Co-occurrence Filter (CoF) is a boundary preserving filter. It is based on the Bilateral Filter (BF) but instead of using a Gaussian on the range values to preserve edges it relies on a co-occurrence matrix. Pixel values that co-occur frequently in the image (i.e., inside textured regions) will have a high weight in the co-occurrence matrix. This, in turn, means that such pixel pairs will be averaged and hence smoothed, regardless of their intensity differences. On the other hand, pixel values that rarely co-occur (i.e., across texture boundaries) will have a low weight in the co-occurrence matrix. As a result, they will not be averaged and the boundary between them will be preserved. The CoF therefore extends the BF to deal with boundaries, not just edges. It learns co-occurrences directly from the image. We can achieve various filtering results by directing it to learn the co-occurrence matrix from a part of the image, or a different image. We give the definition of the filter, discuss how to use it with color images and show several use cases.
Co-occurrence information was first introduced by Haralick @cite_15 . They proposed 14 statistical measures that can be extracted from the co-occurrence matrix and be used to measure similarity between textures. Later, color correlograms, that also rely on co-occurrence data, were used by Huang @cite_22 as image descriptor within an image retrieval system. Finally, co-occurrence statistics was also used with graph cuts by Ladicky @cite_6 where the goal was to solve a label assignment problem such that the labels will satisfy some given co-occurrence matrix.
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We define a new image feature called the color correlogram and use it for image indexing and comparison. This feature distills the spatial correlation of colors, and is both effective and inexpensive for content-based image retrieval. The correlogram robustly tolerates large changes in appearance and shape caused by changes in viewing positions, camera zooms, etc. Experimental evidence suggests that this new feature outperforms not only the traditional color histogram method but also the recently proposed histogram refinement methods for image indexing retrieval. The Markov and Conditional random fields (CRFs) used in computer vision typically model only local interactions between variables, as this is generally thought to be the only case that is computationally tractable. In this paper we consider a class of global potentials defined over all variables in the CRF. We show how they can be readily optimised using standard graph cut algorithms at little extra expense compared to a standard pairwise field. This result can be directly used for the problem of class based image segmentation which has seen increasing recent interest within computer vision. Here the aim is to assign a label to each pixel of a given image from a set of possible object classes. Typically these methods use random fields to model local interactions between pixels or super-pixels. One of the cues that helps recognition is global object co-occurrence statistics, a measure of which classes (such as chair or motorbike) are likely to occur in the same image together. There have been several approaches proposed to exploit this property, but all of them suffer from different limitations and typically carry a high computational cost, preventing their application on large images. We find that the new model we propose produces a significant improvement in the labelling compared to just using a pairwise model and that this improvement increases as the number of labels increases.