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.
@cite_15 @cite_22 @cite_6
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We explore a location based approach for behavior modeling and abnormality detection. In contrast to the conventional object based approach where an object may first be tagged, identified, classified, and tracked, we proceed directly with event characterization and behavior modeling at the pixel(s) level based on motion labels obtained from background subtraction. Since events are temporally and spatially dependent, this calls for techniques that account for statistics of spatiotemporal events. Based on motion labels, we learn co-occurrence statistics for normal events across space-time. For one (or many) key pixel(s), we estimate a co-occurrence matrix that accounts for any two active labels which co-occur simultaneously within the same spatiotemporal volume. This co-occurrence matrix is then used as a potential function in a Markov random field (MRF) model to describe the probability of observations within the same spatiotemporal volume. The MRF distribution implicitly accounts for speed, direction, as well as the average size of the objects passing in front of each key pixel. Furthermore, when the spatiotemporal volume is large enough, the co-occurrence distribution contains the average normal path followed by moving objects. The learned normal co-occurrence distribution can be used for abnormal detection. Our method has been tested on various outdoor videos representing various challenges. Suitable feature representation is essential for performing video analysis and understanding in applications within the smart surveillance domain. In this paper, we propose a novel spatiotemporal feature descriptor based on co-occurrence matrices computed from the optical flow magnitude and orientation. Our method, called Optical Flow Co-occurrence Matrices (OFCM), extracts a robust set of measures known as Haralick features to describe the flow patterns by measuring meaningful properties such as contrast, entropy and homogeneity of co-occurrence matrices to capture local space-time characteristics of the motion through the neighboring optical flow magnitude and orientation. We evaluate the proposed method on the action recognition problem by applying a visual recognition pipeline involving bag of local spatiotemporal features and SVM classification. The experimental results, carried on three well-known datasets (KTH, UCF Sports and HMDB51), demonstrate that OFCM outperforms the results achieved by several widely employed spatiotemporal feature descriptors such as HOF, HOG3D and MBH, indicating its suitability to be used as video representation. Co-occurrence data is quite common in many real applications. Latent Semantic Analysis (LSA) has been successfully used to identify semantic relations in such data. However, LSA can only handle a single co-occurrence relationship between two types of objects. In practical applications, there are many cases where multiple types of objects exist and any pair of these objects could have a pairwise co-occurrence relation. All these co-occurrence relations can be exploited to alleviate data sparseness or to represent objects more meaningfully. In this paper, we propose a novel algorithm, M-LSA, which conducts latent semantic analysis by incorporating all pairwise co-occurrences among multiple types of objects. Based on the mutual reinforcement principle, M-LSA identifies the most salient concepts among the co-occurrence data and represents all the objects in a unified semantic space. M-LSA is general and we show that several variants of LSA are special cases of our algorithm. Experiment results show that M-LSA outperforms LSA on multiple applications, including collaborative filtering, text clustering, and text categorization. In this paper we propose a novel feature descriptor Extended Co-occurrence HOG (ECoHOG) and integrate it with dense point trajectories demonstrating its usefulness in fine grained activity recognition. This feature is inspired by original Co-occurrence HOG (CoHOG) that is based on histograms of occurrences of pairs of image gradients in the image. Instead relying only on pure histograms we introduce a sum of gradient magnitudes of co-occurring pairs of image gradients in the image. This results in giving the importance to the object boundaries and straightening the difference between the moving foreground and static background. We also couple ECoHOG with dense point trajectories extracted using optical flow from video sequences and demonstrate that they are extremely well suited for fine grained activity recognition. Using our feature we outperform state of the art methods in this task and provide extensive quantitative evaluation.