Phase-based Motion Estimation Research Articles

Enhancing Cable Vibration Measurement at Long Distances Through Super-Resolution Reconstruction and Target Foreground Segmentation

This paper presents a comprehensive non-contact computer vision-based system for monitoring cable vibrations in cable-supported bridges, addressing challenges related to low image resolution and feature extraction difficulties at long distances. The proposed system utilizes deep learning techniques to enhance cable vibration recognition accuracy and offers a practical solution for cable monitoring without the need for target assistance. The core of the system is a novel two-stage model, which combines a super-resolution (SR) video reconstruction algorithm with state-of-the-art Resnet-34 and Swin-B models for precise target foreground segmentation. This approach significantly improves the recognition of target details and enhances the accuracy of cable vibration data in monitoring videos. Furthermore, a phase-based motion estimation (PME) algorithm is employed for precise cable vibration measurement. Field tests conducted on two cable-supported bridges validate the effectiveness of the system. The results demonstrate superior accuracy and noise immunity compared to traditional methods, achieving sub-pixel level precision with a maximum error rate below 2%. This system represents a significant advancement in non-contact structural health monitoring for long-distance cable vibration monitoring in cable-supported bridges.

Motion estimation from noisy data with unknown distributions using multi-frame phase-preserving denoising

Phase-based motion estimation method is promising due to its high resolution and wide measurement range. Generally, noise exists in digital images and ruins the constant phase assumption of the same target among different frames. However, traditional image-denoising techniques do not consider the phase and result in inaccurate motion estimation. A novel phase-preserving denoising method considering multiple frames is proposed. In this approach, multi-scale and multi-orientation quadrature filters transform noisy images into complex pyramids to preserve the phase of the content. An instability indicator is designed to evaluate the relative noise intensity at each level of the complex pyramid among multiple frames. The threshold is then estimated to retain the phase of interest and reconstruct a denoised image with unknown noise distributions. Numerical and experimental examples demonstrate that the proposed method effectively preserves the phase of interest and decreases the error of the estimated motion, outperforming other typical denoising methods under various types of noise.

Vibration measurement from an adaptive phase-based motion estimation using parameter optimised log-Gabor filter

Phase-based motion estimation has gained popularity due to its sub-pixel accuracy and high-spatial resolution. Recently, various phase extraction techniques were incorporated to improve its motion extraction performance. However, existing methods cannot directly determine the filter parameters based on the motion estimation accuracy, instead relying on the local amplitude magnitude as the selection index, which may not directly prove that such a filter can give the best motion extraction results. This study proposes a data-driven approach to automatically select optimal filter parameters based on the accuracy of motion extraction. An optimisation algorithm and a synthetic video with predefined motion are combined to find the optimal filter parameters. Log-Gabor filter is introduced to extend the range of parameters. Simulation results demonstrate the feasibility and analyse the impact of various factors. The superiority is validated by a vibration experiment, which demonstrated a significantly higher level of motion extraction accuracy compared to other algorithms.

Phase-based motion estimation and SVR smooth for target-free 3D deformation measurement using stereophotogrammetry

Non-contact measurement methods based on computer vision have shown great potential for measuring structural surface displacement and strain due to their low cost and high efficiency. However, the traditional computer vision technology based on digital image correlation (DIC) is limited by its dependence on natural texture features of the surface and its susceptibility to environmental conditions, making it challenging to obtain effective and robust measurements of surface deformation. Additionally, these methods typically only focus on the structural response in the image plane, which makes it difficult to perform a comprehensive health assessment of complex structural components with asymmetry. Therefore, a time-domain visual measurement technique based on image phase information is proposed for measuring three-dimensional (3D) deformation of structures using stereophotogrammetry. The method involves extracting image phase information using 2D Gabor filters and applying it to dense optical flow estimation based on polynomial approximation and semi-global block matching (SGBM) for obtaining robust 3D displacement measurements. The support vector regression (SVR) is then used to perform hyperplane fitting of the original displacements for improving the smoothness of the 3D displacements. Finally, an intuitive strain conversion method is introduced to convert the 3D displacements into 3D strains. The performance of the proposed technique has been validated through numerical simulation experiments based on a physics-based graphics model (PBGM) in a synthetic environment. The robustness of the proposed method has been further proved through free attenuation vibration experiments on a steel ruler. The initial evaluation of the expected performance of the measurement plan has been enabled by performing a 1:1 reduction of the field measurement process in a synthetic environment. The results indicate that the proposed method is a promising method for accurately and reliably measuring structural deformation in both synthetic and real-world environments, especially for complex structural components with asymmetry.

