Workshop on Bioimaging II / PDEs, Mon, 19 Nov, 2007
Speaker: Atsushi Imiya
Abstract
In this talk, we analyse mathematical properties of three-dimensional optical-flow computation algorithm, since three-dimensional optical flow is a fundamental method for the non-invasive cardiac motion analysis.
Furthermore, classification and separation of the regions on the heart wall using optical flow derives cardiac diagnosis features.
There are two types of evaluation method for inverse problems for non-invasive diagnosis.
First one is analysis the accuracy of the solution using normalised phantoms, that is, evaluate the difference between phantom, which is used the ground truth, and the solution derived by the algorithm.
The second one is mathematics-based evaluation, that is, clarification of the convergence and stability of the algorithm employing numerical analysis.
From the viewpoint of mathematical-based evaluation, we first derive the convergence property on variational optical-flow computation method used for cardiac motion detection.
Secondly, we prove that the divergence-free constraint is dependent to the first order smoothness constraint, which is called the Horn-Schunck regulariser and the vector spline constraint is dependent to the second order smoothness constraint, which is equivalent to thin plate deformation constraint.
Thirdly, from the convergence property of the algorithm, we clarify the condition for the scheduling of the regularisation parameters.
This condition shows that for the accurate and stable computation with scheduling the regularisation coefficients, we are required to control the sampling interval for numerical computation.
Furthermore, using the first and second order derivatives, we show that it is possible to classify the motions of points in an image using the orders of differential-constraints.
Lastly, we develop an algorithm to extract volumetric motion on the surfaces using the orthogonal decomposition of optical flow vectors on the tangent space on the manifold and the higher order constraints for the variational optical flow computation.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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