69 research outputs found
Medical Image Registration and 3D Object Matching
The great challenge in image registration and 3D object matching is to devise computationally efficient algorithms for aligning images so that their details overlap accurately and retrieving similar shapes from large databases of 3D models. The first problem addressed is this thesis is medical image registration, which we formulate as an optimization problem in the information-theoretic framework. We introduce a viable and practical image registration method by maximizing an entropic divergence measure using a modified simultaneous perturbation stochastic approximation algorithm. The feasibility of the proposed image registration approach is demonstrated through extensive experiments.
The rest of the thesis is devoted to a joint exploitation of geometry and topology of 3D objects for as parsimonious as possible representation of models and its subsequent application in 3D object representation, matching, and retrieval problems. More precisely, we introduce a skeletal graph for topological 3D shape representation using Morse theory. The proposed skeletonization algorithm encodes a 3D shape into a topological Reeb graph using a normalized mixture distance function. We also propose a novel graph
matching algorithm by comparing the relative shortest paths between the skeleton endpoints. Moreover, we describe a skeletal graph for 3D object matching and retrieval. This skeleton is constructed from the second eigenfunction of the Laplace-Beltrami operator defined on the surface of the 3D object. Using the generalized eigenvalue decomposition, a matrix computational framework based on the finite element method is presented to compute the spectrum of the Laplace-Beltrami operator. Illustrating experiments on two standard
3D shape benchmarks are provided to demonstrate the feasibility and the much improved performance of the proposed skeletal graphs as shape descriptors for 3D object matching and retrieval
Spectral Clustering with Jensen-type kernels and their multi-point extensions
Motivated by multi-distribution divergences, which originate in information
theory, we propose a notion of `multi-point' kernels, and study their
applications. We study a class of kernels based on Jensen type divergences and
show that these can be extended to measure similarity among multiple points. We
study tensor flattening methods and develop a multi-point (kernel) spectral
clustering (MSC) method. We further emphasize on a special case of the proposed
kernels, which is a multi-point extension of the linear (dot-product) kernel
and show the existence of cubic time tensor flattening algorithm in this case.
Finally, we illustrate the usefulness of our contributions using standard data
sets and image segmentation tasks.Comment: To appear in IEEE Computer Society Conference on Computer Vision and
Pattern Recognitio
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
Sparse Randomized Shortest Paths Routing with Tsallis Divergence Regularization
This work elaborates on the important problem of (1) designing optimal
randomized routing policies for reaching a target node t from a source note s
on a weighted directed graph G and (2) defining distance measures between nodes
interpolating between the least cost (based on optimal movements) and the
commute-cost (based on a random walk on G), depending on a temperature
parameter T. To this end, the randomized shortest path formalism (RSP,
[2,99,124]) is rephrased in terms of Tsallis divergence regularization, instead
of Kullback-Leibler divergence. The main consequence of this change is that the
resulting routing policy (local transition probabilities) becomes sparser when
T decreases, therefore inducing a sparse random walk on G converging to the
least-cost directed acyclic graph when T tends to 0. Experimental comparisons
on node clustering and semi-supervised classification tasks show that the
derived dissimilarity measures based on expected routing costs provide
state-of-the-art results. The sparse RSP is therefore a promising model of
movements on a graph, balancing sparse exploitation and exploration in an
optimal way
Statistical mechanics and information-theoretic perspectives on complexity in the Earth system
This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques
An Information-Theoretic Measure For Face Recognition: Comparison With Structural Similarity
Automatic recognition of people faces is a challenging problem that has received significant attention from signal processing researchers in recent years. This is due to its several applications in different fields, including security and forensic analysis. Despite this attention, face recognition is still one among the most challenging problems. Up to this moment, there is no technique that provides a reliable solution to all situations. In this paper a novel technique for face recognition is presented. This technique, which is called ISSIM, is derived from our recently published information - theoretic similarity measure HSSIM, which was based on joint histogram. Face recognition with ISSIM is still based on joint histogram of a test image and a database images. Performance evaluation was performed on MATLAB using part of the well-known AT&T image database that consists of 49 face images, from which seven subjects are chosen, and for each subject seven views (poses) are chosen with different facial expressions. The goal of this paper is to present a simplified approach for face recognition that may work in real-time environments. Performance of our information - theoretic face recognition method (ISSIM) has been demonstrated experimentally and is shown to outperform the well-known, statistical-based method (SSIM)
Multimodality and Nonrigid Image Registration with Application to Diffusion Tensor Imaging
The great challenge in image registration is to devise computationally efficient algorithms for aligning images
so that their details overlap accurately. The first problem addressed in this thesis is multimodality
medical image registration, which we formulate as an optimization problem in the information-theoretic setting.
