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Results for “mutual information”

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PubMed2000

Image registration by maximization of combined mutual information and gradient information.

Mutual information has developed into an accurate measure for rigid and affine monomodality and multimodality image registration. The robustness of the measure is questionable, however. A possible reason for this is the absence of spatial information in the measure. The present paper proposes to include spatial information by combining mutual information with a term based on the image gradient of the images to be registered. The gradient term not only seeks to align locations of high gradient magnitude, but also aims for a similar orientation of the gradients at these locations. Results of combining both standard mutual information as well as a normalized measure are presented for rigid registration of three-dimensional clinical images [magnetic resonance (MR), computed tomography (CT), and positron emission tomography (PET)]. The results indicate that the combined measures yield a better registration function does mutual information or normalized mutual information per se. The registration functions are less sensitive to low sampling resolution, do not contain incorrect global maxima that are sometimes found in the mutual information function, and interpolation-induced local minima can be reduced. These characteristics yield the promise of more robust registration measures. The accuracy of the combined measures is similar to that of mutual information-based methods.

Entropy↗

PubMed2000

Improved efficiency for MRI-SPET registration based on mutual information.

Mutual information has been proposed as a criterion for image registration. The criterion is calculated from a two-dimensional grey-scale histogram of the image pair being registered. In this paper we study how sparse sampling can be used to increase speed performance using the registration algorithm of Maes et al. (IEEE Trans Med Imaging 1997; 16: 187-198) with a focus on registration of MRI-SPET brain images. In particular we investigate how sparse sampling and parameters such as the number of bins used for the grey-scale histograms and smoothing of the data prior to registration affect accuracy and robustness of the registration. The method was validated using both simulated and human data. Our results show that sparse sampling introduced local maxima into the mutual information similarity function when the number of bins used for the histograms was large. To speed up registration while retaining robustness, smoothing of the data prior to registration was used and a coarse to fine subsampling protocol, where the number of bins in the histograms were dependent on the subsampling factor, was employed, For the simulated data, the method was able to recover known transformations with an accuracy of about 1 mm. Using the human data, there were no significant differences in the recovered transformation parameters when the suggested subsampling scheme was used compared with when no subsampling was used, but there was a more than tenfold increase in speed. Our results show that, with the appropriate choice of parameters, the method can accurately register MRI-SPET brain images even when very efficient sampling protocols are used.

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PubMed2003

Interpolation artifacts in multimodality image registration based on maximization of mutual information.

Mutual information (MI) is an increasingly popular match metric for multimodality image registration. However, its value is affected by interpolation, which may limit registration accuracy. The purpose of this study was to characterize the artifacts from eight interpolators and to investigate efficient strategies to overcome these artifacts. The interpolators were: 1) nearest neighbor; 2) linear; 3) cubic Catmull-Rom; 4) Hamming-windowed sinc; 5) partial volume; 6) NN with jittered sampling (JIT); 7) NN with histogram blurring (BLUR); and 8) NN with JIT and BLUR. The impact of interpolation on MI was evaluated in two dimensions over different translational and rotational misregistration. Interpolation caused spurious fluctuations in MI whenever the voxel grids had coinciding periodicities and were nearly aligned. The artifacts did not lessen by using intensity interpolators with wider support (e.g., cubic Catmull-Rom, Hamming-windowed sinc). PV could lead to either arch artifacts or inverted-arch artifacts, depending on the relative voxel sizes. Several strategies reduced artifacts and improved registration robustness: JIT, BLUR, avoiding an extreme number of intensity bins, and resampling the images in a rotated orientation with different relative voxel sizes (e.g., pi/3). These findings also apply to related methods, including normalized MI, joint entropy, and Hill's third moment.

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PubMed2004

Accuracy and reproducibility of co-registration techniques based on mutual information and normalized mutual information for MRI and SPECT brain images.

