Normalized Cross-correlation Function Research Articles

Anticipation mechanism in body sway control and effect of muscle fatigue

The aim of this work is to quantify the occurrence of an anticipatory mechanism in the control of quiet standing by measuring the lag between the myoelectric activity of the lateral gastrocnemius muscle and the stabilometric signal, as well as to determine the influence of the muscle fatigue on this process. Stabilometric and electromyographic (EMG) signals were synchronously collected from 22 subjects. Gastrocnemius fatigue was induced by a sustained plantar flexed posture until muscle failure. The data acquisition lasted for 120 s before and after the induced fatigue. After mean removal, the root mean square values of the EMG (RMS-EMG) were calculated for each 20 ms period. The normalized cross-correlation function was estimated to find the time delay between RMS-EMG and stabilometric signals. Anticipation values up to 1.62 s were found both before and after fatigue conditions ( p < 0.05), indicating that this mechanism plays an important role in body sway control. The fatigue caused a significant increase in the latency between the myoelectric activity of the gastrocnemius muscle and the movements of the center of pressure ( p < 0.05).

Sensitivity of the cross-correlaton between simulated surface EMGs for two muscles to detect motor unit synchronization

The purpose of the study was to evaluate the use of cross-correlation analysis between simulated surface electromyograms (EMGs) of two muscles to quantify motor unit synchronization. The volume conductor simulated a cylindrical limb with two muscles and bone, fat, and skin tissues. Models of two motor neuron pools were used to simulate 120 s of surface EMG that were detected over both muscles. Short-term synchrony was established using a phenomenological model that aligned the discharge times of selected motor units within and across muscles to simulate physiological levels of motor unit synchrony. The correlation between pairs of surface EMGs was estimated as the maximum of the normalized cross-correlation function. After imposing four levels of motor unit synchrony across muscles, five parameters were varied concurrently in the two muscles to examine their influence on the correlation between the surface EMGs: 1) excitation level (5, 10, 15, and 50% of maximum); 2) muscle size (350 and 500 motor units); 3) fat thickness (1 and 4 mm); 4) skin conductivity (0.1 and 1 S/m); and 5) mean motor unit conduction velocity (2.5 and 4 m/s). Despite a constant and high level of motor unit synchronization among pairs of motor units across the two muscles, the cross-correlation index ranged from 0.08 to 0.56, with variation in the five parameters. For example, cross-correlation of EMGs from pairs of hand muscles, each having thin layers of subcutaneous fat and mean motor unit conduction velocities of 4 m/s, may be relatively insensitive to the level of synchronization across muscles. In contrast, cross-correlation of EMGs from pairs of leg muscles, with larger fat thickness, may exhibit a different sensitivity. These results indicate that cross correlation of the surface EMGs from two muscles provides a limited measure of the level of synchronization between motor units in the two muscles.

Steady State Entanglement in Cavity QED

We investigate steady state entanglement in an open quantum system, specifically a single atom in a driven optical cavity with cavity loss and spontaneous emission. The system reaches a steady pure state when driven very weakly. Under these conditions, there is an optimal value for atom-field coupling to maximize entanglement, as larger coupling favors a loss port due to the cavity enhanced spontaneous emission. We address ways to implement measurements of the entanglement and find that normalized cross-correlation functions are indicators of the entanglement in the system. The equal time intensity-field cross correlation between the transmitted field of the cavity and the fluorescence intensity is proportional to the entanglement of formation for weak driving fields.

ZNCC-based template matching using bounded partial correlation

This paper describes a class of algorithms enabling efficient and exhaustive matching of a template into an image based on the Zero mean Normalized Cross-Correlation function (ZNCC). The approach consists in checking at each image position two sufficient conditions obtained at a reduced computational cost. This allows to skip rapidly most of the expensive calculations required to evaluate the ZNCC at those image points that cannot improve the best correlation score found so far. The algorithms shown in this paper generalize and extend the concept of Bounded Partial Correlation (BPC), previously devised for a template matching process based on the Normalized Cross-Correlation function (NCC).

Overwrite Measurement Method Using Pseudorandom Sequence

A novel overwrite measurement method with pseudorandom bit sequence (PRBS), random pattern overwrite (ROW) to evaluate the recording performance under the more realistic condition is proposed. A pair of 31-b PRBS are utilized in this overwrite measurement. The ROW is defined as the averaged power over a period of normalized cross-correlation function between the waveforms before and after overwriting. The intrinsic correlation between an initially written pattern and an overwritten pattern, and the effect of the noise are eliminated in the ROW calculation. By using this method, we can effectively evaluate the overwrite characteristics in the condition similar to those in a hard disk drive.

