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Segmentation Based on Regularization

 

Methods based on statistical regularizationgif typically set up a definition of ideal image segmentation, normally using Bayesian maximum a posteriori (MAP) criteria, and an energy cost functional made up of two or more components. The image is then modelled as a spatial or spatiotemporal Markov random field (MRF), and iterative minimization is used to find the globally optimal fit to the definition. This approach is usually computationally expensive.

In [69] Murray and Buxton developed the use of statistical regularization for motion segmentation. The assumption is made that the objects are roughly planar and that normal components of flow are available. The cost functional used has the following components: a term measuring the spatial variation in the segmentation labelling, a term measuring the error between the current motion estimate and the normal flow field, a term representing ``line processes'' (i.e.\ motion boundaries) and a term measuring the temporal variation in the segmentation labelling. The functional is minimized iteratively, using simulated annealing, starting with a ``random'' guess at the solution.

In [13] Bouthemy and Lalande use this method on real images taken with a static camera, in order to find moving vehicles. A similar cost functional to that of Murray and Buxton is used (without line processes). Very simple labelling is applied; each image point is either static or moving. In [41] François and Bouthemy extend the method to segment images taken from a moving camera; the BCCE is used to find normal optic flow. Regions are assumed to have linearly varying flow, and are labelled according to their motion type (i.e. qualitatively estimated as having divergence, rotation or shear) in a manner similar to the approach of Verri discussed below. In [63] Meyer and Bouthemy use this approach to achieve segmentation, and then track the moving objects over time. The objects are assumed to be convex, and are matched over time using a polygonal representation. The number of vertices used to track each object is fixed at the instantiation of that object and is not allowed to vary; if the number of vertices becomes unsuitable for accurate representation of the object's image projection then the model must be restarted. Also the scale of the polygon is fixed, so that objects are not allowed to change size in the image. Results are only presented for a sequence taken from a static camera.

In [7] Black uses a much more complicated cost functional than the methods already discussed. He combines measures similar to those of Murray and Buxton with intra-frame intensity information. The intra-frame measures are similar to those used in the weak-membrane approach of [9]. Thus image boundaries are combined with motion information. The problem of the speed of simulated annealing algorithms is reduced by taking the solution (after a relatively low number of iterations) at one frame as the starting state estimate of the next frame in the sequence, by warping the solution using estimated image motion. The results show which image features are likely to be ``physically significant''. In a simple example, the results were good, but in a more complicated sequence, some ``insignificant'' edges were not suppressed, whilst some flow discontinuities were lost.



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Next: Segmentation Based on Globally Organized Clustering Up: Image Segmentation and Object Tracking Previous: Segmentation Based on Analytic Image Transformations



© 1997 Stephen M Smith. LaTeX2HTML conversion by Steve Smith (steve@fmrib.ox.ac.uk)