A new approach is presented for the detection and computation of a two-dimensional motion field in image sequences. This computational model has a multi-channel motion detector and an optimal motion selector. In the motion detector, each channel has an inherent spatial resolution. The detector computes a two-dimensional motion field by the gradient-based method in parallel. The motion selector compares those candidates of the motion field by a correlation value of the intensity patterns hierarchically arranged from low to high resolution. It then determines the most probable motion for each image point. Experimental results are shown for synthetic images. This model can detect more reliable motion fields than the conventional one-chanel model.

The present paper clarifies that the variance of the maximum likelihood estimator (MLE) of a parameter does not reach the Cramer-Rao lower bound (CRLB) when fitting a straight-line to observed two-dimensional data. In addition, the variance of the MLE can be shown to be equal to the CRLB only if observed noise reduces to a one-dimensional Gaussian variable. For most practical applications, it can be assumed that noise is added only to the range direction. In this case, the MLE is clearly an asymptotically effective estimator. However, even if we assume such a noise model, ML line-fitting to the data from many points of view has a high computational cost. The present paper proposes an alternative fitting method in order to provide a cost-effective unbiased estimator. The reliability of this new method is analyzed statistically and by computer simulation.

In conventional methods for detecting vanishing points and vanishing lines, the observed feature points are clustered into collections that represent different lines. The multiple lines are then detected and the vanishing points are detected as points of intersection of the lines. The vanishing line is then detected based on the points of intersection. However, for the purpose of optimization, these processes should be integrated and be achieved simultaneously. In the present paper, we assume that the observed noise model for the feature points is a two-dimensional Gaussian mixture and define the likelihood function, including obvious vanishing points and a vanishing line parameters. As a result, the above described simultaneous detection can be formulated as a maximum likelihood estimation problem. In addition, an iterative computation method for achieving this estimation is proposed based on the EM (Expectation Maximization) algorithm. The proposed method involves new techniques by which stable convergence is achieved and computational cost is reduced. The effectiveness of the proposed method that includes these techniques can be confirmed by computer simulations and real images.