Two-dimensional Gaussian regression for sub-pixel displacement estimation in particle image velocimetry or particle position estimation in particle tracking velocimetry

An explicit solution of two-dimensional Gaussian regression for the estimation of particle displacement from the correlation function in particle image velocimetry (PIV) or particle position from the images in particle tracking velocimetry (PTV) with sub-pixel accuracy is introduced. The accuracy and the ability of the methods to avoid pixel locking due to non-axially orientated, elliptically shaped particle images or correlation peaks are investigated using simulated and experimentally obtained images.     

PIV measurement of flow around an arbitrarily moving body

This paper presents a PIV (particle image velocimetry) image processing method for measuring flow velocities around an arbitrarily moving body. This image processing technique uses a contour-texture analysis based on user-defined textons to determine the arbitrarily moving interface in the particle images. After the interface tracking procedure is performed, the particle images near the interface are transformed into Cartesian coordinates that are related to the distance from the interface. This transformed image always has a straight interface, so the interrogation windows can easily be arranged at certain distances from the interface. Accurate measurements near the interface can then be achieved by applying the window deformation algorithm in concert with PIV/IG (interface gradiometry). The displacement of each window is evaluated by using the window deformation algorithm and was found to result in acceptable errors except for the border windows. Quantitative evaluations of this method were performed by applying it to computer-generated images and actual PIV measurements.     

High-precision sub-pixel interpolation in particle image velocimetry image processing

The task of image interpolation and re-sampling for particle image velocimetry (PIV) is investigated, which is used for window shifting with sub-pixel accuracy and image or window deformation. A new interpolation scheme based on a Gaussian filter is introduced and compared with commonly used and widely accepted interpolation techniques in terms of the achievable root mean square deviation of the displacement estimates.     

Direct measurement of local instantaneous laminar burning velocity by a new PIV algorithm

This paper presents a new experimental approach using PIV technique to measure the local instantaneous laminar burning velocity of a stretched premixed flame. Up to now, from experimental techniques, this physical property was only accessible in average and the instantaneous interactions of flame with flow structures, mixture variations and walls could not be considered. In the present work, the local burning velocity is measured as the difference between the local flame speed and the local fresh gas velocity at the entrance of the flame zone. Two original methods are proposed to deduce these quantities from pair of particle images. The local flame speed is measured from the distance between two successive flame positions. For the flame localization, a new extraction tool combined with a filtering technique is proposed to access to the flame front coordinates with sub-pixel accuracy. The local fresh gas velocity near the flame front is extracted from the maximum of the normal velocity profile, located within 1 mm ahead of the flame front. To achieve the required spatial resolution, a new algorithm based on adaptive interrogation window scheme has been developed by taking into account the flow and flame front topologies. The accuracy and reliability of our developments have been evaluated from two complementary approaches based, respectively, on synthetic images of particle and on the well-established configuration of outwardly propagating spherical flames. In the last part of the paper, an illustration of the potentials of our new approach is shown in the case of a laminar flame propagating through a stratified mixture.     

基于数字图像体相关的物体内部三维位移场分析

在二维数字图像相关算法的基础上,推导了三维数字图像体相关算法,并应用于物体内部的三维位移场分析。用计算机模拟方法对SR-CT重建的物体内部三维图像施加已知变形,对变形前后三维数字图像进行体相关运算,获得三维位移场。在计算亚像素位移时,本文提出了一种三维的基于灰度梯度的算法,给出了梯度函数,阐述了数字模拟三维体相关的计算过程,通过数字模拟实验证明了算法的正确性和可靠性。     

A novel architecture for a super-resolution PIV algorithm developed for the improvement of the resolution of large velocity gradient measurements

