Application of the maximum likelihood (ML) principle and expectation-maximization (EM) technique to estimation of affine modeled image motion
Samir J. Shaltaf · 1992
This dissertation is concerned with the problem of image motion estimation from a pair of consecutive noisy frames. Two approaches for the image motion estimation are presented, the maximum likelihood principle and the expectation-maximization technique. The maximum likelihood (ML) principle is invoked for estimating the nonrandom but unknown displacement function. In the development, both of the observed noisy images are processed jointly through a 2 x 2 matrix filter. The outputs of this filter are the noncausal linear minimum mean square (LMMSE) estimates of the two images. The two LMMSE estimates are correlated with the respective noisy images to produce the first of two terms that constitute the ML function. The other term called the bias term is dependent on the structure of the 2 x 2 matrix filter itself. The image displacement is assumed to satisfy a parametric vector function. The hypothetical motion model is then used to construct the 2 x 2 matrix filter. The steepest ascent method is used to maximize the ML function with respect to the parameters of the motion model. Simulations of the ML based method using affine motion models proves the validity of this method. The affine model for the motion was chosen since it covers important types of motion such as rotation, scaling, skew, reflection, translation separately or in any combination. The Expectation-Maximization (EM) method was employed to estimate the affine image motion parameters under some relaxing assumptions. The EM employed in this work reduced the search for the six coupled affine motion parameters into six decoupled one dimensional parameters which could be obtained iteratively. The EM search for the maximizing parameters does not involve the use of gradient hill climbing methods which suffer from convergence problems. Hence, the EM method is stable and needs no special attention with respect to convergence.