Two-dimensional structural motion estimation via analytical signal enhancement of phase-based video processing

This paper concerns the use of phase information from image sequences for the extraction of structural two-directional motions. The phase-based motion estimation (PME) estimates local phase information via Gabor wavelet transform, and can only estimate the motion in single direction at a time, which will reduce the applicability and efficiency for many structures subject to more sophisticated bidirectional motions. This paper introduces a two-dimensional partial analytical signal to estimate the instantaneous phase and theoretically derives the relationship between the phase variations and the structure motion to achieve bidirectional motion estimations simultaneously. In addition to the analytical signal phase-based motion estimation (APME), this paper designs an ideal narrow-band filter (INF) addressing the limitation of the narrow frequency band in the analytical signals. In the proposed APME method, the acquisition of instantaneous phase improves the accuracy of structural bidirectional motion estimation. Moreover, the realization of the partial analytical signal is based on the fast Fourier transform (FFT) of the image and the dot product in the frequency domain, which bypasses the traditional PME convolution operation in the spatial domain. Therefore, the calculation efficiency of structural motion estimation is greatly improved. The proposed method is validated using a numerical simulation of a moving Gaussian surface with random motions. Results prove a good accuracy of the proposed APME method, and outperforming the traditional PME, the APME demonstrates an outstanding consistence to the true values (correlation coefficient 99.99%) four times better calculation efficiency. Further comparison with the experimental results of a cantilever beam also shows that the proposed method can better identify the structure bidirectional motion estimation.

Two-dimensional motion estimation using phase-based image processing with Riesz transform

As a kind of photogrammetry technique, phase-based motion estimation (PME) has proven to be a powerful image/video processing algorithm in the extraction of structural dynamics, due to its full-filed resolution and no requirement of surface preparation, compared to conventional structural testing. Although images and videos employed in PME are two-dimensional arrays, PME only extracts phase information in a single direction at a time. Therefore, extracting two-directional motions at the same time is needed to avoid two times of PME implementation. To address this issue, Riesz-transform is integrated to the phase-based motion estimation algorithm, and Riesz transform PME (RPME) is proposed in this work. The concept of plane phase is extended to spatial phase using Riesz transform to process images, because Riesz transform is able to extract phase information in two directions simultaneously. Then quaternion is utilized to derive the theoretical relationship between spatial phase and structure motions. In order to obtain the mono-component image sequence required in Riesz transform, an ideal narrow bandpass filter is constructed based on the set of Butterworth low-pass filters. Due to the capability of recognizing two-directional motions simultaneously using the proposed RPME, a much-improved efficiency of structural dynamics identification is observed. In addition, Riesz transform extracts instantaneous phase, thus the motion recognition accuracy is improved as well. To validate the benefit of RPME, both numerical simulation and laboratory-scale experiments are conducted, and motions in x and y directions are extracted simultaneously, with a drastically increased accuracy in both the simulation and experimental validations.

A novel marker for robust and accurate phase-based 2D motion estimation from noisy image data

Markers with high-contrast patterns are commonly used to improve the accuracy of image intensity-based motion estimation techniques. It has been proven that the phase, which can be extracted by using quadrature pair filters, is more robust to light condition changes than the intensity of the image. However, the marker design for utilizing and stabilizing the phases using phase-based motion estimation has rarely been studied, and errors from the nonlinear phase and sub-pixel motion due to the unique phase extraction process still need to be considered. Herein, we introduce a robust and accurate phase-based 2D motion estimation technique using a novel marker comprising an array of evenly spaced white squares and two complex Gabor filters. The causes of the nonlinear phase error and the sub-pixel motion error and their effects on motion estimation were established. With the novel marker design, the nonlinear phase error can be attenuated by using appropriate filter parameters while the sub-pixel motion error can be controlled by adjusting the marker orientations. The pattern of evenly spaced squares in an array also maximizes the filter response to improve the robustness of phase-based motion estimation against image noise. Experimental demonstrations of the two types of errors were carried out on a building structure by comparing the results from the proposed technique and laser Doppler velocimetry. The anti-noise performances were compared to the other markers, the Kernel-Based Optical Sensor, and the image intensity-based optical flow technique at various noise levels. The proposed technique was also applied to a real gas booster in low-light conditions with a maximum vibrating amplitude of 0.05 mm, which further demonstrated its accuracy and robustness.

