We describe a framework for defining high-order image models that can be used in a variety of applications. The approach involves modeling local patterns in a multiscale representation of an image. Local properties of a coarsened image reflect non-local properties of the original image. In the case of binary images local properties are defined by the binary patterns observed over small neighborhoods around each pixel. With the multiscale representation we capture the frequency of patterns observed at different scales of resolution. This framework leads to expressive priors that depend on a relatively small number of parameters. For inference and learning we use an MCMC method for block sampling with very large blocks. We evaluate the approach with two example applications. One involves contour detection. The other involves binary segmentation.
FRAME models @cite_8 and more recently Fields of Experts (FoE) @cite_10 defined high-order energy models using the response of linear filters. FoP models are closely related. The detection of 3x3 patterns at different resolutions corresponds to using filters of increasing size. In FoP we have a fixed set of pre-defined non-linear filters that detect common patterns at different resolutions. This avoids filter learning, which leads to a non-convex optimization problem in FoE.
@cite_10 @cite_8
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We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach provides a practical method for learning high-order Markov random field (MRF) models with potential functions that extend over large pixel neighborhoods. These clique potentials are modeled using the Product-of-Experts framework that uses non-linear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field-of-Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with specialized techniques. This paper proposes a novel framework for labelling problems which is able to combine multiple segmentations in a principled manner. Our method is based on higher order conditional random fields and uses potentials defined on sets of pixels (image segments) generated using unsupervised segmentation algorithms. These potentials enforce label consistency in image regions and can be seen as a strict generalization of the commonly used pairwise contrast sensitive smoothness potentials. The higher order potential functions used in our framework take the form of the robust Pn model. This enables the use of powerful graph cut based move making algorithms for performing inference in the framework [14 ]. We test our method on the problem of multi-class object segmentation by augmenting the conventional CRF used for object segmentation with higher order potentials defined on image regions. Experiments on challenging data sets show that integration of higher order potentials quantitatively and qualitatively improves results leading to much better definition of object boundaries. We believe that this method can be used to yield similar improvements for many other labelling problems.