Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches.

In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.

An Automatic Approach for Learning and Tuning Gaussian Interval Type-2 Fuzzy Membership Functions Applied to Lung CAD Classification System

The potential of type-2 fuzzy sets for managing high levels of uncertainty in the subjective knowledge of experts or of numerical information has focused on control and pattern classification systems in recent years. One of the main challenges in designing a type-2 fuzzy logic system is how to estimate the parameters of type-2 fuzzy membership function (T2MF) and the Footprint of Uncertainty (FOU) from imperfect and noisy datasets. This paper presents an automatic approach for learning and tuning Gaussian interval type-2 membership functions (IT2MFs) with application to multi-dimensional pattern classification problems. T2MFs and their FOUs are tuned according to the uncertainties in the training dataset by a combination of genetic algorithm (GA) and crossvalidation techniques. In our GA-based approach, the structure of the chromosome has fewer genes than other GA methods and chromosome initialization is more precise. The proposed approach addresses the application of the interval type-2 fuzzy logic system (IT2FLS) for the problem of nodule classification in a lung Computer Aided Detection (CAD) system. The designed IT2FLS is compared with its type-1 fuzzy logic system (T1FLS) counterpart. The results demonstrate that the IT2FLS outperforms the T1FLS by more than 30% in terms of classification accuracy.

Development of model observers applied to 3D breast tomosynthesis microcalcifications and masses

The development of model observers for mimicking human detection strategies has followed from symmetric signals in simple noise to increasingly complex backgrounds. In this study we implement different model observers for the complex task of detecting a signal in a 3D image stack. The backgrounds come from real breast tomosynthesis acquisitions and the signals were simulated and reconstructed within the volume. Two different tasks relevant to the early detection of breast cancer were considered: detecting an 8 mm mass and detecting a cluster of microcalcifications. The model observers were calculated using a channelized Hotelling observer (CHO) with dense difference-of-Gaussian channels, and a modified (Partial prewhitening [PPW]) observer which was adapted to realistic signals which are not circularly symmetric. The sustained temporal sensitivity function was used to filter the images before applying the spatial templates. For a frame rate of five frames per second, the only CHO that we calculated performed worse than the humans in a 4-AFC experiment. The other observers were variations of PPW and outperformed human observers in every single case. This initial frame rate was a rather low speed and the temporal filtering did not affect the results compared to a data set with no human temporal effects taken into account. We subsequently investigated two higher speeds at 5, 15 and 30 frames per second. We observed that for large masses, the two types of model observers investigated outperformed the human observers and would be suitable with the appropriate addition of internal noise. However, for microcalcifications both only the PPW observer consistently outperformed the humans. The study demonstrated the possibility of using a model observer which takes into account the temporal effects of scrolling through an image stack while being able to effectively detect a range of mass sizes and distributions.

Three-dimensional ordered-subset expectation maximization iterative protocol for evaluation of left ventricular volumes and function by quantitative gated SPECT: a dynamic phantom study.

The purposes of this study were to characterize the performance of a 3-dimensional (3D) ordered-subset expectation maximization (OSEM) algorithm in the quantification of left ventricular (LV) function with (99m)Tc-labeled agent gated SPECT (G-SPECT), the QGS program, and a beating-heart phantom and to optimize the reconstruction parameters for clinical applications. METHODS: A G-SPECT image of a dynamic heart phantom simulating the beating left ventricle was acquired. The exact volumes of the phantom were known and were as follows: end-diastolic volume (EDV) of 112 mL, end-systolic volume (ESV) of 37 mL, and stroke volume (SV) of 75 mL; these volumes produced an LV ejection fraction (LVEF) of 67%. Tomographic reconstructions were obtained after 10-20 iterations (I) with 4, 8, and 16 subsets (S) at full width at half maximum (FWHM) gaussian postprocessing filter cutoff values of 8-15 mm. The QGS program was used for quantitative measurements. RESULTS: Measured values ranged from 72 to 92 mL for EDV, from 18 to 32 mL for ESV, and from 54 to 63 mL for SV, and the calculated LVEF ranged from 65% to 76%. Overall, the combination of 10 I, 8 S, and a cutoff filter value of 10 mm produced the most accurate results. The plot of the measures with respect to the expectation maximization-equivalent iterations (I x S product) revealed a bell-shaped curve for the LV volumes and a reverse distribution for the LVEF, with the best results in the intermediate range. In particular, FWHM cutoff values exceeding 10 mm affected the estimation of the LV volumes. CONCLUSION: The QGS program is able to correctly calculate the LVEF when used in association with an optimized 3D OSEM algorithm (8 S, 10 I, and FWHM of 10 mm) but underestimates the LV volumes. However, various combinations of technical parameters, including a limited range of I and S (80-160 expectation maximization-equivalent iterations) and low cutoff values (< or =10 mm) for the gaussian postprocessing filter, produced results with similar accuracies and without clinically relevant differences in the LV volumes and the estimated LVEF.

Gaussian process framework for pervasive estimation of swimming velocity with body-worn IMU

Presented is an accurate swimming velocity estimation method using an inertial measurement unit (IMU) by employing a simple biomechanical constraint of motion along with Gaussian process regression to deal with sensor inherent errors. Experimental validation shows a velocity RMS error of 9.0 cm/s and high linear correlation when compared with a commercial tethered reference system. The results confirm the practicality of the presented method to estimate swimming velocity using a single low-cost, body-worn IMU.

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Identification and validation of copy number variants using SNP genotyping arrays from a large clinical cohort.

BACKGROUND: Genotypes obtained with commercial SNP arrays have been extensively used in many large case-control or population-based cohorts for SNP-based genome-wide association studies for a multitude of traits. Yet, these genotypes capture only a small fraction of the variance of the studied traits. Genomic structural variants (GSV) such as Copy Number Variation (CNV) may account for part of the missing heritability, but their comprehensive detection requires either next-generation arrays or sequencing. Sophisticated algorithms that infer CNVs by combining the intensities from SNP-probes for the two alleles can already be used to extract a partial view of such GSV from existing data sets. RESULTS: Here we present several advances to facilitate the latter approach. First, we introduce a novel CNV detection method based on a Gaussian Mixture Model. Second, we propose a new algorithm, PCA merge, for combining copy-number profiles from many individuals into consensus regions. We applied both our new methods as well as existing ones to data from 5612 individuals from the CoLaus study who were genotyped on Affymetrix 500K arrays. We developed a number of procedures in order to evaluate the performance of the different methods. This includes comparison with previously published CNVs as well as using a replication sample of 239 individuals, genotyped with Illumina 550K arrays. We also established a new evaluation procedure that employs the fact that related individuals are expected to share their CNVs more frequently than randomly selected individuals. The ability to detect both rare and common CNVs provides a valuable resource that will facilitate association studies exploring potential phenotypic associations with CNVs. CONCLUSION: Our new methodologies for CNV detection and their evaluation will help in extracting additional information from the large amount of SNP-genotyping data on various cohorts and use this to explore structural variants and their impact on complex traits.

Machine learning analysis and modeling of interest rate curves

The present research deals with the review of the analysis and modeling of Swiss franc interest rate curves (IRC) by using unsupervised (SOM, Gaussian Mixtures) and supervised machine (MLP) learning algorithms. IRC are considered as objects embedded into different feature spaces: maturities; maturity-date, parameters of Nelson-Siegel model (NSM). Analysis of NSM parameters and their temporal and clustering structures helps to understand the relevance of model and its potential use for the forecasting. Mapping of IRC in a maturity-date feature space is presented and analyzed for the visualization and forecasting purposes.