We implemented a 3D co-registration technique based on mutual information (MI) including 2D image matching as a coarse pre-registration. The 2D coarse pre-registration was performed in the transverse, sagittal and coronal planes sequentially, and all six parameters were then optimized as fine registration. Normalized mutual information (NMI) was also examined as another entropy-based measure that was invariant to the overlapped area of two images. In order to compare accuracy and precision of the present method with a conventional two-level multiresolution approach, simulation was performed by 100 trials with the random initial mismatch of +/-10 degrees and +/-17.92 mm (Type-I) and +/-20 degrees and +/-40.32 mm (Type-II). For Type-I, no significant differences were found between registration errors of the multiresolution approach and the present method with the MI criterion. No biases were observed (< or =0.13 degrees and < or =0.57 mm for the multiresolution approach; < or =0.12 degrees and < or =0.57 mm for the present method) and the SDs were very small (< or =0.18 degrees and < or =0.12 mm for the multiresolution approach; < or =0.11 degrees and < or =0.11 mm for the present method). For Type-II, SDs for the multiresolution approach (< or =1.8 degrees and < or =0.88 mm) were markedly larger than those for the present method (< or =0.64 degrees and < or =0.20 mm) with MI. Success rate for the present method was 99.9%, which was higher than 97.6% for the multiresolution approach. Simulation also revealed that MI and NMI performance were almost equivalent. The choice of optimization strategy more affected accuracy and reproducibility than the choice of the registration criterion (MI or NMI) in our simulation condition. The present method is sufficiently accurate and reproducible for MRI-SPECT registration in clinical use.

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PubMed2004

Extending the mutual information measure to rank inferred literature relationships.

BACKGROUND: Within the peer-reviewed literature, associations between two things are not always recognized until commonalities between them become apparent. These commonalities can provide justification for the inference of a new relationship where none was previously known, and are the basis of most observation-based hypothesis formation. It has been shown that the crux of the problem is not finding inferable associations, which are extraordinarily abundant given the scale-free networks that arise from literature-based associations, but determining which ones are informative. The Mutual Information Measure (MIM) is a well-established method to measure how informative an association is, but is limited to direct (i.e. observable) associations. RESULTS: Herein, we attempt to extend the calculation of mutual information to indirect (i.e. inferable) associations by using the MIM of shared associations. Objects of general research interest (e.g. genes, diseases, phenotypes, drugs, ontology categories) found within MEDLINE are used to create a network of associations for evaluation. CONCLUSIONS: Mutual information calculations can be effectively extended into implied relationships and a significance cutoff estimated from analysis of random word networks. Of the models tested, the shared minimum MIM (MMIM) model is found to correlate best with the observed strength and frequency of known associations. Using three test cases, the MMIM method tends to rank more specific relationships higher than counting the number of shared relationships within a network.

Humans↗

PubMed1999

Comparative evaluation of multiresolution optimization strategies for multimodality image registration by maximization of mutual information.

Maximization of mutual information of voxel intensities has been demonstrated to be a very powerful criterion for three-dimensional medical image registration, allowing robust and accurate fully automated affine registration of multimodal images in a variety of applications, without the need for segmentation or other preprocessing of the images. In this paper, we investigate the performance of various optimization methods and multiresolution strategies for maximization of mutual information, aiming at increasing registration speed when matching large high-resolution images. We show that mutual information is a continuous function of the affine registration parameters when appropriate interpolation is used and we derive analytic expressions of its derivatives that allow numerically exact evaluation of its gradient. Various multiresolution gradient- and non-gradient-based optimization strategies, such as Powell, simplex, steepest-descent, conjugate-gradient, quasi-Newton and Levenberg-Marquardt methods, are evaluated for registration of computed tomography (CT) and magnetic resonance images of the brain. Speed-ups of a factor of 3 on average compared to Powell's method at full resolution are achieved with similar precision and without a loss of robustness with the simplex, conjugate-gradient and Levenberg-Marquardt method using a two-level multiresolution scheme. Large data sets such as 256(2) x 128 MR and 512(2) x 48 CT images can be registered with subvoxel precision in <5 min CPU time on current workstations.