Three different particle image processing algorithms have been developed for the improvement of PIV velocity measurements characterized by large velocity gradients. The objectives of this study are to point out the limitations of the standard processing methods and to propose a complete algorithm to enhance the measurement accuracy. The heart of the PIV image processing is a direct cross-correlation calculation in order to obtain complete flexibility in the choice of the size and the shape of the interrogation window (IW). An iterative procedure is then applied for the reduction of the size of IW at each measurement location. This procedure allows taking into account the local particle concentration in the image. The results of this first iterative processing, applied to synthetic images, show both a significant improvement of measurement accuracy and an increase of the spatial resolution. Finally, a super-resolution algorithm is developed to further increase the spatial resolution of the measurement by determining the displacement of each particle. The computer time for a complete image processing is optimized by the introduction of original data storage in Binary Space Partitions trees. It is shown that measurement errors for large velocity gradient flows are similar to those obtained in simpler cases with uniform translation displacements. This last result validates the ability of the developed super-resolution algorithm for the aerodynamic characterization of large velocity gradient flows.     

Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations

High-efficiency and high-accuracy deformation analysis using digital image correlation (DIC) has become increasingly important in recent years, considering the ongoing trend of using higher resolution digital cameras and common requirement of processing a large sequence of images recorded in a dynamic testing. In this work, to eliminate the redundant computations involved in conventional DIC method using forward additive matching strategy and classic Newton–Raphson (FA-NR) algorithm without sacrificing its sub-pixel registration accuracy, we proposed an equivalent but more efficient DIC method by combining inverse compositional matching strategy and Gauss-Newton (IC-GN) algorithm for fast, robust and accurate full-field displacement measurement. To this purpose, first, an efficient IC-GN algorithm, without the need of re-evaluating and inverting Hessian matrix in each iteration, is introduced to optimize the robust zero-mean normalized sum of squared difference (ZNSSD) criterion to determine the desired deformation parameters of each interrogated subset. Then, an improved reliability-guided displacement tracking strategy is employed to achieve further speed advantage by automatically providing accurate and complete initial guess of deformation for the IC-GN algorithm implemented on each calculation point. Finally, an easy-to-implement interpolation coefficient look-up table approach is employed to avoid the repeated calculation of bicubic interpolation at sub-pixel locations. With the above improvements, redundant calculations involved in various procedures (i.e. initial guess of deformation, sub-pixel displacement registration and sub-pixel intensity interpolation) of conventional DIC method are entirely eliminated. The registration accuracy and computational efficiency of the proposed DIC method are carefully tested using numerical experiments and real experimental images. Experimental results verify that the proposed DIC method using IC-GN algorithm and the existing DIC method using classic FA-NR algorithm generate similar results, but the former is about three to five times faster. The proposed reliability-guided IC-GN algorithm is expected to be a new standard full-field displacement tracking algorithm in DIC.     

Suggestive correctional methods for PIV image biasing caused by a rotating mirror system

A rotating mirror is widely used to generate the velocity shift that can resolve the directional ambiguities of PIV (particle image velocimetry) measurements. The rotating mirror system inevitably creates the normal displacement of the resulting PIV images and causes systematic image errors. Two corrective methods are proposed to eliminate or reduce the image biasing in PIV system. The use of two linearly traversing mirrors, instead of a single rotating mirror, shows that image biasing can be eliminated and the velocity shift well generated. As a second option, two co-rotating mirrors, instead of one, can reduce the image biasing with a maximum velocity shift available. Detailed imaging kinematics of the two suggestive methods are presented to lead to designing of practical devices that improve the PIV capabilities by reducing the systematic image errors. The authors like to acknowledge the partial financial support provided from the Turbo and Power Machinery Research Center (TPMRC) of Seoul National University, Seoul, Korea.     

Measurement of instantaneous Eulerian acceleration fields by particle image accelerometry: method and accuracy

Acceleration is a fundamental quantity in fluid mechanics because it reflects the sum of all forces (pressure and viscous) present within the flow. However, measurements of acceleration have been difficult to achieve relative to the ease with which fluid velocity can be measured. A particle image accelerometer (PIA) has been developed to measure Eulerian acceleration fields by time-differencing successive measurements of the Eulerian velocity field as measured by particle image velocimetry (PIV). The measurements can also be made in uniformly translating frames. With current video camera technology, it is often not possible to measure the two velocity fields with a time separation sufficiently small enough to permit accurate finite difference approximation of the time derivative. A two-CCD-camera system has been developed to alleviate this limitation. Polarization filtering is utilized to separate the particle images viewed by each camera. The polarization filtering is achieved using cross-polarized light-sheets and a polarization filter just upstream of the imaging optics of the cameras. In this manner, PIV measurements can be achieved easily at time delays several orders of magnitude smaller than the shutter-time of the CCD cameras. The accuracy of the acceleration measurements is determined by numerical finite differencing errors and random noise and bias errors associated with the measurement of velocity. These errors, and methods of compensating for them, are studied.     

