25 research outputs found
A First Derivative Potts Model for Segmentation and Denoising Using ILP
Unsupervised image segmentation and denoising are two fundamental tasks in
image processing. Usually, graph based models such as multicut are used for
segmentation and variational models are employed for denoising. Our approach
addresses both problems at the same time. We propose a novel ILP formulation of
the first derivative Potts model with the data term, where binary
variables are introduced to deal with the norm of the regularization
term. The ILP is then solved by a standard off-the-shelf MIP solver. Numerical
experiments are compared with the multicut problem.Comment: 6 pages, 2 figures. To appear at Proceedings of International
Conference on Operations Research 2017, Berli
Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts
Formulations of the Image Decomposition Problem as a Multicut Problem (MP)
w.r.t. a superpixel graph have received considerable attention. In contrast,
instances of the MP w.r.t. a pixel grid graph have received little attention,
firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are
hard to solve in practice, and, secondly, due to the lack of long-range terms
in the objective function of the MP. We propose a generalization of the MP with
long-range terms (LMP). We design and implement two efficient algorithms
(primal feasible heuristics) for the MP and LMP which allow us to study
instances of both problems w.r.t. the pixel grid graphs of the images in the
BSDS-500 benchmark. The decompositions we obtain do not differ significantly
from the state of the art, suggesting that the LMP is a competitive formulation
of the Image Decomposition Problem. To demonstrate the generality of the LMP,
we apply it also to the Mesh Decomposition Problem posed by the Princeton
benchmark, obtaining state-of-the-art decompositions
A Multi-cut Formulation for Joint Segmentation and Tracking of Multiple Objects
Recently, Minimum Cost Multicut Formulations have been proposed and proven to
be successful in both motion trajectory segmentation and multi-target tracking
scenarios. Both tasks benefit from decomposing a graphical model into an
optimal number of connected components based on attractive and repulsive
pairwise terms. The two tasks are formulated on different levels of granularity
and, accordingly, leverage mostly local information for motion segmentation and
mostly high-level information for multi-target tracking. In this paper we argue
that point trajectories and their local relationships can contribute to the
high-level task of multi-target tracking and also argue that high-level cues
from object detection and tracking are helpful to solve motion segmentation. We
propose a joint graphical model for point trajectories and object detections
whose Multicuts are solutions to motion segmentation {\it and} multi-target
tracking problems at once. Results on the FBMS59 motion segmentation benchmark
as well as on pedestrian tracking sequences from the 2D MOT 2015 benchmark
demonstrate the promise of this joint approach
A Multi-cut Formulation for Joint Segmentation and Tracking of Multiple Objects
Recently, Minimum Cost Multicut Formulations have been proposed and proven to be successful in both motion trajectory segmentation and multi-target tracking scenarios. Both tasks benefit from decomposing a graphical model into an optimal number of connected components based on attractive and repulsive pairwise terms. The two tasks are formulated on different levels of granularity and, accordingly, leverage mostly local information for motion segmentation and mostly high-level information for multi-target tracking. In this paper we argue that point trajectories and their local relationships can contribute to the high-level task of multi-target tracking and also argue that high-level cues from object detection and tracking are helpful to solve motion segmentation. We propose a joint graphical model for point trajectories and object detections whose Multicuts are solutions to motion segmentation {\it and} multi-target tracking problems at once. Results on the FBMS59 motion segmentation benchmark as well as on pedestrian tracking sequences from the 2D MOT 2015 benchmark demonstrate the promise of this joint approach
A Message Passing Algorithm for the Minimum Cost Multicut Problem
We propose a dual decomposition and linear program relaxation of the NP -hard
minimum cost multicut problem. Unlike other polyhedral relaxations of the
multicut polytope, it is amenable to efficient optimization by message passing.
Like other polyhedral elaxations, it can be tightened efficiently by cutting
planes. We define an algorithm that alternates between message passing and
efficient separation of cycle- and odd-wheel inequalities. This algorithm is
more efficient than state-of-the-art algorithms based on linear programming,
including algorithms written in the framework of leading commercial software,
as we show in experiments with large instances of the problem from applications
in computer vision, biomedical image analysis and data mining.Comment: Added acknowledgment
End-to-end Learning for Graph Decomposition
We propose a novel end-to-end trainable framework for the graph decomposition
problem. The minimum cost multicut problem is first converted to an
unconstrained binary cubic formulation where cycle consistency constraints are
incorporated into the objective function. The new optimization problem can be
viewed as a Conditional Random Field (CRF) in which the random variables are
associated with the binary edge labels of the initial graph and the hard
constraints are introduced in the CRF as high-order potentials. The parameters
of a standard Neural Network and the fully differentiable CRF are optimized in
an end-to-end manner. Furthermore, our method utilizes the cycle constraints as
meta-supervisory signals during the learning of the deep feature
representations by taking the dependencies between the output random variables
into account. We present analyses of the end-to-end learned representations,
showing the impact of the joint training, on the task of clustering images of
MNIST. We also validate the effectiveness of our approach both for the feature
learning and the final clustering on the challenging task of real-world
multi-person pose estimation