Daily target localization for prostate patients based on 3D image correlation

There are several localization techniques that have been used for prostate treatment. Recently, the potential use of a variety of CT-based equipment in the treatment room has been discussed. The goal of our study was to develop an automated procedure for daily treatment table shift calculation based on two CT data sets: simulation CT data and localization CT data. The method suggested in this study is a 3D image cross-correlation of small regions of interest (ROI) within the two data sets. The relative position of the two ROIs with respect to each other is determined by the maximum value of the normalized cross-correlation function, calculated for all possible relative locations of the two ROIs. After the best match is found the shifts are given by the vector connecting the treatment isocentre and the planning isocentre (both determined by the radio opaque fiducial markers on the patient's skin). The results have been compared with shifts calculated through manual fusion. The shift differences, averaged over 17 statistically independent shift calculations, are less then 1 mm in the lateral and longitudinal directions, and about 1 mm in the AP direction. The impact of image noise on the performance of the algorithm has been tested. The results show that the algorithm accurately adjusts for target positional changes even with Gaussian noise levels as high as 20% inserted.

Fast automatic particle picking from cryo-electron micrographs using a locally normalized cross-correlation function: a case study

Recent progress in single-particle reconstruction methods and cryo-EM techniques has led to the determination of macromolecular structures with unprecedented resolution. The number of particles that goes into the reconstruction is a key determinant in achieving high resolution. Interactive manual picking of particles from an electron micrograph is a very time-consuming, tedious, and inefficient process. We have implemented a fast automatic particle picking procedure in the SPIDER environment. The procedure makes use of template matching schemes and employs a recently developed locally normalized correlation algorithm based on Fourier techniques. As a test, we have used this procedure to pick 70S Escherichia coli ribosomes from a cryo-electron micrograph. Different search strategies including use of a circular mask and asymmetric masks for different orientations of the particle have been explored, and their relative efficiencies are discussed. The results indicate that the procedure can be optimally used to pick ribosomes in a fully automatic way within the limit of selecting less than 10% false positives while missing about 15% of true positives.

Determining the View of Chest Radiographs

Automatic identification of frontal (posteroanterior/anteroposterior) vs. lateral chest radiographs is an important preprocessing step in computer-assisted diagnosis, content-based image retrieval, as well as picture archiving and communication systems. Here, a new approach is presented. After the radiographs are reduced substantially in size, several distance measures are applied for nearest-neighbor classification. Leaving-one-out experiments were performed based on 1,867 radiographs from clinical routine. For comparison to existing approaches, subsets of 430 and 5 training images are also considered. The overall best correctness of 99.7% is obtained for feature images of 32 x 32 pixels, the tangent distance, and a 5-nearest-neighbor classification scheme. Applying the normalized cross correlation function, correctness yields still 99.6% and 99.3% for feature images of 32 x 32 and 8 x 8 pixel, respectively. Remaining errors are caused by image altering pathologies, metal artifacts, or other interferences with routine conditions. The proposed algorithm outperforms existing but sophisticated approaches and is easily implemented at the same time.

Polarization resolved intensity noise in vertical-cavity surface-emitting lasers

We report explicit analytical and numerical results for the polarization resolved intensity noise of vertical-cavity surface-emitting lasers operating in the fundamental transverse mode. We describe the fluctuations of the linear and circular polarization components of linearly polarized states on both sides of a nonthermal polarization switching. Our description is valid for small and large birefringence and arbitrary values of the spin flip rate, giving a complete description of the role of these parameters. Normalized cross-correlation functions for both linear and circular components are discussed in detail. They show different degrees of anticorrelated fluctuations in different frequency ranges.

Electromechanical delay in isometric actions initiated from nonresting levels.