We introduce a viable and practical image registration method by maximizing a generalized entropic
dissimilarity measure using a modified simultaneous perturbation stochastic approximation algorithm. The
feasibility of the proposed image registration approach is demonstrated through extensive experiments.
The rest of the thesis is devoted to nonrigid medical image registration. We propose an informationtheoretic
framework by optimizing a non-extensive entropic similarity measure using the quasi-Newton
method as an optimization scheme and cubic B-splines for modeling the nonrigid deformation field between
the fixed and moving 3D image pairs. To achieve a compromise between the nonrigid registration accuracy
and the associated computational cost, we implement a three-level hierarchical multi-resolution approach in
such a way that the image resolution is increased in a coarse to fine fashion. The feasibility and registration
accuracy of the proposed method are demonstrated through experimental results on a 3D magnetic resonance
data volume and also on clinically acquired 4D computed tomography image data sets. In the same vein,
we extend our nonrigid registration approach to align diffusion tensor images for multiple components by
enabling explicit optimization of tensor reorientation. Incorporating tensor reorientation in the registration
algorithm is pivotal in wrapping diffusion tensor images. Experimental results on diffusion-tensor image
registration indicate the feasibility of the proposed approach and a much better performance compared to
the affine registration method based on mutual information, not only in terms of registration accuracy in the
presence of geometric distortions but also in terms of robustness in the presence of Rician noise
Information Theoretic Graph Kernels
This thesis addresses the problems that arise in state-of-the-art structural learning methods for (hyper)graph classification or clustering, particularly focusing on developing novel information theoretic kernels for graphs.
To this end, we commence in Chapter 3 by defining a family of Jensen-Shannon diffusion kernels, i.e., the information theoretic kernels, for (un)attributed graphs. We show that our kernels overcome the shortcomings of inefficiency (for the unattributed diffusion kernel) and discarding un-isomorphic substructures (for the attributed diffusion kernel) that arise in the R-convolution kernels. In Chapter 4, we present a novel framework of computing depth-based complexity traces rooted at the centroid vertices for graphs, which can be efficiently computed for graphs with large sizes. We show that our methods can characterize a graph in a higher dimensional complexity feature space than state-of-the-art complexity measures. In Chapter 5, we develop a novel unattributed graph kernel by matching the depth-based substructures in graphs, based on the contribution in Chapter 4. Unlike most existing graph kernels in the literature which merely enumerate similar
substructure pairs of limited sizes, our method incorporates explicit local substructure correspondence into the process of kernelization. The new kernel thus overcomes the shortcoming of neglecting structural correspondence that arises in most state-of-the-art graph kernels. The novel methods developed in Chapters 3, 4, and 5 are only restricted to graphs. However, real-world data usually tends to be represented by higher order relationships (i.e., hypergraphs). To overcome the shortcoming, in Chapter 6 we present a new hypergraph kernel using substructure isomorphism tests. We show that our kernel limits tottering that arises in the existing walk and subtree based (hyper)graph kernels. In Chapter 7, we summarize the contributions of this thesis. Furthermore, we analyze the proposed methods. Finally, we give some suggestions for the future work
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