Assessment of Digital Image Correlation Measurement Accuracy in the Ultimate Error Regime: Improved Models of Systematic and Random Errors

The literature contains many studies on assessment of DIC uncertainties, particularly in the ultimate error regime, when the shape function used to describe the material transformation perfectly matches the actual transformation. For pure sub-pixel translations, bias and random errors obtained for experimental or synthetic images show more complex evolution versus the fractional part of displacement than those predicted by the existing theoretical models. Indeed, small deviations arise, mainly around integer values of imposed displacements for noisy images, and they are interpreted as the unrepresentativeness of the underlying hypotheses of the theoretical models. In a first step, differences between imposed and measured displacements are analysed: random error is independent of fractional displacement, and systematic error does not decrease for values close to integer displacements whatever the noise level. Therefore, new prediction models are proposed based on the analysis of identified phenomena from synthetic speckle-pattern 8-bit images. The statistical approach used in this paper generalizes the methods proposed in the literature and mimics the experimental methodology usually used for displacement measurements performed in different subsets in the same image. Two closed-form expressions for the systematic and random errors and a linear interpolation scheme are developed. These models, depending only on image properties and the imposed displacement, are built with a very limited number of parameters. It is then possible to predict the evolution of bias and random errors from one to four images.     

Direct measurement of the vorticity field in digital particle images

A new method called direct measurement of vorticity (DMV) for digital particle images is described in this paper. Unlike previous methods for calculating the vorticity in particle image velocimetry (PIV), the vorticity is determined directly from the average angular displacement of rotation between two matched patterns. In order to improve the stability and precision of the angular displacement, polar coordinates are used instead of Cartesian coordinates to depict gray level patterns. The results of a Monte Carlo simulation of an Oseen-vortex flow indicate that the accuracy of the DMV method is independent of the spatial resolution of the velocity sampling, and the errors in the velocity field will not be propagated into the vorticity field as occurs with some finite difference methods. Therefore, the DMV method is a good method to be used to extract the vorticity field from velocity data that has higher levels of uncertainty. Received: 26 November 1999/Accepted: 30 October 2000     

Background extraction from double-frame PIV images

This study presents a simple image pre-processing scheme to extract background information from double-frame particle image velocimetry (PIV) images. Everything that stays stagnant in the image (e.g., image background and light reflections from stationary objects) is assumed to be a source of disturbance and is removed by subtracting the second frame of the image pair from the first frame. This yields a single frame difference image, which is transferred back to a background extracted double-frame image. After the procedure the background in the image does not correlate with itself anymore and therefore a bias error in PIV analysis towards zero displacement is avoided. The simulations show that the procedure conserves the profile of tracer particle images when a displacement between the frames is larger than a particle image size. The performance of this procedure is emphasized with various examples, and extensions of the procedure are introduced. The extended procedure extracts background objects that move between the image frames, e.g. dispersed phase particles in a two-phase flow or laser light sheet reflections from moving objects.     

An orthogonal-plane PIV technique for the investigations of three-dimensional vortical structures in a turbulent boundary layer flow

An experimental investigation was carried out regarding a three-dimensional topology of a zero-pressure gradient turbulent boundary layer. In this study, the polarization separation technique has been applied to the PIV measurements. Two mutually perpendicular measurement planes have been employed in x–y and x–z planes, respectively. Synchronization between a stereoscopic PIV with another plane PIV system was made toward the detection of such salient features of the coherent structure as the legs and the head of the hairpin vortices. Polarization rotation via a half-waveplate and subsequent particle image separation using polarizer minimized the spurious particle images. The PIV results clearly demonstrate the presence of hairpin-like coherent vortical structures and coincidence between the near-wall quasi-streamwise vortex pair and the legs of the hairpin vortex.     

