Efficient SDP Inference for Fully-connected CRFs Based on Low-rank Decomposition

Conditional Random Fields (CRF) have been widely used in a variety of computer vision tasks. Conventional CRFs typically define edges on neighboring image pixels, resulting in a sparse graph such that efficient inference can be performed. However, these CRFs fail to model long-range contextual relationships. Fully-connected CRFs have thus been proposed. While there are efficient approximate inference methods for such CRFs, usually they are sensitive to initialization and make strong assumptions. In this work, we develop an efficient, yet general algorithm for inference on fully-connected CRFs. The algorithm is based on a scalable SDP algorithm and the low- rank approximation of the similarity/kernel matrix. The core of the proposed algorithm is a tailored quasi-Newton method that takes advantage of the low-rank matrix approximation when solving the specialized SDP dual problem. Experiments demonstrate that our method can be applied on fully-connected CRFs that cannot be solved previously, such as pixel-level image co-segmentation.Comment: 15 pages. A conference version of this work appears in Proc. IEEE Conference on Computer Vision and Pattern Recognition, 201

Identifying the community structure of the international food-trade multi network

Achieving international food security requires improved understanding of how international trade networks connect countries around the world through the import-export flows of food commodities. The properties of food trade networks are still poorly documented, especially from a multi-network perspective. In particular, nothing is known about the community structure of food networks, which is key to understanding how major disruptions or 'shocks' would impact the global food system. Here we find that the individual layers of this network have densely connected trading groups, a consistent characteristic over the period 2001 to 2011. We also fit econometric models to identify social, economic and geographic factors explaining the probability that any two countries are co-present in the same community. Our estimates indicate that the probability of country pairs belonging to the same food trade community depends more on geopolitical and economic factors -- such as geographical proximity and trade agreements co-membership -- than on country economic size and/or income. This is in sharp contrast with what we know about bilateral-trade determinants and suggests that food country communities behave in ways that can be very different from their non-food counterparts.Comment: 47 pages, 19 figure

Accurate video object tracking using a region-based particle filter

Usually, in particle filters applied to video tracking, a simple geometrical shape, typically an ellipse, is used in order to bound the object being tracked. Although it is a good tracker, it tends to a bad object representation, as most of the world objects are not simple geometrical shapes. A better way to represent the object is by using a region-based approach, such as the Region Based Particle Filter (RBPF). This method exploits a hierarchical region based representation associated with images to tackle both problems at the same time: tracking and video object segmentation. By means of RBPF the object segmentation is resolved with high accuracy, but new problems arise. The object representation is now based on image partitions instead of pixels. This means that the amount of possible combinations has now decreased, which is computationally good, but an error on the regions taken for the object representation leads to a higher estimation error than methods working at pixel level. On the other hand, if the level of regions detail in the partition is high, the estimation of the object turns to be very noisy, making it hard to accurately propagate the object segmentation. In this thesis we present new tools to the existing RBPF. These tools are focused on increasing the RBPF performance by means of guiding the particles towards a good solution while maintaining a particle filter approach. The concept of hierarchical flow is presented and exploited, a Bayesian estimation is used in order to assign probabilities of being object or background to each region, and the reduction, in an intelligent way, of the solution space , to increase the RBPF robustness while reducing computational effort. Also changes on the already proposed co-clustering in the RBPF approach are proposed. Finally, we present results on the recently presented DAVIS database. This database comprises 50 High Definition video sequences representing several challenging situations. By using this dataset, we compare the RBPF with other state-ofthe- art methods