Accurate Displacement Estimation Research Articles

Accuracy of Displacement Estimation and Selection of Capacitors for a Four Degrees of Freedom Capacitive Force Sensor

Accuracy of Displacement Estimation and Selection of Capacitors for a Four Degrees of Freedom Capacitive Force Sensor

An Approach to Unbiased Subsample Interpolation for Motion Tracking

Accurate subsample displacement estimation is necessary for ultrasound elastography because of the small deformations that occur and the subsequent application of a derivative operation on local displacements. Many of the commonly used subsample estimation techniques introduce significant bias errors. This article addresses a reduced bias approach to subsample displacement estimations that consists of a two-dimensional windowed-sinc interpolation with numerical optimization. It is shown that a Welch or Lanczos window with a Nelder-Mead simplex or regular-step gradient-descent optimization is well suited for this purpose. Little improvement results from a sinc window radius greater than four data samples. The strain signal-to-noise ratio (SNR) obtained in a uniformly elastic phantom is compared with other parabolic and cosine interpolation methods; it is found that the strain SNR ratio is improved over parabolic interpolation from 11.0 to 13.6 in the axial direction and 0.7 to 1.1 in the lateral direction for an applied 1% axial deformation. The improvement was most significant for small strains and displacement tracking in the lateral direction. This approach does not rely on special properties of the image or similarity function, which is demonstrated by its effectiveness with the application of a previously described regularization technique.

Bayesian speckle tracking. Part I: an implementable perturbation to the likelihood function for ultrasound displacement estimation.

Accurate and precise displacement estimation has been a hallmark of clinical ultrasound. Displacement estimation accuracy has largely been considered to be limited by the Cramer-Rao lower bound (CRLB). However, the CRLB only describes the minimum variance obtainable from unbiased estimators. Unbiased estimators are generally implemented using Bayes' theorem, which requires a likelihood function. The classic likelihood function for the displacement estimation problem is not discriminative and is difficult to implement for clinically relevant ultrasound with diffuse scattering. Because the classic likelihood function is not effective, a perturbation is proposed. The proposed likelihood function was evaluated and compared against the classic likelihood function by converting both to posterior probability density functions (PDFs) using a noninformative prior. Example results are reported for bulk motion simulations using a 6λ tracking kernel and 30 dB SNR for 1000 data realizations. The canonical likelihood function assigned the true displacement a mean probability of only 0.070 ± 0.020, whereas the new likelihood function assigned the true displacement a much higher probability of 0.22 ± 0.16. The new likelihood function shows improvements at least for bulk motion, acoustic radiation force induced motion, and compressive motion, and at least for SNRs greater than 10 dB and kernel lengths between 1.5 and 12λ.

Dynamic Modeling of Nanoparticle Pushing Based on V-Shape Cantilevered AFM

In this paper, dynamics of pushing process based on V-shape cantilevered atomic force microscopy (VSC-AFM) is studied and the effect of VSC-AFM on required force and time of nanoparticle manipulation is discussed. The VSC is proved to be the most popular design, and the present model offers a more accurate estimation of nanoparticle displacement in pushing based on VSC-AFM. The proposed model takes both adhesion and normal friction forces into account. Pull-off forces are modeled using the Johnson–Kendall–Roberts model. Cantilever forces are modeled using various proposed stiffness models including Butt, Sader, and Neumeister and Ducker (ND) equations for normal stiffness Kz, and Hazel, ND equations for torsional stiffness Kθ, and lateral stiffness Ky by Sader et al. Results of simulations show that the assumption of parallel beam approximation theory is not accurate enough and therefore, it is not suitable for estimation of VSC stiffness in manipulation purposes. Moreover, in nanoparticle pushing based on VSC-AFM, the required pushing force is decreased in comparison with the obtained values based on rectangular cantilevered AFM (RC-AFM). The nanoparticle begins to move very soon with a VSC-AFM in comparison with a practically similar RC-AFM. Furthermore, as a comparison between torsional stiffness equations, ND and Hazel equations are examined. It is observed that Hazel equation are overestimated the torsional stiffness in comparison with ND.

3D coseismic Displacement of 2010 Darfield, New Zealand earthquake estimated from multi-aperture InSAR and D-InSAR measurements

Differential interferometric synthetic aperture radar (D-InSAR) measures ground deformation only along the line-of-sight (LOS) of the radar, which limits the capability of D-InSAR in investigating the surface damages and the focus mechanisms of earthquakes. We do a three-dimensional (3D) decomposition of the coseismic displacement of the Darfield, New Zealand earthquake that occurred on 3 September 2010 by exploiting the Multi-Aperture InSAR (MAI) and D-InSAR measurements from both ascending and descending L-band PALSAR data. Due to the dispersive nature of the ionosphere and the slight Doppler shift between the forward- and backward-looking interferograms, the ionospheric effects can be more serious in MAI measurements than in D-InSAR. We propose mitigating the ionospheric effects in the MAI processing with the directional filtering and interpolation procedure that has been applied in Offset-tracking. The rupture revealed by the 3D surface displacement fits closely to the Greendale fault, which is believed to be responsible for the earthquake. The horizontal ground motions, mostly eastwards in the hanging wall and westwards in the footwall, reached up to 2.5 m and are anti-symmetric with respect to the Greendale fault. Up to 2.5 m subsidence occurred in the hanging wall, while uplift is found in the footwall with an extreme case of 1.6 m in the far left of the fault. This makes us conclude that the Greendale fault is a normal and dextral strike-slip. It is seen that the MAI measurements are very helpful in the derivation of 3D coseismic displacement fields as it provides more accurate displacement estimation in the north–south direction.

Locally adaptive template sizes for matching repeat images of Earth surface mass movements

This paper presents an algorithm for locally adaptive template sizes in normalized cross-correlation (NCC) based image matching for measuring horizontal surface displacements of mass movements. After adaptively identifying candidate templates based on the image signal-to-noise ratio (SNR), the algorithm iteratively looks for the size at which the maximum cross-correlation coefficient attains a local peak and the matching position gets fixed. The algorithm is tested on modeled (deformed) images and applied to real bi-temporal images of different Earth surface mass movements. It is evaluated in comparison with globally (image-wide) fixed template sizes ranging from 11 to 101pixels based on the improvement in the accuracy of displacement estimation and the SNR of image reconstruction. The results show that the algorithm could reduce the error of displacement estimation by up to over 90% (in the modeled case) and improve the SNR of the matching by up to over four times compared to the globally fixed template sizes highly reducing the effects of geometric distortion and noise. The algorithm pushes terrain displacement measurement from repeat images one step forward towards full automation.

Measurement of Surface Displacement and Deformation of Mass Movements Using Least Squares Matching of Repeat High Resolution Satellite and Aerial Images

Displacement and deformation are fundamental measures of Earth surface mass movements such as glacier flow, rockglacier creep and rockslides. Ground-based methods of monitoring such mass movements can be costly, time consuming and limited in spatial and temporal coverage. Remote sensing techniques, here matching of repeat optical images, are increasingly used to obtain displacement and deformation fields. Strain rates are usually computed in a post-processing step based on the gradients of the measured velocity field. This study explores the potential of automatically and directly computing velocity, rotation and strain rates on Earth surface mass movements simultaneously from the matching positions and the parameters of the geometric transformation models using the least squares matching (LSM) approach. The procedures are exemplified using bi-temporal high resolution satellite and aerial images of glacier flow, rockglacier creep and land sliding. The results show that LSM matches the images and computes longitudinal strain rates, transverse strain rates and shear strain rates reliably with mean absolute deviations in the order of 10−4 (one level of significance below the measured values) as evaluated on stable grounds. The LSM also improves the accuracy of displacement estimation of the pixel-precision normalized cross-correlation by over 90% under ideal (simulated) circumstances and by about 25% for real multi-temporal images of mass movements.

Micro-pixel accuracy centroid displacement estimation and detector calibration

Conventional centroid estimation fits a template point spread function (PSF) to image data. Because the PSF is typically not known to high accuracy, systematic errors exist. Here, we present an accurate centroid displacement estimation algorithm by reconstructing the PSF from Nyquist-sampled images. In absence of inter-pixel response variations, this method can estimate centroid displacement between two 32×32 images to sub-micropixel accuracy. Inter-pixel response variations can be calibrated in Fourier space by using laser metrology. The inter-pixel variations of Fourier transforms of the pixel response functions can be conveniently expressed in terms of powers of spatial wavenumbers. Calibrating up to the third-order terms in the expansion, the displacement estimation is accurate to a few micro-pixels. This algorithm is applicable to a new mission concept of performing mirco-arcsecond level relative astrometry using a 1 m telescope for detecting terrestrial exoplanets and high-precision photometry missions.

MR-Guided Thermotherapy of Abdominal Organs Using a Robust PCA-Based Motion Descriptor

Thermotherapies can now be guided in real-time using magnetic resonance imaging (MRI). This technique is rapidly gaining importance in interventional therapies for abdominal organs such as liver and kidney. An accurate online estimation and characterization of organ displacement is mandatory to prevent misregistration and correct for motion related thermometry artifacts. In addition, when the ablation is performed with an extracorporal heating device such as high intensity focused ultrasound (HIFU), the continuous estimation of the organ displacement is the basis for the dynamic adjustment of the focal point position to track the targeted pathological tissue. In this paper, we describe the use of an optimized principal component analysis (PCA)-based motion descriptor to characterize in real-time the complex organ deformation during the therapy. The PCA was used to detect, in a preparative learning step, spatio-temporal coherences in the motion of the targeted organ. During hyperthermia, incoherent motion patterns could be discarded, which enabled improvements in motion estimation robustness, the compensation of motion related errors in thermal maps, and the adjustment of the beam position. The suggested method was evaluated for a moving phantom, and tested in vivo in the kidney and the liver of 12 healthy volunteers under free breathing conditions. The ability to perform a MR-guided thermotherapy in vivo during HIFU intervention was finally demonstrated on a porcine kidney.

Rate Distortion Analysis for Spatially Scalable Video Coding

In this paper, we derive the rate distortion lower bounds of spatially scalable video coding techniques. The methods we evaluate are subband and pyramid motion compensation where temporal redundancies in the same spatial layer as well as interlayer spatial redundancies are exploited in the enhancement layer encoding. The rate distortion bounds are derived from rate distortion theory for stationary Gaussian signals where mean square error is used as the distortion criteria. Assuming that the base layer is encoded by a non-scalable video coder, we derive the rate distortion functions for the enhancement layer, which depend on the power spectral density of the input signal, the motion prediction error probability density function and the base layer encoding performance. We will show that pyramid and subband methods are expected to outperform independently encoding the enhancement layer using motion-compensated prediction, in terms of rate distortion efficiency, when the base layer is encoded at a relatively higher quality or less accurate displacement estimation happens in the enhancement layer.

A Generalized Speckle Tracking Algorithm for Ultrasonic Strain Imaging Using Dynamic Programming

This study developed an improved motion estimation algorithm for ultrasonic strain imaging that employs a dynamic programming technique. In this article, we model the motion estimation task as an optimization problem. Since tissue motion under external mechanical stimuli often should be reasonably continuous, a set of cost functions combining correlation and various levels of motion continuity constraint were used to regularize the motion estimation. To solve the optimization problem with a reasonable computational load, a dynamic programming technique that does not require iterations was used to obtain displacement vectors in integer precision. Then, a subsample estimation algorithm was used to calculate local displacements in fractional precision. Two implementation schemes were investigated with in vivo ultrasound echo data sets. We found that the proposed algorithm provides more accurate displacement estimates than our previous algorithm for in vivo clinical data. In particular, the new algorithm is capable of tracking motion in more complex anatomy and increases strain image consistency in a sequence of images. Preliminary results also suggest that a significantly longer sequence of high contrast strain images could be obtained with the new algorithm compared with the previous algorithm. The new algorithm can also tolerate larger motion discontinuities ( e.g., cavity in an anthropomorphic uterine phantom). (E-mail: jjiang2@wisc.edu)

Ambulatory Estimation of Center of Mass Displacement During Walking

The center of mass (CoM) and the center of pressure (CoP) are two variables that are crucial in assessing energy expenditure and stability of human walking. The purpose of this study is to estimate the CoM displacement continuously using an ambulatory measurement system. The measurement system consists of instrumented shoes with 6 DOF force/moment sensors beneath the heels and the forefeet. Moreover, two inertial sensors are rigidly attached to the force/moment sensors for the estimation of position and orientation. The estimation of CoM displacement is achieved by fusing low-pass filtered CoP data with high-pass filtered double integrated CoM acceleration, both estimated using the instrumented shoes. Optimal cutoff frequencies for the low-pass and high-pass filters appeared to be 0.2 Hz for the horizontal direction and 0.5 Hz for the vertical direction. The CoM estimation using this ambulatory measurement system was compared to CoM estimation using an optical reference system based on the segmental kinematics method. The rms difference of each component of the CoM displacement averaged over a hundred trials obtained from seven stroke patients was ( 0.020 +/-0.007 ) m (mean +/- standard deviation) for the forward x-direction, ( 0.013 +/-0.005) m for the lateral y-direction, and ( 0.007 +/-0.001) m for the upward z-direction. Based on the results presented in this study, it is concluded that the instrumented shoe concept allows accurate and continuous estimation of CoM displacement under ambulatory conditions.

Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation

Many published research works regarding digital image correlation (DIC) have been focused on the improvements of the accuracy of displacement estimation. However, the original displacement fields calculated at discrete locations using DIC are unavoidably contaminated by noises. If the strain fields are directly computed by differentiating the original displacement fields, the noises will be amplified even at a higher level, and the resulting strain fields are untrustworthy. Based on the principle of local least-square fitting using two-dimensional (2D) polynomials, a 2D Savitzky-Golay (SG) digital differentiator is deduced and used to calculate strain fields from the original displacement fields obtained by DIC. The calculation process can be easily implemented by convolving the SG digital differentiator with the estimated displacement fields. Both homogeneous and inhomogeneous deformation images are employed to verify the proposed technique. The calculated strain fields clearly demonstrate that the proposed technique is simple and effective.

The combined effect of nonlinear filtration and window size on the accuracy of tissue displacement estimation using detected echo signals

In cardiac elastography, the regional strain and strain rate imaging is based on displacement estimation of tissue sections within the heart muscle carried out with various block-matching techniques (cross-correlation, sum of absolute differences, sum of squared differences, etc.). The accuracy of these techniques depends on a combination of ultrasonic imaging parameters such as ultrasonic frequency of interrogation, signal-to-noise ratio, size of a kernel used in a block-matching algorithm, type of data and speckle decorrelation. In this paper, we discuss the possibility to enhance the accuracy of the displacement estimation via nonlinear filtering of B-mode images before block-matching operation. The combined effect of a filter algorithm and a kernel size on the accuracy of the displacement estimation is analyzed using a 36-frame sequence of grayscale B-mode images of a human heart acquired by an ultrasound system operating at 1.77 MHz. It is shown that the nonlinear filtering of images enables to obtain the desired accuracy (less than one pixel) of the displacement estimation with smaller kernels than without filtering. These results are obtained for two filters––an adaptive anisotropic diffusion filter and a nonlinear Gaussian filter chain.

Lateral Ambiguity Analysis of Complex One-Bit Correlational Method for Two-Dimensional Speckle-Echo Tracking

We have previously reported that highly accurate displacement estimation in the lateral direction is possible using the complex one-bit correlational method, and that the first practical application of dynamic distortion diagnosis has been realized. In this paper, in order to clarify displacement estimation performance of the complex one-bit correlational method, we report that the stepwise displacement response characteristics in the lateral direction were estimated using measured displacement data. Furthermore, the relationship between the point spread function (PSF) of the measurement system and the estimation capacity was obtained by computer simulation.

General motion estimation from correlation sonar

The displacement of a sonar array can be estimated accurately using the correlation of bottom reverberation signals, at successive sweeps. This is the principle of the pulsed correlation log. In this paper, the conditions and accuracy of array horizontal translation estimation are analyzed. The case of a three-dimensional array is considered first, to show that in this case arbitrary translation and rotation can be estimated. The case of a plane array is then analyzed and it is shown that such an array allows estimation of horizontal translation. The derivation relies on modeling the space-time correlation function of bottom reverberation, which is assumed isotropic. Both directive and omnidirectional transmissions are considered. Accuracy of displacement estimates are derived, showing the influence of wavelength, grazing angle, bandwidth, number of overlapping hydrophones, and reverberation-to-noise ratio.

On Accurate and Robust Estimation of Fundamental Matrix

This paper is concerned with accurate and robust estimation of the fundamental matrix. We show that, given certain conditions, a basic linear algorithm can yield excellent accuracy, in some cases two orders of magnitude better than sophisticated algorithms. The key element of the success is the relative accuracy of displacement estimates used as input and the use of statistical distribution of the errors. We propose a low-level, gradient-based (as opposed to feature-based) algorithm based on the Hough Transform to extract the low-level measurements. We show that it is much more efficient, both in terms of computational expense and accuracy of the final estimate, to remove the errors in the intermediate representation (optic-flow) than to attempt to improve the final estimate by complicated nonlinear algorithms. Experimental results are also included.

General motion estimation from correlation sonar

The displacement of a sonar array can be estimated accurately using the correlation of bottom reverberation signals, at successive sweeps. This is the principle of the pulsed correlation log. In this paper, the conditions and accuracy of array horizontal translation estimation are analyzed. The case of a three-dimensional array is considered first, to show that in this case arbitrary translation and rotation can be estimated. The case of a plane array is then analyzed and it is shown that such an array allows estimation of horizontal translation. The derivation relies on modeling the space-time correlation function of bottom reverberation, which is assumed isotropic. Both directive and omnidirectional transmissions are considered. Accuracy of displacement estimates are derived, showing the influence of wavelength, grazing angle, bandwidth, number of overlapping hydrophones, and reverberation-to-noise ratio.

Error analysis in acoustic elastography. II. Strain estimation and SNR analysis.

Accurate displacement estimates are required to obtain high-quality strain estimates in elastography. In this paper the strain variance is derived from the statistical properties of the displacement field to define a point signal-to-noise ratio for elastography (SNR0). Displacements caused by compressional forces applied along the axis of the transducer beam are modeled by scaling and shifting the axial reflectivity profile of the tissue. The strain variance is given as a function of essential experimental parameters, such as the amount of tissue compression, echo waveform window length, and the amount of window overlap. SNR0 is defined in terms of applied compression and strain variance and normalized by the input signal-to-noise ratio (SNRi) for echo signals, to formulate the performance metric SNR0/SNRi. This quantity characterizes the noise properties, dynamic range, and sensitivity of strain images based on the spatial resolution requirements. The results indicate that low noise, high sensitivity, and limited dynamic range strain images are obtained for high-frequency bandpass signals when the applied strain is small. For large strains, however, one strategy for low-noise strain imaging employs base-band signals to obtain images with large dynamic range but limited peak sensitivity and noise figure. A better strategy includes companding, which eliminates the average strain in the echo signal before cross-correlation to reduce the dynamic range requirement and increase peak sensitivity for strain estimates.

A spatial correlation technique for estimating velocity fields using molecular tagging velocimetry (MTV)

A direct spatial image correlation technique is presented for estimating the Lagrangian displacement vector from image pairs based on molecular tagging diagnostics. The procedure provides significant improvement in measurement accuracy compared to existing approaches for molecular tagging velocimetry (MTV) analysis. Furthermore, this technique is of more general utility in that it is able to accommodate other laser tagging patterns besides the usual grid arrangement. Simulations are performed to determine the effects of many experimental and processing issues on the sub-pixel accuracy of displacement estimates. The results provide guidelines for optimizing the implementation of MTV. Experimental data in support of this processing technique are provided.