Recurrent 3D Pose Sequence Machines

3D human articulated pose recovery from monocular image sequences is very challenging due to the diverse appearances, viewpoints, occlusions, and also the human 3D pose is inherently ambiguous from the monocular imagery. It is thus critical to exploit rich spatial and temporal long-range dependencies among body joints for accurate 3D pose sequence prediction. Existing approaches usually manually design some elaborate prior terms and human body kinematic constraints for capturing structures, which are often insufficient to exploit all intrinsic structures and not scalable for all scenarios. In contrast, this paper presents a Recurrent 3D Pose Sequence Machine(RPSM) to automatically learn the image-dependent structural constraint and sequence-dependent temporal context by using a multi-stage sequential refinement. At each stage, our RPSM is composed of three modules to predict the 3D pose sequences based on the previously learned 2D pose representations and 3D poses: (i) a 2D pose module extracting the image-dependent pose representations, (ii) a 3D pose recurrent module regressing 3D poses and (iii) a feature adaption module serving as a bridge between module (i) and (ii) to enable the representation transformation from 2D to 3D domain. These three modules are then assembled into a sequential prediction framework to refine the predicted poses with multiple recurrent stages. Extensive evaluations on the Human3.6M dataset and HumanEva-I dataset show that our RPSM outperforms all state-of-the-art approaches for 3D pose estimation.Comment: Published in CVPR 201

Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs

Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution with controllable exponent beta, and high clustering that can be controlled via the temperature T. We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to T = 0. We also support parallelization, although this is not the focus of this paper. Moreover, we note that our generators draw from the correct probability distribution, i.e., they involve no approximation. Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify the desired expected average degree as input. Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straight-forward inclusion does not hold in practice. However, the difference is negligible for most use cases

Scalable Kernelization for Maximum Independent Sets

The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic algorithms---or by repeatedly kernelizing recursively in the branch-and-reduce paradigm. It is of critical importance for these algorithms that kernelization is fast and returns a small kernel. Current algorithms are either slow but produce a small kernel, or fast and give a large kernel. We attempt to accomplish both of these goals simultaneously, by giving an efficient parallel kernelization algorithm based on graph partitioning and parallel bipartite maximum matching. We combine our parallelization techniques with two techniques to accelerate kernelization further: dependency checking that prunes reductions that cannot be applied, and reduction tracking that allows us to stop kernelization when reductions become less fruitful. Our algorithm produces kernels that are orders of magnitude smaller than the fastest kernelization methods, while having a similar execution time. Furthermore, our algorithm is able to compute kernels with size comparable to the smallest known kernels, but up to two orders of magnitude faster than previously possible. Finally, we show that our kernelization algorithm can be used to accelerate existing state-of-the-art heuristic algorithms, allowing us to find larger independent sets faster on large real-world networks and synthetic instances.Comment: Extended versio

Parallel scheduling of recursively defined arrays

A new method of automatic generation of concurrent programs which constructs arrays defined by sets of recursive equations is described. It is assumed that the time of computation of an array element is a linear combination of its indices, and integer programming is used to seek a succession of hyperplanes along which array elements can be computed concurrently. The method can be used to schedule equations involving variable length dependency vectors and mutually recursive arrays. Portions of the work reported here have been implemented in the PS automatic program generation system