The purpose of this study was to determine whether electromechanical delay (EMD) was associated exclusively with the onset of tension from a resting state and whether EMD remained constant across different rates of force development. Twenty-four subjects (23.9 +/- 5.4 yr, 171.7 +/- 7.3 cm, 72.9 +/- 12.8 kg) performed isometric elbow flexion trials in the transverse plane by using the dominant arm during which isometric force data and surface EMG activity were collected. Subjects completed three trials to establish a maximal force (MF) reference. Subjects then completed trials in which pulse forces of varying magnitudes were elicited at a frequency of 1 Hz from different baseline intensities. All forces were expressed relative to MF. Three trials of the following conditions (baseline-pulse) were performed in random order: 0-25%, 25-50%, 50-75%, 0-50%, and 0-75%. EMG and force data were collected for 10 pulse cycles during these trials. EMD was defined as the temporal shift that maximized a normalized cross-correlation function. EMD for a 25% pulse force developed from rest (83.5 +/- 12.9 ms) was significantly longer than that developed from 25% (66.3 +/- 11.5 ms) or 50% (60.6 +/- 16.6 ms) baselines. EMD values were not different when force was developed from 25% and 50% baselines. EMD associated with a 25% pulse force from rest was significantly longer than 50% (70.3 +/- 10.0 ms) and 75% (68.9 +/- 8.7 ms) pulse forces from rest. EMD for 50% and 75% pulse forces from rest were not statistically different. It was concluded that EMD is present during exertions initiated from both resting and nonresting states but is reduced when exertions are initiated from non-resting states and with higher rates of force development.

Mining genomes: correlating tandem mass spectra of modified and unmodified peptides to sequences in nucleotide databases.

The correlation of uninterpreted tandem mass spectra of modified and unmodified peptides, produced under low-energy (10-50 eV) collision conditions, with nucleotide sequences is demonstrated. In this method nucleotide databases are translated in six reading frames, and the resulting amino acid sequences are searched "on the fly" to identify and fit linear sequences to the fragmentation patterns observed in the tandem mass spectra of peptides. A cross-correlation function is then used to provide a measurement of similarity between the mass-to-charge ratios for the fragment ions predicted by amino acid sequences translated from the nucleotide database and the fragment ions observed in the tandem mass spectrum. In general, a difference greater than 0.1 between the normalized cross-correlation functions for the first- and second-ranked search results indicates a successful match between sequence and spectrum. Measurements of the deviation from maximum similarity employing the spectral reconstruction method are made. The search method employing nucleotide databases is also demonstrated on the spectra of phosphorylated peptides. Specific sites of modification are identified even though no specific information relevant to sites of modification is contained in the character-based sequence information of nucleotide databases.

Imaging through random media by use of low-coherence optical heterodyning

Optical heterodyning is a detection scheme that permits the preferential detection of ballistic photons transmitted through a random medium, providing the imaging of absorbing structures within. We introduce a normalized cross-correlation function as a quantitative measure of image quality and employ it to investigate the effect of source coherence length on the ability of optical heterodyning to detect these absorbing structures. The ability to image in transmission is found to be greatly enhanced by use of a reduced-coherence-length source. The effect on image quality of the transport mean-free-path length is quantified and found to depend on source coherence length. The necessity of considering scatterer particle–particle correlations is also presented.

An approach to correlate tandem mass spectral data of peptides with amino acid sequences in a protein database

A method to correlate the uninterpreted tandem mass spectra of peptides produced under low energy (10–50 eV) collision conditions with amino acid sequences in the Genpept database has been developed. In this method the protein database is searched to identify linear amino acid sequences within a mass tolerance of ± 1 u of the precursor ion molecular weight. A cross-correlation function is then used to provide a measurement of similarity between the mass-to-charge ratios for the fragment ions predicted from amino acid sequences obtained from the database and the fragment ions observed in the tandem mass spectrum. In general, a difference greater than 0.1 between the normalized cross-correlation functions of the first- and second-ranked search results indicates a successful match between sequence and spectrum. Searches of species-specific protein databases with tandem mass spectra acquired from peptides obtained from the enzymatically digested total proteins of E. coli and S. cerevisiae cells allowed matching of the spectra to amino acid sequences within proteins of these organisms. The approach described in this manuscript provides a convenient method to interpret tandem mass spectra with known sequences in a protein database.

Correlation between amplitude and frequency fluctuations of spontaneous otoacoustic emissions.

The normalized cross-correlation function between the amplitude and frequency fluctuations of 11 spontaneous otoacoustic emissions was measured. A significant correlation was found in seven subjects. The correlation coefficient ranged from -0.37 to +0.65 across subjects. In four subjects, the amplitude fluctuation lagged the frequency fluctuation. The time lag was between 1.6 and 5.5 ms. The results were interpreted using a noise-perturbed limit-cycle oscillator with nonlinear (Duffing) stiffness as a model for a spontaneous emission. The data show that the relative increase of the nonlinear stiffness in this model was between -0.010 and +0.015. This indicates that an even-order nonlinear stiffness plays a minor role in the emission generator.

