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ASYMPTOTIC BAYESIAN SURFACE ESTIMATION USING AN IMAGE SEQUENCE
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DOI：10.1007/BF00128152.png)
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A new approach is introduced to estimating object surfaces in three-dimensional space from a sequence of images. A 3D surface of interest here is modeled as a function known up to the values of a few parameters. Surface estimation is then treated as the general problem of maximum-likelihood parameter estimation based on two or more functionally related data sets. In our case, these data sets constitute a sequence of images taken at different locations and orientations. Experiments are run to illustrate the various advantages of using as many images as possible in the estimation and of distributing camera positions from first to last over as large a baseline as possible. In order to extract all the usable information from the sequence of images, all the images should be available simultaneously for the parameter estimation. We introduce the use of asymptotic Bayesian approximations in order to summarize the useful information in a sequence of images, thereby drastically reducing both the storage and the amount of processing required. This leads to a sequential Bayesian estimator for the surface parameters, where the information extracted from previous images is summarized in a quadratic form. The attractiveness of our approach is that now all the usual tools of statistical signal analysis, for example, statistical decision theory for object recognition, can be brought to bear; the information extraction appears to be robust and computationally reasonable; the concepts are geometric and simple; and essentially optimal accuracy should result. Experimental results are shown for extending this approach in two ways. One is to model a highly variable surface as a collection of small patches jointly constituting a stochastic process (e.g., a Markov random field) and to reconstruct this surface using maximum a posteriori probability (MAP) estimation. The other is to cluster together those patches constituting the same primitive object through the use of MAP segmentation. This provides a simultaneous estimation and segmentation of a surface into primitive constituent surfaces.
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