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PubMed2002

Influence of implementation parameters on registration of MR and SPECT brain images by maximization of mutual information.

UNLABELLED: Mutual-information maximization is one of the most popular algorithms for automatic image registration. However, many implementation issues have not been evaluated in a single, coherent context. METHODS: Twenty-one registrations between MR and SPECT brain images (8 patients) were achieved by mutual-information maximization with different implementation strategies. The results of a popular strategy were chosen as the standard. All other results were compared with the standard, and the statistics of misregistrations were computed. The registration speed, accuracy, precision, and success rate were assessed. RESULTS: Compared with trilinear interpolation, nearest-neighbor interpolation slightly sped the registration process, but with a lower success rate. The number of bins used to estimate the probability density function (pdf) affects the speed and robustness. Using fewer bins yielded a less robust registration. Adaptively changing the number of bins increased the registration speed and robustness. Simplex optimization increased the registration speed considerably, with a slightly degraded success rate. Simplex optimization with adaptive bin strategy improved the success rate and further decreased the registration time. Multiresolution optimization yielded a better success rate, with little effect on the accuracy and precision of registration. An increase in the number of resolution levels increased the success rate. Multisampling optimization also improved the success rate, but the results were less accurate and precise than those obtained with multiresolution optimization, with an increase in the number of levels decreasing the performance. Segmentation affected the registration speed and success rate. Because segmentation is problem specific, the effects were not conclusive. CONCLUSION: Different implementation strategies considerably affect the performance of automatic image registration by mutual-information maximization. On the basis of the experimental findings, we suggest that the best implementation strategy would include trilinear interpolation, adaptive change of the number of bins when estimating pdf, and exploitation of a simplex optimization algorithm with a multiresolution scheme.

Adult↗

PubMed2003

Mutual information as an index of diagnostic test performance.

OBJECTIVES: This paper demonstrates that diagnostic test performance can be quantified as the average amount of information the test result (R) provides about the disease state (D). METHODS: A fundamental concept of information theory, mutual information, is directly applicable to this problem. This statistic quantifies the amount of information that one random variable contains about another random variable. Prior to performing a diagnostic test, R and D are random variables. Hence, their mutual information, I(D;R), is the amount of information that R provides about D. RESULTS: I(D;R) is a function of both 1). the pretest probabilities of the disease state and 2). the set of conditional probabilities relating each possible test result to each possible disease state. The area under the receiver operating characteristic curve (AUC) is a popular measure of diagnostic test performance which, in contrast to I(D;R), is independent of the pretest probabilities; it is a function of only the set of conditional probabilities. The AUC is not a measure of diagnostic information. CONCLUSIONS: Because I(D;R) is dependent upon pretest probabilities, knowledge of the setting in which a diagnostic test is employed is a necessary condition for quantifying the amount of information it provides. Advantages of I(D;R) over the AUC are that it can be calculated without invoking an arbitrary curve fitting routine, it is applicable to situations in which multiple diagnoses are under consideration, and it quantifies test performance in meaningful units (bits of information).

Area Under Curve↗

PubMed2002

[Method of multi-resolution 3D image registration by mutual information].

Maximization of mutual information is a powerful criterion for 3D medical image registration, allowing robust and fully accurate automated rigid registration of multi-modal images in a various applications. In this paper, a method based on normalized mutual information for 3D image registration was presented on the images of CT, MR and PET. Powell's direction set method and Brent's one-dimensional optimization algorithm were used as optimization strategy. A multi-resolution approach is applied to speedup the matching process. For PET images, pre-procession of segmentation was performed to reduce the background artefacts. According to the evaluation by the Vanderbilt University, Sub-voxel accuracy in multi-modality registration had been achieved with this algorithm.

Algorithms↗

PubMed2003

[Implementation of mutual information based medical image registration methods].

Image registration methods based on mutual information, including mutual information and normalized mutual information, have been accepted as the most accurate and efficient methods. But there are many fluctuations in the registration functions that hinder the optimization procedure and lead to registration failure in intra-modal registration. We found that besides the interpolation artifacts, the uncertainty of the changing of entropy with the changing of overlap also contributes to the fluctuations. The effect of interpolation artifacts can be eliminated, but it is difficult to eliminate the effect of uncertainty of entropy. Luckily, this effect is not significant in normalized mutual information. Normalized mutual information is more stable and robust than standard mutual information and its better performance and wider application can be expected.

Algorithms↗

PubMed2004

Automatic image registration of three-dimensional images of the head of cats and dogs by use of maximization of mutual information.

OBJECTIVE: To validate mutual information criterion as a ready-to-use technique for automated alignment (ie, registration) of 3-dimensional (3-D) multimodal image data of the head of cats and dogs. SAMPLE POPULATION: Corresponding 3-D magnetic resonance imaging (MRI) and computed tomography (CT) brain scans of a 6-month-old Doberman Pinscher with a brain cyst; CT images of the head of a European shorthair cat with a meningioma before and immediately, 3, and 6 months after surgical resection; and CT and corresponding stacked anatomic cryosection images of the entire head of a 2-year-old sexually intact female Beagle. PROCEDURE: All images were matched retrospectively by use of an in-house computer program developed on the basis of a mutual information image registration algorithm. Accuracy of the resulting registrations was evaluated by visual inspection. RESULTS: All registrations were judged to be highly accurate. Additional manual corrections were not necessary. CONCLUSIONS AND CLINICAL RELEVANCE: Mutual information registration criterion can by applied to 3-D multimodal head images of cats and dogs for full automatic rigid-body image registration. The combination of such aligned images would considerably facilitate efforts of veterinary clinicians as indicated by its widespread use in brain surgery and radiation therapy of humans.

Animals↗

PubMed1997

Multimodality image registration by maximization of mutual information.

A new approach to the problem of multimodality medical image registration is proposed, using a basic concept from information theory, mutual information (MI), or relative entropy, as a new matching criterion. The method presented in this paper applies MI to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images, which is assumed to be maximal if the images are geometrically aligned. Maximization of MI is a very general and powerful criterion, because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved. The accuracy of the MI criterion is validated for rigid body registration of computed tomography (CT), magnetic resonance (MR), and photon emission tomography (PET) images by comparison with the stereotactic registration solution, while robustness is evaluated with respect to implementation issues, such as interpolation and optimization, and image content, including partial overlap and image degradation. Our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation, feature extraction, or other preprocessing steps which makes this method very well suited for clinical applications.

Algorithms↗

PubMed2004

Minimax mutual information approach for independent component analysis.

Minimum output mutual information is regarded as a natural criterion for independent component analysis (ICA) and is used as the performance measure in many ICA algorithms. Two common approaches in information-theoretic ICA algorithms are minimum mutual information and maximum output entropy approaches. In the former approach, we substitute some form of probability density function (pdf) estimate into the mutual information expression, and in the latter we incorporate the source pdf assumption in the algorithm through the use of nonlinearities matched to the corresponding cumulative density functions (cdf). Alternative solutions to ICA use higher-order cumulant-based optimization criteria, which are related to either one of these approaches through truncated series approximations for densities. In this article, we propose a new ICA algorithm motivated by the maximum entropy principle (for estimating signal distributions). The optimality criterion is the minimum output mutual information, where the estimated pdfs are from the exponential family and are approximate solutions to a constrained entropy maximization problem. This approach yields an upper bound for the actual mutual information of the output signals - hence, the name minimax mutual information ICA algorithm. In addition, we demonstrate that for a specific selection of the constraint functions in the maximum entropy density estimation procedure, the algorithm relates strongly to ICA methods using higher-order cumulants.

