Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate segmentation. To this end, we reformulate the problem by imposing piecewise constancy of the parameter field, and derive a specific proximal splitting optimization scheme. A key component of our framework is an efficient 1D piecewise-affine estimator for vector-valued signals. The first advantage of our approach over segmentation-based methods is its absence of initialization. The second advantage is its lower computational cost, which is independent of the complexity of the motion field. In addition to these features, we demonstrate competitive accuracy with other piecewise-parametric methods on standard evaluation benchmarks. Our new regularization scheme also outperforms the more standard use of total variation and total generalized variation.
Most of the computational effort is spent on the image-partitioning problem. The earliest works retain at most five regions to make the problem tractable . More recently, the layered approach handles a larger number of regions but requires several hours of computation, and the primal dual approach can take up to one hour despite a GPU implementation. The method proposed in @cite_36 achieves around fifteen minutes for @math image, with a graph cut minimization approach.
@cite_36
1915301860
Balanced graph partitioning in the streaming setting is a key problem to enable scalable and efficient computations on massive graph data such as web graphs, knowledge graphs, and graphs arising in the context of online social networks. Two families of heuristics for graph partitioning in the streaming setting are in wide use: place the newly arrived vertex in the cluster with the largest number of neighbors or in the cluster with the least number of non-neighbors. In this work, we introduce a framework which unifies the two seemingly orthogonal heuristics and allows us to quantify the interpolation between them. More generally, the framework enables a well principled design of scalable, streaming graph partitioning algorithms that are amenable to distributed implementations. We derive a novel one-pass, streaming graph partitioning algorithm and show that it yields significant performance improvements over previous approaches using an extensive set of real-world and synthetic graphs. Surprisingly, despite the fact that our algorithm is a one-pass streaming algorithm, we found its performance to be in many cases comparable to the de-facto standard offline software METIS and in some cases even superiror. For instance, for the Twitter graph with more than 1.4 billion of edges, our method partitions the graph in about 40 minutes achieving a balanced partition that cuts as few as 6.8 of edges, whereas it took more than 81 2 hours by METIS to produce a balanced partition that cuts 11.98 of edges. We also demonstrate the performance gains by using our graph partitioner while solving standard PageRank computation in a graph processing platform with respect to the communication cost and runtime.