Random set modelling of three-dimensional objects in a hierarchical Bayesian context

We present a Bayesian approach to modelling and estimating objects in three dimensions. A general stochastic model for object recognition based on points in the domain of observation is created via hierarchical mixtures, allowing for the inclusion of important prior information about the objects under consideration. Objects under consideration are created based on three-dimensional (3D) points in space, with each point having some probability of membership to different objects. This is the first object-oriented statistical approach that models 3D objects in a true 3D environment. A data-augmentation approach and a Birth–Death Markov Chain Monte Carlo algorithm are incorporated to provide classification probabilities of each data point to one or more of the identified objects and to obtain estimates of the parameters that describe each object. Strengths of the methodology include its ease in accommodating different data and process models, its flexibility in handling varying numbers of mixture components, and most importantly, its ability to allow for inference on individual characteristics of objects. These strengths are demonstrated on an application for a forest (tree objects) near Olympia, WA, based on remotely sensed Light Detection and Ranging point observations.

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