Alignment by Maximization of Mutual Information

A new information-theoretic approach is presented for finding the pose of an object in an image. The technique does not require information about the surface properties of the object, besides its shape, and is robust with respect to variations of illumination. In our derivation, few assumptions are made about the nature of the imaging process. As a result the algorithms are quite general and can foreseeably be used in a wide variety of imaging situations. Experiments are presented that demonstrate the approach registering magnetic resonance (MR) images with computed tomography (CT) images, aligning a complex 3D object model to real scenes including clutter and occlusion, tracking a human head in a video sequence and aligning a view-based 2D object model to real images. The method is based on a formulation of the mutual information between the model and the image called EMMA. As applied here the technique is intensity-based, rather than feature-based. It works well in domains where edge or gradient-magnitude based methods have difficulty, yet it is more robust than traditional correlation. Additionally, it has an efficient implementation that is based on stochastic approximation. Finally, we will describe a number of additional real-world applications that can be solved efficiently and reliably using EMMA. EMMA can be used in machine learning to find maximally informative projections of high-dimensional data. EMMA can also be used to detect and correct corruption in magnetic resonance images (MRI).

Robustness of mutual information to inter-subject variability for automatic artefact removal from EEG

The externally recorded electroencephalogram (EEG) is contaminated with signals that do not originate from the brain, collectively known as artefacts. Thus, EEG signals must be cleaned prior to any further analysis. In particular, if the EEG is to be used in online applications such as Brain-Computer Interfaces (BCIs) the removal of artefacts must be performed in an automatic manner. This paper investigates the robustness of Mutual Information based features to inter-subject variability for use in an automatic artefact removal system. The system is based on the separation of EEG recordings into independent components using a temporal ICA method, RADICAL, and the utilisation of a Support Vector Machine for classification of the components into EEG and artefact signals. High accuracy and robustness to inter-subject variability is achieved.

Quantitative experimental comparison of single-beam, sidescan, and multibeam benthic habitat maps

Map comparison is a relatively uncommon practice in acoustic seabed classification to date, contrary to the field of land remote sensing, where it has been developed extensively over recent decades. The aim here is to illustrate the benefits of map comparison in the underwater realm with a case study of three maps independently describing the seabed habitats of the Te Matuku Marine Reserve (Hauraki Gulf, New Zealand). The maps are obtained from a QTC View classification of a single-beam echosounder (SBES) dataset, manual segmentation of a sidescan sonar (SSS) mosaic, and automatic classification of a backscatter dataset from a multibeam echosounder (MBES). The maps are compared using pixel-to-pixel similarity measures derived from the literature in land remote sensing. All measures agree in presenting the MBES and SSS maps as the most similar, and the SBES and SSS maps as the least similar. The results are discussed with reference to the potential of MBES backscatter as an alternative to SSS mosaic for imagery segmentation and to the potential of joint SBES–SSS survey for improved habitat mapping. Other applications of map-similarity measures in acoustic classification of the seabed are suggested.

Statistical mechanics of mutual information maximization

An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker S. and Hinton G., Nature, 355 (1992) 161). By exploiting a formal analogy to supervised learning in parity machines, the theory of zero-temperature Gibbs learning for the unsupervised procedure is presented for the case that the networks are perceptrons and for the case of fully connected committees.

Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications - the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

Unifying energy minimization and mutual information maximization for robust 2D/3D registration of X-ray and CT images

Similarity measure is one of the main factors that affect the accuracy of intensity-based 2D/3D registration of X-ray fluoroscopy to CT images. Information theory has been used to derive similarity measure for image registration leading to the introduction of mutual information, an accurate similarity measure for multi-modal and mono-modal image registration tasks. However, it is known that the standard mutual information measure only takes intensity values into account without considering spatial information and its robustness is questionable. Previous attempt to incorporate spatial information into mutual information either requires computing the entropy of higher dimensional probability distributions, or is not robust to outliers. In this paper, we show how to incorporate spatial information into mutual information without suffering from these problems. Using a variational approximation derived from the Kullback-Leibler bound, spatial information can be effectively incorporated into mutual information via energy minimization. The resulting similarity measure has a least-squares form and can be effectively minimized by a multi-resolution Levenberg-Marquardt optimizer. Experimental results are presented on datasets of two applications: (a) intra-operative patient pose estimation from a few (e.g. 2) calibrated fluoroscopic images, and (b) post-operative cup alignment estimation from single X-ray radiograph with gonadal shielding.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Relating thermodynamics to information theory : the equality of free energy and mutual information

In this thesis we uncover a new relation which links thermodynamics and information theory. We consider time as a channel and the detailed state of a physical system as a message. As the system evolves with time, ever present noise insures that the "message" is corrupted. Thermodynamic free energy measures the approach of the system toward equilibrium. Information theoretical mutual information measures the loss of memory of initial state. We regard the free energy and the mutual information as operators which map probability distributions over state space to real numbers. In the limit of long times, we show how the free energy operator and the mutual information operator asymptotically attain a very simple relationship to one another. This relationship is founded on the common appearance of entropy in the two operators and on an identity between internal energy and conditional entropy. The use of conditional entropy is what distinguishes our approach from previous efforts to relate thermodynamics and information theory.