Algorithms↗

PubMed2002

The mutual information: detecting and evaluating dependencies between variables.

MOTIVATION: Clustering co-expressed genes usually requires the definition of 'distance' or 'similarity' between measured datasets, the most common choices being Pearson correlation or Euclidean distance. With the size of available datasets steadily increasing, it has become feasible to consider other, more general, definitions as well. One alternative, based on information theory, is the mutual information, providing a general measure of dependencies between variables. While the use of mutual information in cluster analysis and visualization of large-scale gene expression data has been suggested previously, the earlier studies did not focus on comparing different algorithms to estimate the mutual information from finite data. RESULTS: Here we describe and review several approaches to estimate the mutual information from finite datasets. Our findings show that the algorithms used so far may be quite substantially improved upon. In particular when dealing with small datasets, finite sample effects and other sources of potentially misleading results have to be taken into account.

Algorithms↗

PubMed2004

Feature selection based on mutual information and redundancy-synergy coefficient.

Mutual information is an important information measure for feature subset. In this paper, a hashing mechanism is proposed to calculate the mutual information on the feature subset. Redundancy-synergy coefficient, a novel redundancy and synergy measure of features to express the class feature, is defined by mutual information. The information maximization rule was applied to derive the heuristic feature subset selection method based on mutual information and redundancy-synergy coefficient. Our experiment results showed the good performance of the new feature selection method.

Algorithms↗

PubMed2004

Estimating mutual information using B-spline functions--an improved similarity measure for analysing gene expression data.

BACKGROUND: The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. In the context of the clustering of genes with similar patterns of expression it has been suggested as a general quantity of similarity to extend commonly used linear measures. Since mutual information is defined in terms of discrete variables, its application to continuous data requires the use of binning procedures, which can lead to significant numerical errors for datasets of small or moderate size. RESULTS: In this work, we propose a method for the numerical estimation of mutual information from continuous data. We investigate the characteristic properties arising from the application of our algorithm and show that our approach outperforms commonly used algorithms: The significance, as a measure of the power of distinction from random correlation, is significantly increased. This concept is subsequently illustrated on two large-scale gene expression datasets and the results are compared to those obtained using other similarity measures.A C++ source code of our algorithm is available for non-commercial use from kloska@scienion.de upon request. CONCLUSION: The utilisation of mutual information as similarity measure enables the detection of non-linear correlations in gene expression datasets. Frequently applied linear correlation measures, which are often used on an ad-hoc basis without further justification, are thereby extended.

Algorithms↗

PubMed2005

[Advances in medical image registration based on mutual information].

The matching algorithm based on mutual information, which has the advantages of high speed, good automation and superion accuracy, is widely used in medical image registration. In this paper are presented the basic conception of mutual information, the transform model, the insert value algorithm, the optimization algorithm and the strategy in computing mutual information. Furthermore, we introduce some efficient methods for solving the problems in registration technique based on mutual information, and look forward to the future research work.

Algorithms↗

PubMed2006

A method on calculating high-dimensional mutual information and its application to registration of multiple ultrasound images.

Using mutual information as a criterion for medical image registration, which requires no prior segmentation or preprocessing, has been both theoretically and practically proved to be an effective method in these years. However, this technique is confined in registering two images and hard to apply to multiple ones. The reason is that unlike mutual information between two variables, high-dimensional mutual information is ill defined. In textbooks and theoretical essays, three-dimensional mutual information is proposed based on Venn diagram. Unfortunately, mutual information defined in this way is not necessarily nonnegative. In order to overcome the problem, in this paper, we introduce the mutual information matrix. By calculating its eigenvalues, high-dimensional mutual information is defined. This definition is nonnegative, bounded, and could be extended to higher dimensions, thus enables us to register more than three images. In the end, this definition is tested and proved to be effective on registration of multiple US images through simulation.

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