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Julian Yarkony

Publications and source records attributed to Julian Yarkony.

28 records · Page 2Linked to original sources
arXiv2017

Multi-Person Pose Estimation via Column Generation

We study the problem of multi-person pose estimation in natural images. A pose estimate describes the spatial position and identity (head, foot, knee, etc.) of every non-occluded body part of a person. Pose estimation is difficult due to issues such as deformation and variation in body configurations and occlusion of parts, while multi-person settings add complications such as an unknown number of people, with unknown appearance and possible interactions in their poses and part locations. We give a novel integer program formulation of the multi-person pose estimation problem, in which variables correspond to assignments of parts in the image to poses in a two-tier, hierarchical way. This enables us to develop an efficient custom optimization procedure based on column generation, where columns are produced by exact optimization of very small scale integer programs. We demonstrate improved accuracy and speed for our method on the MPII multi-person pose estimation benchmark.

cs.CV↗
arXiv2017

Exploiting skeletal structure in computer vision annotation with Benders decomposition

Many annotation problems in computer vision can be phrased as integer linear programs (ILPs). The use of standard industrial solvers does not to exploit the underlying structure of such problems eg, the skeleton in pose estimation. The leveraging of the underlying structure in conjunction with industrial solvers promises increases in both speed and accuracy. Such structure can be exploited using Bender's decomposition, a technique from operations research, that solves complex ILPs or mixed integer linear programs by decomposing them into sub-problems that communicate via a master problem. The intuition is that conditioned on a small subset of the variables the solution to the remaining variables can be computed easily by taking advantage of properties of the ILP constraint matrix such as block structure. In this paper we apply Benders decomposition to a typical problem in computer vision where we have many sub-ILPs (eg, partitioning of detections, body-parts) coupled to a master ILP (eg, constructing skeletons). Dividing inference problems into a master problem and sub-problems motivates the development of a plethora of novel models, and inference approaches for the field of computer vision.

cs.CV↗
arXiv2016

Efficient Pose and Cell Segmentation using Column Generation

We study the problems of multi-person pose segmentation in natural images and instance segmentation in biological images with crowded cells. We formulate these distinct tasks as integer programs where variables correspond to poses/cells. To optimize, we propose a generic relaxation scheme for solving these combinatorial problems using a column generation formulation where the program for generating a column is solved via exact optimization of very small scale integer programs. This results in efficient exploration of the spaces of poses and cells.

cs.CV↗
arXiv2016

Tracking Objects with Higher Order Interactions using Delayed Column Generation

We study the problem of multi-target tracking and data association in video. We formulate this in terms of selecting a subset of high-quality tracks subject to the constraint that no pair of selected tracks is associated with a common detection (of an object). This objective is equivalent to the classic NP-hard problem of finding a maximum-weight set packing (MWSP) where tracks correspond to sets and is made further difficult since the number of candidate tracks grows exponentially in the number of detections. We present a relaxation of this combinatorial problem that uses a column generation formulation where the pricing problem is solved via dynamic programming to efficiently explore the space of tracks. We employ row generation to tighten the bound in such a way as to preserve efficient inference in the pricing problem. We show the practical utility of this algorithm for tracking problems in natural and biological video datasets.

cs.CV↗
arXiv2016

Convex Optimization For Non-Convex Problems via Column Generation

We apply column generation to approximating complex structured objects via a set of primitive structured objects under either the cross entropy or L2 loss. We use L1 regularization to encourage the use of few structured primitive objects. We attack approximation using convex optimization over an infinite number of variables each corresponding to a primitive structured object that are generated on demand by easy inference in the Lagrangian dual. We apply our approach to producing low rank approximations to large 3-way tensors.

cs.LG↗
arXiv2015

Planar Ultrametric Rounding for Image Segmentation

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect matching as a subroutine in order to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentation.

cs.DS↗
arXiv2012

Fast Planar Correlation Clustering for Image Segmentation

We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation clustering that are typically fast to compute and tight in practice. We demonstrate our algorithm on the problem of image segmentation where this approach outperforms existing global optimization techniques in minimizing the objective and is competitive with the state of the art in producing high-quality segmentations.

cs.CV↗
arXiv2012

Tightening MRF Relaxations with Planar Subproblems

We describe a new technique for computing lower-bounds on the minimum energy configuration of a planar Markov Random Field (MRF). Our method successively adds large numbers of constraints and enforces consistency over binary projections of the original problem state space. These constraints are represented in terms of subproblems in a dual-decomposition framework that is optimized using subgradient techniques. The complete set of constraints we consider enforces cycle consistency over the original graph. In practice we find that the method converges quickly on most problems with the addition of a few subproblems and outperforms existing methods for some interesting classes of hard potentials.

cs.LG↗
arXiv2011

Planar Cycle Covering Graphs

We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture the effect of unary potentials. A ground state of the resulting approximation can be computed efficiently by reduction to minimum-weight perfect matching. We show that optimization of variational parameters achieves the same lower-bound as dual-decomposition into the set of all cycles of the original graph. We demonstrate that our variational optimization converges quickly and provides high-quality solutions to hard combinatorial problems 10-100x faster than competing algorithms that optimize the same bound.

stat.ML↗