landmarks locations for pointwise registration with application to MRI registration. Landmarks are given along with covariance information or a particular direction.
(Stewart 2005) with dual bootstrap ICP for points cloud registration is using uncertainty estimate on the transformation to select the area where registration is performed and the complexity of the transformation.
It can be shown that the Hessian of this energy presents a first order approximation that does not require the use of second derivatives on the distance maps.
Expression of the Hessian:
Enforce invertible matrix with the use of regularization term.
Part 1 – Uncertainty Estimation
20.
An different approach : Data Based Uncertainty
Data corresponds to the location of the Target Shape boundary.
Study the variations of under small normal variation of .
Assume sampled points of the boundary undergo Gaussian independent displacements with variance , data-based uncertainty propagates local covariance to the vector of parameters .
Although Uncertainty is computed under the form of a matrix, one can only visualize the uncertainty on every control points, considered as independent. This does not account for covariance factors between control points.
Transform a shape according to a deformation model with parameter .
Define an objective function which accounts for image support and prior knowledge.
: Region based energy term.
Intensity distribution of different regions is known a-priori and the model is aligned to maximize the likelihood of each regions.
: Shape based Energy term.
Assess the quality of the current segmentation with respect the statistical model.
Part 3 - Introduction
38.
Cardiac Left Ventricle Segmentation : Region Based Image Term
Consider 4 Regions for segmentation. Left Ventricle, and interfaces with Lung, Blood Pool and Right Ventricle :
Where refers to the log-likelihood of the grey level density associated to the region
Differentiation lead to an expression on the considered interfaces
Blood Pool LV Lung RV Setting Set of Points on Interfaces between regions Setting Set of Points on Interfaces between regions Part 3 – Left Ventricle Segmentation Animation
M. Taron, N. Paragios & M.-P. Jolly. Registration with Uncertainties and Statistical Modeling of Shapes with Variable Metric Kernels. IEEE Transactions on Pattern Analysis and Machine (to appear)
Conferences:
M. Taron, N. Paragios & M.-P. Jolly. Modelling Shapes with Uncertainties : Higher Order Polynomials, Variable Bandwidth Kernels and Non-Parametric Density Estimation. IEEE International Conference in Computer Vision, 2005.
M. Taron, N. Paragios & M.-P. Jolly. Uncertainty-driven Non-parametric Knowledge-based Segmentation:The Corpus Callosum Case. 3rd ICCV workshop on Variational Geometric and Level Set Methods (VLSM), 2005.
M. Taron, C. Ghys & N. Paragios. Uncertainties -driven Surface Morphing: The case of Photo-realistic Transitions between Facial Expressions. In 18th International Conference on Pattern Recognition (ICPR), Hong Kong, 2006.
M. Taron, N. Paragios & M.-P. Jolly. From Uncertainties to Statistical Model Building and Segmentation of the Left Ventricle. Mathematical Methods in Biomedical Image Analysis (MMBIA), 2007.
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