6,181 research outputs found
Active Contour Models for Manifold Valued Image Segmentation
Image segmentation is the process of partitioning a image into different
regions or groups based on some characteristics like color, texture, motion or
shape etc. Active contours is a popular variational method for object
segmentation in images, in which the user initializes a contour which evolves
in order to optimize an objective function designed such that the desired
object boundary is the optimal solution. Recently, imaging modalities that
produce Manifold valued images have come up, for example, DT-MRI images, vector
fields. The traditional active contour model does not work on such images. In
this paper, we generalize the active contour model to work on Manifold valued
images. As expected, our algorithm detects regions with similar Manifold values
in the image. Our algorithm also produces expected results on usual gray-scale
images, since these are nothing but trivial examples of Manifold valued images.
As another application of our general active contour model, we perform texture
segmentation on gray-scale images by first creating an appropriate Manifold
valued image. We demonstrate segmentation results for manifold valued images
and texture images
Total variation regularization for manifold-valued data
We consider total variation minimization for manifold valued data. We propose
a cyclic proximal point algorithm and a parallel proximal point algorithm to
minimize TV functionals with -type data terms in the manifold case.
These algorithms are based on iterative geodesic averaging which makes them
easily applicable to a large class of data manifolds. As an application, we
consider denoising images which take their values in a manifold. We apply our
algorithms to diffusion tensor images, interferometric SAR images as well as
sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds
(which includes the data space in diffusion tensor imaging) we show the
convergence of the proposed TV minimizing algorithms to a global minimizer
Approximate matrix and tensor diagonalization by unitary transformations: convergence of Jacobi-type algorithms
We propose a gradient-based Jacobi algorithm for a class of maximization
problems on the unitary group, with a focus on approximate diagonalization of
complex matrices and tensors by unitary transformations. We provide weak
convergence results, and prove local linear convergence of this algorithm.The
convergence results also apply to the case of real-valued tensors
Characterizing Distances of Networks on the Tensor Manifold
At the core of understanding dynamical systems is the ability to maintain and
control the systems behavior that includes notions of robustness,
heterogeneity, or regime-shift detection. Recently, to explore such functional
properties, a convenient representation has been to model such dynamical
systems as a weighted graph consisting of a finite, but very large number of
interacting agents. This said, there exists very limited relevant statistical
theory that is able cope with real-life data, i.e., how does perform analysis
and/or statistics over a family of networks as opposed to a specific network or
network-to-network variation. Here, we are interested in the analysis of
network families whereby each network represents a point on an underlying
statistical manifold. To do so, we explore the Riemannian structure of the
tensor manifold developed by Pennec previously applied to Diffusion Tensor
Imaging (DTI) towards the problem of network analysis. In particular, while
this note focuses on Pennec definition of geodesics amongst a family of
networks, we show how it lays the foundation for future work for developing
measures of network robustness for regime-shift detection. We conclude with
experiments highlighting the proposed distance on synthetic networks and an
application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex
Networks 201
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