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Full-Text Articles in Engineering

In Vivo Ultrasonic Attenuation Slope Estimates For Detecting Cervical Ripening In Rats: Preliminary Results, Timothy A. Bigelow, Barbara L. Mcfarlin, William D. O'Brien Jr., Michael L. Oelze Mar 2008

In Vivo Ultrasonic Attenuation Slope Estimates For Detecting Cervical Ripening In Rats: Preliminary Results, Timothy A. Bigelow, Barbara L. Mcfarlin, William D. O'Brien Jr., Michael L. Oelze

Timothy A. Bigelow

To effectively postpone preterm birth, cervical ripening needs to be detected and delayed. As the cervix ripens, the spacing between the collagen fibers increases and fills with water, hyaluronan, decorin, and enzymes suggesting that the ultrasonic attenuation of the cervix should decrease. The decrease in ultrasonic attenuation may be detectable, leading to an effective means of detecting cervical ripening. Herein, the traditional attenuation slope-estimation algorithm based on measuring the downshift in center frequency of the ultrasonic backscattered signal with propagation depth was modified and applied to the cervix of rats. The modified algorithm was verified using computer simulations and an …


Cognitive State Estimation In Mobile Environments, Michael C. Dorneich, Santosh Mathan, Patricia May Ververs, Stephen D. Whitlow Jan 2008

Cognitive State Estimation In Mobile Environments, Michael C. Dorneich, Santosh Mathan, Patricia May Ververs, Stephen D. Whitlow

Michael C. Dorneich

This chapter presents the unique challenges encountered, difficult trade-offs required, and promising techniques em-ployed when moving cognitive state assessment from the la-boratory to a mobile field environment.


Estimation Of Second Order Phase Transition Temperature Of The Orthorhombic Phase Of Gd5(Sixge1−X)4 Using Arrott Plots, Ravi L. Hadimani, Y. Melikhov, J. E. Snyder, David C. Jiles Jan 2008

Estimation Of Second Order Phase Transition Temperature Of The Orthorhombic Phase Of Gd5(Sixge1−X)4 Using Arrott Plots, Ravi L. Hadimani, Y. Melikhov, J. E. Snyder, David C. Jiles

David C. Jiles

Gd5(SixGe1−x)4 for 0.41⩽x⩽0.5 is orthorhombic and ferromagnetic at lower temperature, monoclinic and paramagnetic at higher temperature, and shows a first order magnetic-structural phase transition between the two. Magnetic moment versus magnetic field (MH) isotherms were measured just above the first order transitiontemperature for Gd5Si1.95Ge2.05 and Gd5Si2Ge2 samples and the field-induced coupled phase transition from paramagnetic/monoclinic to ferromagnetic/orthorhombic phase was observed. Using the method developed by Arrott [Phys. Rev.108, 1394 (1957)], the ferromagnetic portions of the MH isotherms were used to project the second order magnetic phase transitiontemperature of the orthorhombic phase, a region where the transition does not occur due …


Supporting Real-Time Cognitive State Classification On A Mobile Individual, Michael C. Dorneich, Stephen D. Whitlow, Santosh Mathan, Patricia May Ververs, Deniz Erdogmus, Andre Adami, Misha Pavel, Tian Lan Jan 2007

Supporting Real-Time Cognitive State Classification On A Mobile Individual, Michael C. Dorneich, Stephen D. Whitlow, Santosh Mathan, Patricia May Ververs, Deniz Erdogmus, Andre Adami, Misha Pavel, Tian Lan

Michael C. Dorneich

The effectiveness of neurophysiologically triggered adaptive systems hinges on reliable and effective signal processing and cognitive state classification. Although this presents a difficult technical challenge in any context, these concerns are particularly pronounced in a system designed for mobile contexts. This paper describes a neurophysiologically derived cognitive state classification approach designed for ambulatory task contexts. We highlight signal processing and classification components that render the electroencephalogram (EEG) -based cognitive state estimation system robust to noise. Field assessments show classification performance that exceeds 70% for all participants in a context that many have regarded as intractable for cognitive state classification using …


Markov Chain Monte Carlo Defect Identification In Nde Images, Aleksandar Dogandžić, Benhong Zhang Jan 2007

Markov Chain Monte Carlo Defect Identification In Nde Images, Aleksandar Dogandžić, Benhong Zhang

Aleksandar Dogandžić

We derive a hierarchical Bayesian method for identifying elliptically‐shaped regions with elevated signal levels in NDE images. We adopt a simple elliptical parametric model for the shape of the defect region and assume that the defect signals within this region are random following a truncated Gaussian distribution. Our truncated‐Gaussian model ensures that the signals within the defect region are higher than the baseline level corresponding to the noise‐only case. We derive a closed‐form expression for the kernel of the posterior probability distribution of the location, shape, and defect‐signal distribution parameters (model parameters). This result is then used to develop Markov …


Including Effects Of Microstructure And Anisotropy In Theoretical Models Describing Hysteresis Of Ferromagnetic Materials, H. Hauser, Y. Melikhov, David C. Jiles Jan 2007

Including Effects Of Microstructure And Anisotropy In Theoretical Models Describing Hysteresis Of Ferromagnetic Materials, H. Hauser, Y. Melikhov, David C. Jiles

David C. Jiles

Two recent theoreticalhysteresis models (Jiles-Atherton model and energetic model) are examined with respect to their capability to describe the dependence of the magnetization on magnetic field, microstructure, and anisotropy. It is shown that the classical Rayleigh law for the behavior of magnetization at low fields and the Stoner-Wohlfarth theory of domain magnetization rotation in noninteracting magnetic single domain particles can be considered as limiting cases of a more general theoretical treatment of hysteresis in ferromagnetism.


Impact Of Local Attenuation Approximations When Estimating Correlation Length From Backscattered Ultrasound Echoes, Timothy A. Bigelow, William D. O'Brien Jul 2006

Impact Of Local Attenuation Approximations When Estimating Correlation Length From Backscattered Ultrasound Echoes, Timothy A. Bigelow, William D. O'Brien

Timothy A. Bigelow

Estimating the characteristic correlation length of tissue microstructure from the backscattered power spectrum could improve the diagnostic capability of medical ultrasound. Previously, size estimates were obtained after compensating for source focusing, the frequency-dependent attenuation along the propagation path (total attenuation), and the frequency-dependent attenuation in the scattering region (local attenuation). In this study, the impact of approximations of the local attenuation on the scatterer size estimate was determined using computer simulations and theoretical analysis. The simulations used Gaussian impedance distributions with an effective radius of 25 μm randomly positioned in a homogeneous half-space sonified by a spherically focused source (f/1 …


Signal Processing Strategies That Improve Performance And Understanding Of The Quantitative Ultrasound Spectral Fit Algorithm, Timothy A. Bigelow, William D. O'Brien Sep 2005

Signal Processing Strategies That Improve Performance And Understanding Of The Quantitative Ultrasound Spectral Fit Algorithm, Timothy A. Bigelow, William D. O'Brien

Timothy A. Bigelow

Quantifying the size of the tissue microstructure using the backscattered power spectrum has had limited success due to frequency-dependent attenuation along the propagation path, thus masking the frequency dependence of the scatterer size. Previously, the SPECTRAL FIT algorithm was developed to solve for total attenuation and scatterer size simultaneously [Bigelow et al., J. Acoust. Soc. Am. 117, 1431-1439 (2005)]. Herein, the outcomes from signal processing strategies on the SPECTRAL FIT algorithm are investigated. The signal processing methods can be grouped into two categories, viz., methods that improve the performance of the algorithm and methods that provide insight. The methods that …


A Model For Estimating Ultrasound Attenuation Along The Propagation Path To The Fetus From Backscattered Waveforms, Timothy A. Bigelow, William D. O'Brien Aug 2005

A Model For Estimating Ultrasound Attenuation Along The Propagation Path To The Fetus From Backscattered Waveforms, Timothy A. Bigelow, William D. O'Brien

Timothy A. Bigelow

Accurate estimates of the ultrasound pressure and/or intensity incident on the developing fetus on a patient-specific basis could improve the diagnostic potential of medical ultrasound by allowing the clinician to increase the transmit power while still avoiding the potential for harmful bioeffects. Neglecting nonlinear effects, the pressure/intensity can be estimated if an accurate estimate of the attenuation along the propagation path (i.e., total attenuation) can be obtained. Herein, a method for determining the total attenuation from the backscattered power spectrum from the developing fetus is proposed. The boundaries between amnion and either the fetus' skull or soft tissue are each …


Estimation Of Total Attenuation And Scatterer Size From Backscattered Ultrasound Waveforms, Timothy A. Bigelow, Michael L. Oelze, William D. O'Brien Mar 2005

Estimation Of Total Attenuation And Scatterer Size From Backscattered Ultrasound Waveforms, Timothy A. Bigelow, Michael L. Oelze, William D. O'Brien

Timothy A. Bigelow

Quantitative ultrasound techniques using backscattered echoes have had limited success in vivo due to the frequency-dependent attenuation along the entire propagation path masking the frequency dependence of the backscatter. Herein, total attenuation and scatterer size are estimated simultaneously by an analysis of the in vivo backscattered power spectrum using two approaches. The simulations used to evaluate the two approaches used frequencies between 4 and 11 MHz with an effective scatterer radius of 25 μm. The first approach was based on approximations of the in vivo backscattered power spectrum (i.e., assumed Gaussian function), wherein attenuation and size were estimated by assuming …


Scatterer Size Estimation In Pulse-Echo Ultrasound Using Focused Sources: Calibration Measurements And Phantom Experiments, Timothy A. Bigelow, William D. O'Brien Jul 2004

Scatterer Size Estimation In Pulse-Echo Ultrasound Using Focused Sources: Calibration Measurements And Phantom Experiments, Timothy A. Bigelow, William D. O'Brien

Timothy A. Bigelow

In a companion paper [T. A. Bigelow and W. D. O'Brien Jr., J. Acoust. Soc. Am. 116, 578 (2004)], theory, supported by simulations, showed that accurate scatterer size estimates could be obtained using highly focused sources provided that the derived generalized attenuation-compensation function was used and the velocity potential field near the focus could be approximated as a three-dimensional Gaussian. Herein, the theory is further evaluated via experimental studies. A calibration technique is developed to find the necessary equivalent Gaussian dimensions for a focused source using reflections obtained from a rigid plane scanned through the focus. Then, the theoretical analysis …


Scatterer Size Estimation In Pulse-Echo Ultrasound Using Focused Sources: Theoretical Approximations And Simulation Analysis, Timothy A. Bigelow, William D. O'Brien Jul 2004

Scatterer Size Estimation In Pulse-Echo Ultrasound Using Focused Sources: Theoretical Approximations And Simulation Analysis, Timothy A. Bigelow, William D. O'Brien

Timothy A. Bigelow

The speckle in ultrasound images has long been thought to contain information related to the tissue microstructure. Many different investigators have analyzed the frequency characteristics of the backscattered signals to estimate the scatterer acoustic concentration and size. Previous work has been mostly restricted to unfocused or weakly focused ultrasound sources, thus limiting its implementation with diagnostically relevant fields. Herein, we derive equations capable of estimating the size of a-scatterer for any reasonably focused source provided that the velocity potential field in the focal region can be approximated as a three-dimensional Gaussian beam, scatterers are a sufficient distance from the source, …


A Superior Tool For Airline Operations, Michael C. Dorneich, Stephen D. Whitlow, Christopher A. Miller, John A. Allen Jan 2004

A Superior Tool For Airline Operations, Michael C. Dorneich, Stephen D. Whitlow, Christopher A. Miller, John A. Allen

Michael C. Dorneich

The Diversion Off-Gate Management Assistant (DOGMA) is a decision support tool that mitigates problems in making diversion decisions in the airline industry. DOGMA helps inexperienced dispatchers to provide superior and consistent diversion decisions that translate into minimizing the impact of time-critical diversion decisions and increasing the airline's ability to recover from severe schedule disruptions. The tool integrates multiple information sources to improve dispatchers' situation awareness of the current state of flight, aircraft, maintenance, crew, and passenger schedules.


Cramér-Rao Bounds For Estimating Range, Velocity, And Direction With An Active Array, Aleksandar Dogandžić, Arye Nehorai Jan 2001

Cramér-Rao Bounds For Estimating Range, Velocity, And Direction With An Active Array, Aleksandar Dogandžić, Arye Nehorai

Aleksandar Dogandžić

We derive Cramer-Rao bound (CRB) expressions for the range (time delay), velocity (Doppler shift), and direction of a point target using an active radar or sonar array. First, general CRB expressions are derived for a narrowband signal and array model and a space-time separable noise model that allows both spatial and temporal correlation. We discuss the relationship between the CRB and ambiguity function for this model. Then, we specialize our CRB results to the case of temporally white noise and the practically important signal shape of a linear frequency modulated (chirp) pulse sequence. We compute the CRB for a three-dimensional …


Estimating Evoked Dipole Responses In Unknown Spatially Correlated Noise With Eeg/Meg Arrays, Aleksandar Dogandžić, Arye Nehorai Jan 2000

Estimating Evoked Dipole Responses In Unknown Spatially Correlated Noise With Eeg/Meg Arrays, Aleksandar Dogandžić, Arye Nehorai

Aleksandar Dogandžić

We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current dipoles at fixed locations and the head as a spherical conductor. We permit the dipoles' moments to vary with time by modeling them as linear combinations of parametric or nonparametric basis functions. We estimate the dipoles' locations and moments and derive the Cramer-Rao bound for the unknown parameters. We also propose an ML based method for scanning the brain response data, …


Facial Features Localization In Front View Head And Shoulders Images, Adnan M. Alattar, Sarah A. Rajala Mar 1999

Facial Features Localization In Front View Head And Shoulders Images, Adnan M. Alattar, Sarah A. Rajala

Sarah A. Rajala

The computerized process of locating human facial features such as the eyes, nose and mouth in a head and shoulders image is crucial to such applications as automatic face identification and model-based video coding. A new model-based algorithm for locating these major features is developed. The algorithm estimates the parameters of the ellipse which best fits the head view in the image and uses these parameters to calculate the estimated locations of the facial features. It then refines the estimated coordinates of the eyes, mouth, and nose by exploiting the vertical and horizontal projections of the pixels in windows around …


Error Analysis For The Numerical Evaluation Of The Diagonal Forms Of The Scalar Spherical Addition Theorem, S. Koc, Jiming Song, W. C. Chew Jan 1999

Error Analysis For The Numerical Evaluation Of The Diagonal Forms Of The Scalar Spherical Addition Theorem, S. Koc, Jiming Song, W. C. Chew

Jiming Song

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate -but fast - methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained. The error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed. The total error introduced in …


Conductivity Of A Periodic Particle Composite With Spheroidal Inclusions, Nicola Harfield Jan 1999

Conductivity Of A Periodic Particle Composite With Spheroidal Inclusions, Nicola Harfield

Nicola Bowler

The effective electrical conductivity of a two-phase material consisting of a lattice of identical spheroidal inclusions in a continuous matrix is determined analytically. The inclusions are located at the node points of a simple-cubic lattice and the axis of rotation of each spheroid coincides with one of the lattice vectors, such that the spheroids are aligned with each other and with the lattice. With an electric field applied in the direction of the rotation axes of the spheroids, the electric potential is found by solving Laplace's equation. The solution is found by analytically continuing the interstitial field into the particle …


Theory Of Thin-Skin Eddy-Current Interaction With Surface Cracks, Nicola Harfield, John R. Bowler Jan 1997

Theory Of Thin-Skin Eddy-Current Interaction With Surface Cracks, Nicola Harfield, John R. Bowler

Nicola Bowler

Eddy-current non-destructive evaluation is commonly performed at relatively high frequencies at which the skin depths are significantly smaller than the dimensions of a typical crack. A thin-skin analysis of eddy currents is presented in which the electromagnetic fields on the crack faces are described in terms of a potential which obeys a two-dimensional Laplace equation. Solutions of this equation for defects in both magnetic and non-magnetic materials are determined by applying thin-skin boundary conditions at the crack perimeter. The impedance change of an eddy-current coil due to the defect is then calculated by numerical evaluation of one-dimensional integrals over the …


Subband Absolute Moment Block Truncation Coding, Kai-Kuang Ma, Sarah A. Rajala Jan 1996

Subband Absolute Moment Block Truncation Coding, Kai-Kuang Ma, Sarah A. Rajala

Sarah A. Rajala

In this paper, a new subband coding system called subband absolute moment block truncation coding (SAMBTC) is introduced to compress monochrome images and color images recorded in YIQ and L*u*v* uniform color spaces. The SAMBTC incorporates full‐band absolute moment block truncation coding (AMBTC) into subbands along with a new subband dynamic bit allocation algorithm which is derived from the Shannon rate‐distortion bound. Simulation results show that the proposed Shannon/bound‐based bit allocation algorithm outperforms the commonly used standard‐deviation‐based bit allocation scheme. Compared with ABMTC, SAMBTC achieves superior imaging without blocking artifacts at low bit rates


Low‐Frequency Perturbation Theory In Eddy‐Current Non‐Destructive Evaluation, Nicola Harfield, Y. Yoshida, John R. Bowler Jan 1996

Low‐Frequency Perturbation Theory In Eddy‐Current Non‐Destructive Evaluation, Nicola Harfield, Y. Yoshida, John R. Bowler

Nicola Bowler

A method is presented by which series solutions for the impedance change in an eddy‐current test probe due to closed cracks in a non‐magnetic, conducting half‐space can be derived at low frequency. The series solution is applicable for flaws whose dimensions are much smaller than the electromagnetic skin‐depth. The problem is formulated using an approach in which the flaw is represented by an equivalent distribution of current dipoles. The electric field scattered by the flaw is then written as an integral, over the flaw, of the product of the dipole density distribution and an appropriate Green’s function. Terms in the …


Three-Dimensional Location Estimation Of Trajectories Of Point Targets Using A Projection-Based Transformation Method, Jae-Ho Choi, Sarah A. Rajala Mar 1995

Three-Dimensional Location Estimation Of Trajectories Of Point Targets Using A Projection-Based Transformation Method, Jae-Ho Choi, Sarah A. Rajala

Sarah A. Rajala

A new computational approach for determining the parameters that characterize the locations of trajectories of point targets in a 3-D space is described. The targets of concern are dim, unresolved point targets moving along straight paths across the same field of view. Since the target's signal-to-noise ratio is low and the spatial extent of the target is less than a pixel, one must rely on integration over a target track that spans many image frames. The proposed method estimates these parameters by transforming the entire set of time-sequential images of a constant field of view into the projection space by …


Impact Of Human Visual Perception Of Color On Very Low Bit-Rate Image Coding, Sarah A. Rajala Sep 1994

Impact Of Human Visual Perception Of Color On Very Low Bit-Rate Image Coding, Sarah A. Rajala

Sarah A. Rajala

One of the keys to obtaining acceptable quality imagery/video encoded at very low bit rates is to transmit only that information which is critical to human perception. To successfully achieve this goal, one must not only understand the human visual system, but be able to utilize this information in the design of their codec. This paper will present an overview of the properties associated with color science and human visual perception, and how they could make an impact on very low bit-rate image coding.


Reducing Respiratory Artifacts In Chest Mr Images Through Hybrid Space Motion Tracking And Postprocessing, John N. Campbell, Wesley E. Snyder, Peter Santago Ii, Sarah A. Rajala, Craig A. Hamilton May 1994

Reducing Respiratory Artifacts In Chest Mr Images Through Hybrid Space Motion Tracking And Postprocessing, John N. Campbell, Wesley E. Snyder, Peter Santago Ii, Sarah A. Rajala, Craig A. Hamilton

Sarah A. Rajala

A new postprocessing method of correcting for respiratory motion induced artifacts in MRI is presented. The motion of the chest during respiration is modeled as a combination of translation and dilation. Displacements of the chest wall are tracked via a thin, MR-sensitive plate placed on the patient's chest during a scan. Scanning with phase encoding left/right (L/R) and frequency encoding anterior/posterior (A/P) causes the motion artifacts to be repeated in the L/R direction, thus not overlapping on the plate. By performing the inverse A/P Fourier transform, the resulting hybrid space data has A/P spatial data and L/R spatial frequency data, …


Use Of Extrapolation In Computing Color Look-Up Tables, Sarah A. Rajala, H. Joel Trussell, Atish P. Kakodkar Apr 1994

Use Of Extrapolation In Computing Color Look-Up Tables, Sarah A. Rajala, H. Joel Trussell, Atish P. Kakodkar

Sarah A. Rajala

Colorimetric reproduction requires calibrated color output devices. One way to characterize a color output device is with a 3D look-up table which maps the tristimulus values, t, to the control values, c of the output device. The functional form of the output device can be written in vector notation as t equals F(c). The purpose of calibration is to define an inverse mapping from tristimulus values to control values. Since the function F((DOT)) has no closed form, it is defined by interpolation from a table of values. Given a set of control values ]ci[ on a regular grid and the …


Analysis Of Eddy‐Current Interaction With A Surface‐Breaking Crack, Nicola Harfield, John R. Bowler Jan 1994

Analysis Of Eddy‐Current Interaction With A Surface‐Breaking Crack, Nicola Harfield, John R. Bowler

Nicola Bowler

The change in electromagnetic impedance of a conductor due to the presence of a long, perpendicular surface‐breaking crack in a normally incident, uniform electric field is calculated in closed form in the high‐frequency limit. At high frequencies, where the skin depth is much smaller than the depth of the crack, the fields near the edge and corners of the crack are effectively decoupled. This means that the solution may be formulated as the sum of contributions from the corners, faces, and edge of the crack. Simple analytical expressions for the electric field are found and used to calculate the impedance …


Eddy Current Interaction With An Ideal Crack, Part I: The Forward Problem, John R. Bowler Jan 1994

Eddy Current Interaction With An Ideal Crack, Part I: The Forward Problem, John R. Bowler

John R. Bowler

The impedance of an eddy-current probe changes when the current it induces in an electrical conductor is perturbed by a flaw such as a crack. In predicting the probe signals, it is expedient to introduce idealizations about the nature of the flaw. Eddy-current interaction is considered with an ideal crack having a negligible opening and acting as a impenetrable barrier to electric current. The barrier gives rise to a discontinuity in the electromagnetic field that has been calculated by finding an equivalent electrical source distribution that produces the same effect. The choice of source is between a current dipole layer …


Eddy-Current Interaction With An Ideal Crack. Ii. The Inverse Problem, John R. Bowler, David Harrison, Steve Norton Jan 1994

Eddy-Current Interaction With An Ideal Crack. Ii. The Inverse Problem, John R. Bowler, David Harrison, Steve Norton

John R. Bowler

Eddy-current inversion is the process whereby the geometry of a flaw in a metal is derived from electromagnetic probe measurements. An inversion scheme is described for finding the shape and size of cracks from eddy-current probe impedance measurements. The approach is based on an optimization scheme that seeks to minimize a global error function quantifying the difference between predicted and observed probe impedances. The error minimum is sought using a standard descent algorithm that requires a knowledge of the gradient of the error with respect to a variation of the flaw geometry. Computation of the gradient is based on a …


Parallel Image Segmentation Using A Hopfield Neural Network With Annealing Schedule For Neural Gains, Yungsik Kim, Sarah A. Rajala Oct 1993

Parallel Image Segmentation Using A Hopfield Neural Network With Annealing Schedule For Neural Gains, Yungsik Kim, Sarah A. Rajala

Sarah A. Rajala

Neural network architectures have been proposed as new computer architectures and a Hopfield neural network has been shown to find good solutions very fast in solving complex optimization problems. It should be noted, however, that a Hopfield neural network with fixed neural gains only guarantees to find local optimum solutions, not the global optimum solution. Image segmentation, like other engineering problems, can be formalized as an optimization problem and implemented using neural network architectures if an appropriate optimization function is defined. To achieve a good image segmentation, the global or the nearly global optimum solutions of the appropriate optimization function …


Optimum Displacement Estimates Using Mean Field Annealing, Ikhlas M. Abdelqader, Sarah A. Rajala, Griff L. Bilbro, Wesley E. Snyder Jun 1993

Optimum Displacement Estimates Using Mean Field Annealing, Ikhlas M. Abdelqader, Sarah A. Rajala, Griff L. Bilbro, Wesley E. Snyder

Sarah A. Rajala

In this paper a new algorithm to estimate dense displacement fields from a sequence of images is developed. The algorithm is based on modeling the displacement fields as Markov Random fields. The Markov Random fields-Gibbs equivalence is then used to convert the problem into one of finding an appropriate energy function that describes the motion and any constraints imposed on it. Mean field annealing, a technique which finds global minima in nonconvex optimization problems, is used to minimize the energy function, and solve for the optimum displacement fields. The algorithm results in accurate estimates even for scenes with noise or …