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Efficient probability distribution function estimation for energy based image segmentation methods

  • Dedovic, Ines
Publication Date
Jan 01, 2016
Publikationsserver der RWTH Aachen University
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This work investigates efficient energy based image segmentation methods when only little prior knowledge about an object is given. It is concentrated on implementing stochastic approaches, utilizing the channel framework for modelling probability distribution functions within the data terms of energy functionals. In addition, an approach is developed that uses the block Gibbs sampler within an edge-detection algorithm. Traditionally, in related segmentation methods, PDFs are approximated using either histograms or kernel density estimation (KDE). The channel framework tries to combine advantages of both, keeping the complexity similarly low as in the histogram approach, while tending to approach similar performance as KDE methods. The channel framework can be interpreted as a soft histogram where bins overlap in the amplitude space. This allows sub-bin accuracy and, in segmentation methods, less bins are necessary to approximate the PDF better than by original histograms. Another interpretation of the channel framework is that it is a discrete version of the KDE approach. This way, the channel framework gives reasonably fast performance even for large images and the speed is not image content dependent. On the other hand, to achieve similar performance as KDE, a large number of channels is required. It is shown that an efficient implementation is still possible by using a look-up table, which however requires an increased amount of memory as the cost for the decrease in computational complexity. The following variants of image segmentation methods have been extended to use the channel framework: automatic/unsupervised image segmentation in two regions using the Chan-Vese functional; supervised image segmentation in two regions using the Chan-Vese functional; interactive segmentation in multiple regions using the Potts model. All methods have been tested on different evaluation data sets. In most cases, the channel framework has given comparable results to the state of the art, while being more efficient to implement.In addition to segmentation methods, an edge-detection method is introduced, which provides a stochastic approach to solving the Ambrosio and Tortorelli functional by using the block Gibbs sampler. Unlike previous approaches, whole images are sampled at once and not pixel-wise. This leads to a faster converging solution than conventional convex optimization.

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