Phase-based motion estimation in complex environments using the illumination-invariant log-Gabor filter

The phase-based motion estimation method is promising because the phase is sensitive to the motion information embedded in the pixel values. Unfortunately, complex environments such as extra textures and illumination changes exist in practice, whereas their effects have not been studied. This study theoretically discovers that the large spatial size and DC component of the filter adversely affect the performance of the motion estimation method under complex environments. The traditional method adopting the Gabor filter with a large bandwidth may suppress extra textures while cause a significant drift in the estimated motion due to the negative frequency and DC components. To tackle this, a log-Gabor-based new motion estimation method is proposed, in which the log-Gabor filter intrinsically without the DC and negative frequency components can extract the local phase and filter out the illumination change. A localization index based on the amplitude map is designed to determine the optimal parameters of the log-Gabor filter and maximize its spatial localization capability. Numerical and experimental examples demonstrate that the proposed method outperforms the traditional Gabor filter in motion estimation under the complex environment.

Vibration-based structural damage detection via phase-based motion estimation using convolutional neural networks

Detection of structural damage is a major concern for engineers. In recent years, convolutional neural networks (CNNs) have been used for feature extraction and classification of vibration signals that reveal structural damage. Damage detection by CNNs greatly depends on high-quality learning data which are usually difficult to be obtained in actual engineering scenarios. To solve this problem, we combine phase-based motion estimation (PME) with the use of CNNs. By PME method, each pixel in a video can be regarded as a separate displacement sensor. Thus, it is possible to obtain millions of vibration signals from a single video, greatly facilitating CNN applications. We used a two-story steel structure for experimental validation. It was demonstrated that only one measured video sample obtained under each structural condition is possible to train a CNN model accurately detecting the location and severity of bolt looseness damage. This verified the outstanding performance of the proposed method.

Streamlined particle filtering of phase-based magnified videos for quantified operational deflection shapes

Non-contact optical measurements are commonly used in industrial and research domains to obtain displacement measurements. This can be attributed to their noninvasive advantages over traditional instrumentation approaches. Phase-based motion estimation (PME) and magnification (PMM) are targetless methods that have been utilized recently to extract qualitative data from structures via experimental modal analysis (EMA) and operational modal analysis (OMA). Transforming the motion-magnified sequence of images into quantified operating deflection shape (ODS) vectors is currently being conducted via edge detection. Although effective, these methods require human supervision and interference; such that, accurate characteristics of the structure are guaranteed. Within this study, a new hybrid computer vision approach is introduced to extract the quantified ODS vectors from motion-magnified images with minimal human supervision. The particle filter (PF) point tracking method is utilized to track the desired feature points in the motion-magnified sequence of images. Moreover, the k-means clustering method is employed as an unsupervised learning approach to perform the segmentation of the particles and assign them to specific feature points in the motion-magnified sequence of images. Total variation denoising is used to smooth the motion-magnified artifacts, which improves ODS vector extraction and provides a robust outlier removal. The results show that the cluster centers can be applied to estimate the ODS vectors, and the performance of the proposed methodology is evaluated experimentally on a lab-scale cantilever beam.

Video-Based Vibration Measurement for Large Structure: A Spatiotemporal Disturbance-Adaptive Morphological Component Analysis

Recently, phase-based motion estimation method is able to extract the full-field vibration of large structure from video, which has attracted widely attention. However, it suffers from diverse disturbances in the realistic measurement, such as periodic texture pattern from the surface and shake caused by unstable tripod. To address this issue, a spatiotemporal disturbance-adaptive morphological component analysis (DAMCA) is proposed in this paper. This method focuses on separating texture component from structure component in each video frame, and separating shake component from vibration component in the global motion signal extracted from video. Firstly, it constructs a spatiotemporal model to remove the disturbances respectively from the space domain and time domain of the video. Subsequently, it incorporates morphological component analysis (MCA) into this model, aiming to obtain the optimal separation results in the space domain and time domain by finding the sparsest representations of different components. Finally, to adapt to various texture surfaces, MCA is developed in the space domain by exploiting the low rank structure of the texture’s sparse representation. Similarly, to adapt to various shake, MCA is also developed in the time domain. Simulated and actual test demonstrate the effectiveness and accuracy of the proposed method. Spatiotemporal DAMCA has valuable potential to acquire video-based vibration measurement for large structure with the disturbances involving texture surface and tripod shake.

Revealing Intraosseous Blood Flow in the Human Tibia With Ultrasound.

ABSTRACTIntraosseous blood circulation is thought to have a critical role in bone growth and remodeling, fracture healing, and bone disorders. However, it is rarely considered in clinical practice because of the absence of a suitable noninvasive in vivo measurement technique. In this work, we assessed blood perfusion in tibial cortical bone simultaneously with blood flow in the superficial femoral artery with ultrasound imaging in five healthy volunteers. After suppression of stationary signal with singular‐value‐decomposition, pulsatile blood flow in cortical bone tissue is revealed, following the heart rate measured in the femoral artery. Using a method combining transverse oscillations and phase‐based motion estimation, 2D vector flow was obtained in the cortex of the tibia. After spatial averaging over the cortex, the peak blood velocity along the long axis of the tibia was measured at four times larger than the peak blood velocity across the bone cortex. This suggests that blood flow in central (Haversian) canals is larger than in perforating (Volkmann's) canals, as expected from the intracortical vascular organization in humans. The peak blood velocity indicates a flow from the endosteum to the periosteum and from the heart to the foot for all subjects. Because aging and the development of bone disorders are thought to modify the direction and velocity of intracortical blood flow, their quantification is crucial. This work reports for the first time an in vivo quantification of the direction and velocity of blood flow in human cortical bone. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Structural motion estimation via Hilbert transform enhanced phase-based video processing

The non-contact sensing techniques using image/video processing have flourished in recent years benefited from the rapid development of digital cameras. However, high-fidelity motion extraction from acquired image frames is still challenging. A novel motion estimation method based on phase-domain image processing, named Hilbert phase-based motion estimation, is proposed in this study to identify motions in a more accurate and efficient manner if compared to traditional phase-based motion estimation. The theoretical relationship between phase variation and physical motion is established based on the Hilbert transform; and then in order to reduce the computation cost, the forward and inverse fast Fourier transforms are integrated with the Hilbert transform. Under the proposed framework, phase variations are therefore obtained from the corresponding analytical signal. Furthermore, peak-picking procedure and the Butterworth ideal band-pass filter are employed to decompose the original video to its mono-component signal prior to identifying displacements. The proposed method is verified using a synthetic video containing a bell-shaped surface with randomly assigned motions. The proposed Hilbert phase-based motion estimation approach avoids the influence from manual parameter selection, and the correlation coefficient of the identification results can reach 99.55%. Experimental verification using a simply supported beam is also deployed, and comparison with the state of the art demonstrates the outperformance of the proposed algorithm.

Computer vision‐based real‐time cable tension estimation in Dubrovnik cable‐stayed bridge using moving handheld video camera

Cables are essential components of the cable-stayed bridges as they serve as the main load-bearing component. Hence, continuous monitoring of such cables becomes necessary as they are vulnerable to the fatigue damage induced by dynamic loads. Sensors are attached to the cables to examine the health of the cables; however, these contact-based sensors can malfunction in harsh weather condition, which makes impossible to estimate the cable health in such unfavorable condition. Therefore, in this paper, we propose a completely noncontact video-based stay-cable tension measurement technique where the video is recorded using a moving handheld camera at a significant distance from the structure itself. Here, the cable tension is determined from vibration-based measurement, but the vibration of the cable recorded in the video includes the true vibration of the cable along with the camera motion. Hence, we amalgamated a series of image processing techniques to nullify the camera movement. First, we detect the camera movement based on the movement of the bridge deck and pylon, which are fixed objects, using Kanade–Lucas–Tomasi (KLT) feature tracking algorithm. Then we nullify the camera movement by using the affine transformation matrix obtained by random sample consensus (RANSAC) algorithm. Subsequently from the steady video, the cable motions are estimated using the phase-based motion estimation technique. From the time history of the cable vibration, real-time frequency variations are estimated using Short-Time Fourier Transform (STFT). Finally, the real-time tension is determined from this dominant frequency variation history using the taut-string theory. This paper shows the significant potential of camera-based sensing techniques in structural health monitoring as the mean estimated tension and the design cable tension are found to be comparable.

Clutter Filter Wave Imaging

The elastic properties of human tissue can be evaluated through the study of mechanical wave propagation captured using high frame rate ultrasound imaging. Methods such as block-matching or phase-based motion estimation have been used to estimate the displacement induced by the mechanical waves. In this paper, a new method for detecting mechanical wave propagation without motion estimation is presented, where the motion of interest is accentuated by an appropriate clutter filter. Thus, the mechanical wave propagation will directly appear as bands of the attenuated signal moving in the B-mode sequence and corresponding anatomical M-mode images. While only the locality of tissue velocity induced by the mechanical wave is detected, it is shown that the method is more sensitive to subtle tissue displacements when compared to motion estimation techniques. The technique was evaluated for the propagation of the pulse wave in a carotid artery, mechanical waves on the left ventricle, and shear waves induced by radiation force on a tissue-mimicking phantom. The results were compared to tissue Doppler imaging (TDI) and demonstrated that clutter filter wave imaging (CFWI) was able to detect the mechanical wave propagating in tissue with a relative temporal and spatial resolution 30% higher and a relative consistency 40% higher than TDI. The results showed that CFWI was able to detect mechanical waves with a relative frequency content 40% higher than TDI in a shear wave imaging experiment.

Vibration-based damage detection in wind turbine blades using Phase-based Motion Estimation and motion magnification

Vibration-based Structural Health Monitoring (SHM) techniques are among the most common approaches for structural damage identification. The presence of damage in structures may be identified by monitoring the changes in dynamic behavior subject to external loading, and is typically performed by using experimental modal analysis (EMA) or operational modal analysis (OMA). These tools for SHM normally require a limited number of physically attached transducers (e.g. accelerometers) in order to record the response of the structure for further analysis. Signal conditioners, wires, wireless receivers and a data acquisition system (DAQ) are also typical components of traditional sensing systems used in vibration-based SHM. However, instrumentation of lightweight structures with contact sensors such as accelerometers may induce mass-loading effects, and for large-scale structures, the instrumentation is labor intensive and time consuming. Achieving high spatial measurement resolution for a large-scale structure is not always feasible while working with traditional contact sensors, and there is also the potential for a lack of reliability associated with fixed contact sensors in outliving the life-span of the host structure. Among the state-of-the-art non-contact measurements, digital video cameras are able to rapidly collect high-density spatial information from structures remotely. In this paper, the subtle motions from recorded video (i.e. a sequence of images) are extracted by means of Phase-based Motion Estimation (PME) and the extracted information is used to conduct damage identification on a 2.3-m long Skystream® wind turbine blade (WTB). The PME and phased-based motion magnification approach estimates the structural motion from the captured sequence of images for both a baseline and damaged test cases on a wind turbine blade. Operational deflection shapes of the test articles are also quantified and compared for the baseline and damaged states. In addition, having proper lighting while working with high-speed cameras can be an issue, therefore image enhancement and contrast manipulation has also been performed to enhance the raw images. Ultimately, the extracted resonant frequencies and operational deflection shapes are used to detect the presence of damage, demonstrating the feasibility of implementing non-contact video measurements to perform realistic structural damage detection.

Feasibility of extracting operating shapes using phase-based motion magnification technique and stereo-photogrammetry

Optically-based vibration measurements can be used to determine the full-field dynamic response of structures without the need of mounted transducers (e.g. accelerometers, strain gages, and LVDTs) that can add cost, have wiring, power signal transmission issues, and may affect the dynamic characteristics by adding mass or stiffness. The three-dimensional digital image correlation (3D DIC) and three-dimensional point tracking (3DPT) methods based on a stereo-vision system can provide the full-field dynamic displacements of a structure with sub-pixel accuracy. However, stereo-photogrammetry systems are limited by camera resolution and intrinsic noise of the acquired images. Moreover, exciting a structure with only a small amount of energy may result in a subtle mechanical response that is not perceptible by observing the raw data of the conventional optical measurement systems (i.e. 3D DIC and 3DPT). Thus, in order to use the optical-sensing techniques to identify dynamic characteristics of a structure at high frequencies, the signal-to-noise ratio (SNR) in the sequence of images captured with a stereo-vision system needs to be improved. Within this paper, phase-based video magnification in conjunction with the stereo-photogrammetry techniques are used to measure the higher-frequency operating shapes of a cantilever beam and a 2.3-m long Skystream 4.7 wind turbine blade. The phase-based motion estimation method uses complex steerable pyramids to decompose the original sequence of images to amplitude and phase at different spatial resolutions (subsampled images). Motion information is conserved within the phase values which can be filtered in the time domain and amplified to detect the subtle motions. The magnified sequence of images using the motion magnification technique are post-processed using 3D DIC or 3DPT to quantify infinitesimal deformations that are not recognizable using only the traditional stereo-photogrammetry methods. The results obtained within this paper reveal the great potential of motion magnification in conjunction with stereo-photogrammetry techniques in detecting small motions of structures and extracting 3D operating shapes from the optically measured data with low SNR. Compared to traditional stereo-photogrammetry, additional modes of the test structures are obtainable by means of combining the phase based motion magnification and conventional image-sensing techniques (i.e. 3D DIC and 3DPT). The proposed methodology could be used to enhance the established procedure to extract more information about the dynamic characteristics of structures (only once effectively calibrated), compared to existing image-sensing techniques and contact measurement sensors.

Robust and high-frame-rate visualization of arterial pulse wave propagation dynamics

Crucial to the facilitation of early detection of vascular diseases is the development of new imaging techniques that can track vascular dynamics at sub-millisecond time resolution. Previously, we have designed new high-frame-rate ultrasound imaging solutions that can track complex flow dynamics at >1000 fps frame rate, thereby providing hemodynamic insights for vascular diagnostics. Here, we have expanded our suite of vascular diagnostic tools by developing new imaging modes for mapping the structural dynamics of arterial walls. We have particularly devised a novel framework for robust ultrasound-based mapping of the spatiotemporal dynamics of arterial pulse wave (PW) propagation. Our framework involves: 1) plane wave data acquisition; 2) eigen-based data processing; and 3) phase-based motion estimation. The eigen-processing module represents a novel application of singular value decomposition, and its purpose is to isolate the desired forward PW through identifying the corresponding left singular vector through a frequency analysis algorithm, thus making our framework robust against the biasing impact of PW reflections. Also, to visualize PW propagation, positions of PW front were mapped and trailed with its past positions. Using this new eigen-based PW visualization framework, we can now accurately identify differences in PW propagation dynamics in arterial segments of different wall thicknesses and wall elasticity. Corresponding cineloops will be shown at the meeting.

Full 3-D transverse oscillations: a method for tissue motion estimation.

We present a new method to estimate 4-D (3-D + time) tissue motion. The method used combines 3-D phase based motion estimation with an unconventional beamforming strategy. The beamforming technique allows us to obtain full 3-D RF volumes with axial, lateral, and elevation modulations. Based on these images, we propose a method to estimate 3-D motion that uses phase images instead of amplitude images. First, volumes featuring 3-D oscillations are created using only a single apodization function, and the 3-D displacement between two consecutive volumes is estimated simultaneously by applying this 3-D estimation. The validity of the method is investigated by conducting simulations and phantom experiments. The results are compared with those obtained with two other conventional estimation methods: block matching and optical flow. The results show that the proposed method outperforms the conventional methods, especially in the transverse directions.

Analytic signal phase-based myocardial motion estimation in tagged MRI sequences by a bilinear model and motion compensation.

Different mathematical tools, such as multidimensional analytic signals, allow for the calculation of 2D spatial phases of real-value images. The motion estimation method proposed in this paper is based on two spatial phases of the 2D analytic signal applied to cardiac sequences. By combining the information of these phases issued from analytic signals of two successive frames, we propose an analytical estimator for 2D local displacements. To improve the accuracy of the motion estimation, a local bilinear deformation model is used within an iterative estimation scheme. The main advantages of our method are: (1) The phase-based method allows the displacement to be estimated with subpixel accuracy and is robust to image intensity variation in time; (2) Preliminary filtering is not required due to the bilinear model. The proposed algorithm, integrating phase-based optical flow motion estimation and the combination of global motion compensation with local bilinear transform, allows spatio-temporal cardiac motion analysis, e.g. strain and dense trajectory estimation over the cardiac cycle. Results from 7 realistic simulated tagged magnetic resonance imaging (MRI) sequences show that our method is more accurate compared with state-of-the-art method for cardiac motion analysis and with another differential approach from the literature. The motion estimation errors (end point error) of the proposed method are reduced by about 33% compared with that of the two methods. In our work, the frame-to-frame displacements are further accumulated in time, to allow for the calculation of myocardial Lagrangian cardiac strains and point trajectories. Indeed, from the estimated trajectories in time on 11 in vivo data sets (9 patients and 2 healthy volunteers), the shape of myocardial point trajectories belonging to pathological regions are clearly reduced in magnitude compared with the ones from normal regions. Myocardial point trajectories, estimated from our phase-based analytic signal approach, seem therefore a good indicator of the local cardiac dynamics. Moreover, they are shown to be coherent with the estimated deformation of the myocardium.