Rapid sampling of model space using genetic algorithms: examples from seismic waveform inversion

SUMMARY The seismic waveform inversion problem is usually cast into the framework of Bayesian statistics in which prior information on the model parameters is combined with the data and physics of the forward problem to estimate the a posteriori probability density (PPD) in model space. The PPD is a function of an objective or fitness function computed from the observed and synthetic data. In general, the PPD or the fitness function is multimodal and its shape is unknown. Global optimization methods such as simulated annealing (SA) and genetic algorithms (GA) do not require that the shape of the fitness function be known. In this paper, we investigate GA to rapidly sample the most significant portion or portions of the PPD, when very little prior information is available. First, we use a simple three operator (selection, crossover and mutation) GA acting on a randomly chosen finite population of haploid binary coded models. We use plane wave transformed synthetic seismic data and a normalized cross-correlation function [E(m)] in the frequency domain as a fitness function. A moderate value of crossover probability, a low value of mutation probability, a high value of update probability and a proper population size are required to reach very close to the global maximum of the fitness function. Next, with an attempt to accelerate convergence we show that the concepts from simulated annealing can be used in stretching of the fitness function, i.e., we use exp [E(m)/T] rather than E(m) as the fitness function, where T is a control parameter analogous to temperature in simulated annealing. By a schemata analysis, we show that at low temperatures, schemata with above average fitness values are reproduced in large numbers causing a much more rapid convergence of the algorithm. A high value of temperature T assigns nearly equal selection probability to most of the schemata and thus retains diversity among the members of the population. Thus a GA with a step function type cooling schedule (very high temperature in the beginning followed by rapid cooling to a very low temperature) improves the performance dramatically: high values of the fitness function are obtained rapidly using only half as many models as would be required by a conventional GA. Similar performance could also be achieved by first using a high mutation probability and then decreasing the mutation probability to a very low value, while retaining the same low temperature throughout. We also address the problem of ‘genetic drift’ which causes the finite GAs to converge to one peak or the other when the algorithm is applied to a highly multimodal fitness function with several peaks of nearly the same height. A parallel genetic algorithm based on the concept of ‘punctuated equilibria’ is implemented to circumvent the problem. We run several GAs each with a finite subpopulation in parallel and collect many good models from each one of these runs. These are then used to grasp the most significant portion(s) of the PPD in model space. We then compute the weighted mean model and use the derived good models to estimate uncertainty in the derived model parameters.

Segmentation and statistical analysis of ground-based infrared cloudy sky images

The statistical behavior of ground-based IR cloudy sky images are analyzed to acquire a priori knowledge of the background necessary for the development of sophisticated infrared target detection and recognition systems. Infrared cloudy sky images can be automatically segmented into their related groups of interest, according to the radiance statistical distribution, by implementing specialized image processing techniques. Once the images have been segmented, the cloud cover, statistical distribution, and other parameters of interest are readily obtained. It was found that, in the 8- to 1 2-μm spectral window, cloudy sky images must be divided into at least five regions of interest, and in the 3- to 5-μm spectral window, a distinction must be made between shaded cloud images and sunlit cloud images. Shaded cloud images have only three regions of interest, whereas sunlit cloud images are more complex and have at least five regions of interest. If each region is approximated by a Gaussian distribution, then the normalized cross-correlation function ofthe measured data with the multinormal function gives a value in excess of 0.9.

Nonlinear multiparameter optimization using genetic algorithms: Inversion of plane‐wave seismograms

Seismic waveform inversion is one of many geophysical problems which can be identified as a nonlinear multiparameter optimization problem. Methods based on local linearization fail if the starting model is too far from the true model. We have investigated the applicability of “Genetic Algorithms” (GA) to the inversion of plane‐wave seismograms. Like simulated annealing, genetic algorithms use a random walk in model space and a transition probability rule to help guide their search. However, unlike a single simulated annealing run, the genetic algorithms search from a randomly chosen population of models (strings) and work with a binary coding of the model parameter set. Unlike a pure random search, such as in a “Monte Carlo” method, the search used in genetic algorithms is not directionless. Genetic algorithms essentially consist of three operations, selection, crossover, and mutation, which involve random number generation, string copies, and some partial string exchanges. The choice of the initial population, the probabilities of crossover and mutation are crucial for the practical implementation of the algorithm. We investigated the effects of these parameters in the inversion of plane‐wave seismograms in which a normalized crosscorrelation function was used as the objective or fitness function (E). We also introduce the concept of “update” probability to control the influence of past generations. The combination of a low value of mutation probability (∼0.01), a moderate value of the crossover probability (∼0.6) and a high value of update probability (∼0.9) are found to be optimal for the convergence of the algorithm. Further, we show that concepts from simulated annealing can be used effectively for the stretching of the fitness function which helps in the convergence of the algorithm. Thus, we propose to use exp (E/T) rather than E as the fitness function, where T (analogous to temperature in simulated annealing) is a properly chosen parameter which can change slowly with each generation. Also, by repeating the GA optimization procedure several times with different randomly chosen initial model populations, we derive “a very good subset” of models from the entire model space and calculate the a posteriori probability density σ(m) ∝ exp (E(m)/T). The σ(m) ’s are then used to calculate a “mean” model, which is found to be close to the true model.

Estimation of depth dependence of compressional velocity from cross correlation of measured and simulated waveforms

This article describes an approach for using broadband acoustic data to determine the depth dependence of the compressional (P) velocity in the upper several hundred meters of the seafloor in deep water areas. The technique used here does not rely upon ‘‘picks’’ of arrival time from acoustic data from many ranges or upon deconvolution of the received signal. Rather, the waveform of the first bottom bounce arrival at a single range is simulated and R (the ratio of the P-wave velocity of the sediment to the water sound speed) and g (the gradient of P-wave velocity) are adjusted to maximize the similarity between the measured and simulated signals. A low-frequency band is used to reduce complications caused by small scale layering in the seafloor and a long-range source is chosen to avoid acoustic interaction with the substrate. For an objective measure of similarity, Cmax, the maximum magnitude of the normalized cross-correlation function of measured and simulated time series is used. In the implementation discussed in this article, the simulated time series were produced by a ray-based computational model that includes eigenrays that travel through the seafloor. It was found that the dependence of Cmax on R and g is strong enough to allow precise estimates (within 10%) of their values. The procedure begins with waveforms simulated for the reported experimental geometry, measured sound velocity profile, measured or calculated source waveform, and initial estimates of geoacoustic parameters. First, the geometrical parameters are refined by maximizing Cmax with respect to the range and depth of source and receiver, and then the P-wave parameters are obtained by maximizing with respect to R and g. The method is demonstrated by obtaining R and g from explosive source data collected in an abyssal hills environment in the Pacific Ocean. Maximizing Cmax in the 25- to 250-Hz band yielded estimates of R and g that agree with reported values.

Molecular Dynamics of Coat Proteins of the Human Rhinovirus

Abstract The effects of the oxazole antiviral WIN 52084 on the thermal vibrations of the coat proteins of the human rhinovirus were studied by means of a comparison of two molecular dynamics simulations. One simulation involved only a protomeric unit (cluster of four proteins) of the viral coat, while the other included the antiviral drug bound to the protein cluster. Analysis of the RMS fluctations for all atoms indicates that the drug did not cause any statistically significant global changes in the amplitude of atomic motion. However, the RMS fluctuation of seventeen residues in the vicinity of the drug decreased by about 11%. Two global effects were observed. Most importantly, the drug was found to make the decay times of the atomic fluctuations more uniform. Also, the drug lowered the average correlation time for displacements of atoms in the drug-bound cluster. Finally, a comparison of the differences in the normalized cross-correlation functions of residues close to the binding site showed that the...

Cross-correlation analysis of intracellularly recorded synaptic activities: An evaluation of the method through computer simulation

Cross-correlation of ‘spontaneous’ synaptic activities intracellularly recorded from pairs of neurons may be used to detect shared synaptic input, which could remain hidden in the raw data by the non-synchronized postsynaptic potentials (PSPs); besides, if a normalized cross-correlation function is adopted, the fraction of synchronized activity may be quantitatively estimated. To evaluate power and limits of this method, computer-simulated synaptic activities of pairs of neurons, in which a given percentage of PSPs were simultaneous, were subjected to this type of analysis. It was shown that percentages of shared activities as low as 4% and in some cases 2% could be revealed, with a conspicuity which was influenced by the types of associated PSPs.