Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy

The Cramer-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramer-Rao lower bound for the estimation of a feature's position (e.g. of a single molecule) in a registered image is also derived. In the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix (e.g. the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramer-Rao lower bound are given. Under certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators. Theoretical results are verified with simulations and experimental data

MR to Ultrasound Registration for Image-Guided Prostate Biopsy

Transrectal ultrasound (TRUS) guided prostate biopsy is the standard approach for diagnosis of prostate cancer (PCa). However, due to the lack of image contrast of prostate tumors, it often results in false negatives. Magnetic Resonance Imaging (MRI) has been considered to be a promising imaging modality for noninvasive identification of PCa, since it can provide a high sensitivity and specificity for the detection of early stage PCa. Our main objective is to develop a registration method of 3D MR-TRUS images, allowing generation of volumetric 3D maps of targets identified in 3D MR images to be biopsied using 3D TRUS images. We proposed an image-based non-rigid registration approach which employs the modality independent neighborhood descriptor (MIND) as the local similarity feature. An efficient duality-based convex optimization-based algorithmic scheme was introduced to extract the deformations. The registration accuracy was evaluated using 20 patient images by calculating the target registration error (TRE) using manually identified corresponding intrinsic fiducials. Additional performance metrics (DSC, MAD, and MAXD) were also calculated by comparing the MR and TRUS manually segmented prostate surfaces in the registered images. Experimental results showed that the proposed method yielded an overall median TRE of 1.76 mm. In addition, we proposed a surface-based registration method, which first makes use of an initial rigid registration of 3D MR to TRUS using 6 manually placed corresponding landmarks in each image. Following the manual initialization, two prostate surfaces are segmented from 3D MR and TRUS images and then non-rigidly registered using a thin-plate spline algorithm. The registration accuracy was evaluated using 17 patient images by measuring TRE. Experimental results show that the proposed method yielded an overall mean TRE of 2.24 mm, which is favorably comparable to a clinical requirement for an error of less than 2.5 mm

Extension of the MIRS computer package for the modeling of molecular spectra : from effective to full ab initio ro-vibrational hamiltonians in irreducible tensor form

The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version (Nikitin, et al. JQSRT, 2003, pp. 239--249) was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possibilities for spectra calculations and modeling by getting rid of several previous limitations particularly for the size of polyads and the number of tensors involved. It allows dealing with overlapping polyads and includes more efficient and faster algorithms for the calculation of coefficients related to molecular symmetry properties (6C, 9C and 12C symbols for C_{3v}, T_{d}, and O_{h} point groups) and for better convergence of least-square-fit iterations as well. The new version is not limited to polyad effective models. It also allows direct predictions using full ab initio ro-vibrational normal mode hamiltonians converted into the irreducible tensor form. Illustrative examples on CH_{3} D, CH_{4}, CH_{3} Cl, CH_{3} F and PH_{3} are reported reflecting the present status of data available. It is written in C++ for standard PC computer operating under Windows. The full package including on-line documentation and recent data are freely available at [http://www.iao.ru/mirs/mirs.htm] or [http://xeon.univ-reims.fr/Mirs/||http://xeon.univ-reims.fr/Mirs/] or [http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/MIRS.html].Comment: Journal of Quantitative Spectroscopy and Radiative Transfer (2012) xxx-xx

Estimation of the standard deviation by order statistics: the range, the average range, and some quasi ranges

Thesis (M.A.)--Boston UniversitySome rapid approximate methods of estimating the standard deviation from samples of moderate size (20 < n < 100) are presented. The emphasis is placed on solutions of problems commonly encountered in statistical quality control, especially in the electronics industry. Factors and efficiency values are given for the use of these estimators on normally distributed data. Statistical and practical engineering and administrative criteria are suggested for testing whether particular estimators are desirable in the usual industrial situation. The estimates discussed in this paper are all order statistics, i.e. statistics which are a function of only a small number of observations selected from the whole sample. These observations are selected because of the position they occupy among the other observations when all sample observations are arranged in order of magnitude. The first estimator discussed, for instance, is the range. The range of a sample is merely the numerical difference between the largest member of the sample and the smallest member of the sample. The standard deviation of the distribution from which the sample was drawn may be estimated by dividing the range by a suitable constant. The constant is a function of the sample size and of the shape of the distribution. Factors are given for sample sizes up to ten, for the normal distribution only. [TRUNCATED

Large Oligomeric Complex Structures Can Be Computationally Assembled by Efficiently Combining Docked Interfaces

Macromolecular oligomeric assemblies are involved in many biochemical processes of living organisms. The benefits of such assemblies in crowded cellular environments include increased reaction rates, efficient feedback regulation, cooperativity and protective functions. However, an atom‐level structural determination of large assemblies is challenging due to the size of the complex and the difference in binding affinities of the involved proteins. In this study, we propose a novel combinatorial greedy algorithm for assembling large oligomeric complexes from information on the approximate position of interaction interfaces of pairs of monomers in the complex. Prior information on complex symmetry is not required but rather the symmetry is inferred during assembly. We implement an efficient geometric score, the transformation match score, that bypasses the model ranking problems of state‐of‐the‐art scoring functions by scoring the similarity between the inferred dimers of the same monomer simultaneously with different binding partners in a (sub)complex with a set of pregenerated docking poses. We compiled a diverse benchmark set of 308 homo and heteromeric complexes containing 6 to 60 monomers. To explore the applicability of the method, we considered 48 sets of parameters and selected those three sets of parameters, for which the algorithm can correctly reconstruct the maximum number, namely 252 complexes (81.8%) in, at least one of the respective three runs. The crossvalidation coverage, that is, the mean fraction of correctly reconstructed benchmark complexes during crossvalidation, was 78.1%, which demonstrates the ability of the presented method to correctly reconstruct topology of a large variety of biological complexes. Proteins 2015; 83:1887–1899. © 2015 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc