Displacement Estimation Error Research Articles

Displacement field estimation for a two-dimensional structure using fiber Bragg gratingsensors

The structure shape itself is of great interest for many aerospace applications. For example,the stability of the surface shape of large, high precision or space reflectors isessential for the communication performance. The knowledge of static and dynamicdisplacements of these structures would provide the possibility to enhance theirperformance by appropriate countermeasures. During operation, however, the directmeasurement of displacements of the whole structure is often difficult. This studyinvestigates whole displacement field estimation using strain measurement and adisplacement–strain-transformation approach. The use of fiber Bragg gratings (FBGs) asstrain sensors for this application offers the possible implementation of an integrated sensornetwork including many measurement points within only a few optical fibers.This paper discusses many issues related to the displacement field estimation ofa dynamically excited plate using a transformation matrix based on a modalapproach. In order to reduce systematic displacement estimation errors due toaliasing, a parametric study was performed and the sensor locations were optimized.Experimental validation was also conducted using a cantilever plate equipped with 16FBG sensors in an optimized configuration. The estimated displacements showedgood agreements with those measured directly from laser displacement sensors.

Elasticity reconstruction from displacement and confidence measures of a multi-compressed ultrasound RF sequence

Ultrasound elasticity imaging shows promise as a new way for early detection of cancers by assessing the elastic characteristics of soft tissue. So far the commonly used approach involves solving the so-called inverse elasticity problem of recovering elastic parameters from displacement measurements. We propose a finite-elementbased nonlinear scheme to estimate the elasticity distribution of soft tissue from multi-compressed ultrasound radio frequency (RF) data. An experimental ultrasound workstation has been developed to acquire multi-compressed data. A composite probe was employed as the compression plate. The contact forces and torques were acquired at the same time as imaging. Axial displacements under different static loads are estimated from the RF data before and after deformation using a cross-correlation technique. The confidence of displacement estimates is employed as a weighting factor in solving the objective function describing the inverse elasticity reconstruction problem. A novel splitand- merge strategy is employed over the image sequence in which strain images are used to provide a priori knowledge of the relative stiffness distribution of the tissue to constrain the inverse problem solution. The experimental study has allowed us to investigate the performance of our approach in the controlled environment of simulated and phantom data. For a simulated single inclusion model with 5% axial displacement estimation error, the L2-error between the target and the reconstructed Young's modulus was found to be about 1%. In vivo validation of the proposed method has been carried out and some preliminary results are presented.

A method for vector displacement estimation with ultrasound imaging and its application for thyroid nodular disease

Ultrasound elastography is a promising imaging technique that can assist in diagnosis of thyroid cancer. However, the complexity of the tissue movements under freehand compression requires the use of a parametric displacement model and a specific estimation method adapted to sub-pixel motion. Therefore, the aim of this study was to develop a motion estimation method for ultrasound elastography and test its performances compared to a classical block matching technique. The proposed method, referred to as Bilinear Deformable Block Matching (BDBM), uses a bilinear model with eight parameters for controlling the local mesh deformation. In addition, a technique of motion initialization based on a triangle scan of the images adapted to ultrasound elastography is proposed. The BDBM method includes an iterative multi-scale process. This iterative approach is shown to decrease the absolute error of the displacement estimation by a factor of 1.4 when passing from 1 to 2 iterations. The method was tested on simulated images and the results show that absolute displacement estimation error was reduced by a factor of 4 compared to classical block matching. We applied the BDBM method on three experimental sets of data. In the first data set, a phantom designed for ultrasound elastography was used. The two other sets of data involve the thyroid gland and were acquired using freehand tissue compression by ultrasound probe of a clinical ultrasound scanner modified for research. A similarity measurement based on local cross-correlation shows that, for experimental data, the BDBM method outperforms the usual block matching.

Rate-Distortion Analysis of Motion-Compensated Interpolation at the Decoder in Distributed Video Coding

This letter analyzes the coding efficiency of distributed video coding (DVC) schemes that perform motion-compensated interpolation at the decoder. The decoder has access only to the key frames, when generating the side information for intermediate frames. Therefore, the true motion field necessary for this operation is not directly available, and the motion vectors must be estimated at the decoder side, thus introducing displacement estimation errors. The accuracy of the motion-compensated interpolation at the decoder depends on several factors: 1, the overall motion complexity; 2, the temporal coherence of the motion field; and 3, the temporal distance between successive key frames. Adopting a state-space model and a Kalman filtering framework, we obtain an estimate of the displacement error variance. This is used to determine the rate-distortion function of the overall coding scheme, that takes into account both intra-coded key frames and DVC-coded frames. The proposed model shows that motion-compensated interpolation is unable to achieve the coding efficiency of conventional motion-compensated predictive coding. In addition, the model provides a good estimate of the group of pictures size that optimizes the coding efficiency. Experimental results on real video sequences validate the results of the proposed model.

Adaptive interpolation filters and high-resolution displacements for video coding

Standardized hybrid video coding systems are based on motion compensated prediction with fractional-pel displacement vector resolution. In the recent video coding standard H.264/AVC, a displacement vector resolution of 1/4-pel is applied. In order to estimate and compensate these fractional-pel displacements, interpolation filters are used. So far, these interpolation filters are invariant. The same filter with the same filter-coefficients is applied for all sequences and for all images of a sequence. Therefore, it is not possible to consider nonstationary statistical properties of the video signal and the motion compensated prediction process like aliasing, quantization errors, and displacement estimation errors. This paper presents two techniques that improve the motion compensated prediction and accordingly the coding efficiency. The first technique applies an adaptive interpolation filter that uses filter-coefficients which are adapted once per image. The adapted filter-coefficients are coded and transmitted. The second technique is based on an increased displacement vector resolution of 1/8-pel. In combination, the developed techniques indicate bit-rate reductions up to 25 % compared to H.264/AVC.

Image processing of 2D resistivity data for imaging faults

A methodology to locate automatically limits or boundaries between different geological bodies in 2D electrical tomography is proposed, using a crest line extraction process in gradient images. This method is applied on several synthetic models and on field data set acquired on three experimental sites during the European project PALEOSIS where trenches were dug. The results presented in this work are valid for electrical tomographies data collected with a Wenner-alpha array and computed with an l 1 norm (blocky inversion) as optimization method. For the synthetic cases, three geometric contexts are modelled: a vertical and a dipping fault juxtaposing two different geological formations and a step-like structure. A superficial layer can cover each geological structure. In these three situations, the method locates the synthetic faults and layer boundaries, and determines fault displacement but with several limitations. The estimated fault positions correlate exactly with the synthetic ones if a conductive (or no superficial) layer overlies the studied structure. When a resistive layer with a thickness of 6 m covers the model, faults are positioned with a maximum error of 1 m. Moreover, when a resistive and/or a thick top layer is present, the resolution significantly decreases for the fault displacement estimation (error up to 150%). The tests with the synthetic models for surveys using the Wenner-alpha array indicate that the proposed methodology is best suited to vertical and horizontal contacts. Application of the methodology to real data sets shows that a lateral resistivity contrast of 1:5–1:10 leads to exact faults location. A fault contact with a resistivity contrast of 1:0.75 and overlaid by a resistive layer with a thickness of 1 m gives an error location ranging from 1 to 3 m. Moreover, no result is obtained for a contact with very low contrasts (∼1:0.85) overlaid by a resistive soil. The method shows poor results when vertical gradients are greater than horizontal ones. This kind of image processing technique should be systematically used for improving the objectiveness of tomography interpretation when looking for limits between geological objects.

A modified block matching method for real-time freehand strain imaging.

This manuscript reports a technical innovation that has been developed for real-time, freehand strain imaging. This work is based on a well-known block-matching algorithm with two significant modifications. First, since displacements are estimated row-by-row, displacement estimates from the previous row are used to predict the displacement estimates in the current row, thereby drastically reducing the search-region size and increasing computational efficiency. Second, a displacement error detection and correction method is developed to overcome the local tracking errors that may be more severe with freehand scanning and thereby improve the robustness of the algorithm. This algorithm has been implemented on a clinical ultrasound imaging system, and with real-time imaging feedback, long sequences of high quality strain images are observed using freehand compression. Displacement estimation errors with this method are experimentally measured and compared with results from simulation. We report only a specific implementation, with no comparison to other displacement estimators in the literature and no optimization of this specific technique. Images of tissue-mimicking phantoms with small spherical targets are used to test the ability to detect small lesions using the strain imaging technique. In vivo strain images of breast and thyroid are also shown.

A new technique for real-time freehand ultrasonic elasticity imaging

A method for high-speed, freehand ultrasonic elasticity imaging will be described. The method is based on a modified block matching technique. The modification serves two purposes. First, in order to achieve real-time performance a forward prediction mechanism is used to reduce the computational load that a conventional block matching technique requires. Second, in order to accommodate the waveform decorrelation associated with freehand scanning a statistical error detection and correction method was developed. This prevents the displacement estimation errors from propagating to affect a larger area. This new algorithm has been implemented on a Siemens Elegra (a high-end clinical ultrasound imaging system). The initial tests show that the new system can perform B-mode and strain display task at real-time frame rates. The strain images have low noise and excellent contrast. Some results obtained with this system will also be presented. [Support by USAMRAA DAMD17-00-1-0596, NSF BES-9708221, and Siemens Medical Systems is gratefully acknowledged.]

Adaptive strain estimation using retrospective processing [medical US elasticity imaging

Because errors in displacement and strain estimates depend on the magnitude of the induced strain, the strain signal-to-noise ratio (SNR) will be a function of the applied deformation. If deformation is applied at the body surface, it is difficult during data acquisition to select a single surface displacement providing the highest strain SNR throughout the image. By applying continuous deformation and capturing data in real-time, the surface displacement providing the highest strain SNR can be selected retrospectively. A method to adaptively optimize strain SNR over the image plane using retrospective processing is presented and demonstrated with experimental results.

Testing the limitations of 2-D companding for strain imaging using phantoms

Companding may be used as a technique for generating low-noise strain images. It involves warping radio-frequency echo fields in two dimensions and at several spatial scales to minimize decorrelation errors in correlation-based displacement estimates. For the appropriate experimental conditions, companding increases the sensitivity and dynamic range of strain images without degrading contrast or spatial resolution significantly. In this paper, we examine the conditions that limit the effectiveness of 2-D local companding through a series of experiments using phantoms with tissue-like acoustic and elasticity properties. We found that strain noise remained relatively unchanged as the applied compression increased to 5% of the phantom height, while target contrast increased in proportion to the compression. Controlling the image noise at high compressions improves target visibility over the broad range induced in elastically heterogeneous media, such as biological tissues. Compressions greater than 5% introduce large strains and complex motions that reduce the effectiveness of companding. Control of boundary conditions and ultrasonic data sampling rates is critical for a successful implementation of our algorithms.

The Efficiency of Motion-Compensating Prediction for Hybrid Coding of Video Sequences

Performance bounds for generalized hybrid coding of video sequences with motion-compensating prediction are derived based on rate-distortion theory. It is shown that the spatial power spectrum of the motion-compensated prediction error can be calculated from the signal power spectrum and the displacement estimation error p.d.f.. A spatial Wiener filter can improve the efficiency of motion-compensating prediction. Memoryless encoding of the motion-compensated prediction error and intraframe encoding of the motion-compensated prediction error are compared. An evaluation of the rate-distortion functions for a typical videoconference sampling format shows that for integer pel accuracy of the displacement estimate the additional gain by motion-compensating prediction over pure intraframe coding is limited to ∼ 0.8 bits/sample in moving areas. Required accuracies of the displacement estimate for a gain of motion-compensating interframe coding over intraframe coding are given.