Parameterizing probabilities for estimating age-composition distributions for mixture models

When estimating parameters that constitute a discrete probability distribution {pj}, it is difficult to determine how constraints should be made to guarantee that the estimated parameters { pˆj} constitute a probability distribution (i.e., pˆj>0, Σ pˆj =1). For age distributions estimated from mixtures of length-at-age distributions, the EM (expectationmaximization) algorithm (Hasselblad, 1966; Hoenig and Heisey, 1987; Kimura and Chikuni, 1987), restricted least squares (Clark, 1981), and weak quasisolutions (Troynikov, 2004) have all been used. Each of these methods appears to guarantee that the estimated distribution will be a true probability distribution with all categories greater than or equal to zero and with individual probabilities that sum to one. In addition, all these methods appear to provide a theoretical basis for solutions that will be either maximum-likelihood estimates or at least convergent to a probability distribut

Image sequence segmentation using mixture-models with uniqueness and spatio-temporal consistency constraints

The use of mixture-model techniques for motion estimation and image sequence segmentation was discussed. The issues such as modeling of occlusion and uncovering, determining the relative depth of the objects in a scene, and estimating the number of objects in a scene were also investigated. The segmentation algorithm was found to be computationally demanding, but the computational requirements were reduced as the motion parameters and segmentation of the frame were initialized. The method provided a stable description, in whichthe addition and removal of objects from the description corresponded to the entry and exit of objects from the scene.