28 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
Disparity and Optical Flow Partitioning Using Extended Potts Priors
This paper addresses the problems of disparity and optical flow partitioning
based on the brightness invariance assumption. We investigate new variational
approaches to these problems with Potts priors and possibly box constraints.
For the optical flow partitioning, our model includes vector-valued data and an
adapted Potts regularizer. Using the notation of asymptotically level stable
functions we prove the existence of global minimizers of our functionals. We
propose a modified alternating direction method of minimizers. This iterative
algorithm requires the computation of global minimizers of classical univariate
Potts problems which can be done efficiently by dynamic programming. We prove
that the algorithm converges both for the constrained and unconstrained
problems. Numerical examples demonstrate the very good performance of our
partitioning method
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data