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The hybrid tracker uses a nonlinear optimization framework to incorporate both feature correspondence and brightness constraints, and achieves reliable 3D face tracking in real-time.
VB-ECD is a point-source inversion method that uses a nonlinear optimization algorithm to fit a number of dipoles simultaneously, with different prior distributions on their locations and moments, to all of the sensor data (i.e., with no a priori selection of channels).
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Maximization is achieved using a nonlinear optimization technique, where the optimal multiplication factors as a function of the hyper-parameters are found as α p ( f ) = − | b | − ( | b | 2 − 4 ac ) 1 / 2 2 a b | b | (31).
where J α p ( f ) = α p I 2 ( f ) is the Jacobian of the scaling transform and Ψ p (f) is the inverse scale matrix in (15) which depends on p. Maximization with respect to m can be achieved using a nonlinear optimization technique [34], where the optimal scaling factors for a given m are given by α p ( f ) = tr ( Ψ p ( f ) R p − 1 ( f ) ) Im. (17).
The solutions for both formulations are obtained by using a nonlinear optimization software.
Then, design optimization for accuracy has been performed by using a nonlinear optimization technique.
The modeling parameters have been extracted using a nonlinear optimization algorithm.
They are then merged into a single metric which is minimized over the set of 20 test utterances using a nonlinear optimization technique.
The parameters are estimated such that an overall measure of errors is minimized, which can be accomplished using a nonlinear optimization procedure.
The initial projection matrix is then refined by minimizing the distance from the original and reprojected head points by using a nonlinear optimization algorithm.
The convergence can also be improved by means of enhanced line search [41, 42] or, using a nonlinear optimization algorithm such as the Levenberg Marquardt algorithm [43].
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