Volumetric correlation PIV: a new technique for 3D velocity vector field measurement

A method is proposed that allows three-dimensional (3D) two-component measurements to be made by means of particle image velocimetry (PIV) in any volume illuminated over a finite thickness. The method is based on decomposing the cross-correlation function into various contributions at different depths. Because the technique is based on 3D decomposition of the correlation function and not reconstruction of particle images, there is no limit to particle seeding density as experienced by 3D particle tracking algorithms such as defocusing PIV and tomographic PIV. Correlations from different depths are differentiated by the variation in point spread function of the lens used to image the measurement volume over that range of depths. A number of examples are demonstrated by use of synthetic images which simulate micro-PIV (μPIV) experiments. These examples vary from the trivial case of Couette flow (linear variation of one velocity component over depth) to a general case where both velocity components vary by different complex functions over the depth. A final validation—the measurement of a parabolic velocity profile over the depth of a microchannel flow—is presented. The same method could also be applied using a thick light sheet in macro-scale PIV and in a stereo configuration for 3D three-component PIV.     

Statistical investigation of errors in particle image velocimetry

The accuracy of the particle image velocimetry technique was investigated using synthetic images having known characteristics. Algorithms were developed to extract two-dimensional velocity information by tracking particles between successive frames of a movie automatically without operator assistance. This allowed to parametrically investigate the influence of the various parameters (image contrast, image noise, particle density, distribution of sizes of particles and particle displacement between frames) on the accuracy of the technique. It was found that as long as the images have a good contrast, particle locations can be determined with sub-pixel accuracy and particle velocities can be determined within a few percent.     

The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings

 This paper describes how the accuracy for estimating the location of the displacement-correlation peak in (digital) particle image velocimetry (PIV) can be optimized by the use of a window offset equal to the integer-pixel displacement. The method works for both cross-correlation analysis of single-exposure image pairs and multiple-exposure images. The effect is predicted by an analytical model for the statistical properties of estimators for the displacement, and it is observed in the analysis of synthetic PIV images of isotropic turbulence, and in actual measurements of grid-generated turbulence and of fully-developed turbulent pipe flow. Received: 29 April 1996/Accepted: 29 October 1996     

Development and validation of echo PIV

The combination of ultrasound echo images with digital particle image velocimetry (DPIV) methods has resulted in a two-dimensional, two-component velocity field measurement technique appropriate for opaque flow conditions including blood flow in clinical applications. Advanced PIV processing algorithms including an iterative scheme and window offsetting were used to increase the spatial resolution of the velocity measurement to a maximum of 1.8 mm×3.1 mm. Velocity validation tests in fully developed laminar pipe flow showed good agreement with both optical PIV measurements and the expected parabolic profile. A dynamic range of 1 to 60 cm/s has been obtained to date.     

Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings

Non-scanning volume flow measurement techniques such as 3D-PTV, holographic and tomographic particle image velocimetry (PIV) permit reconstructions of all three components (3C) of velocity and vorticity vectors in a fluid volume (3D). In this study, we present a novel 3D3C technique termed Multiple-Color-Plane Stereo Particle-Image-Velocimetry (color PIV), which allows instantaneous measurements of 3C velocity vectors in six parallel, colored light sheets. We generated the light sheets by passing white light of two strobes through dichroic color filters and imaged the slices by two 3CCD color cameras in Stereo-PIV configuration. The stereo-color images were processed by custom software routines that sorted each colored fluid particle into one of six gray-scale images according to its hue, saturation, and luminance. We used conventional Stereo PIV cross-correlation algorithms to compute a 3D planar vector field for each light sheet and subsequently interpolated a volume flow map from the six vector fields. As a first application, we quantified the wake and axial flow in the vortical structures of a robotic insect (fruit fly) model wing. In contrast to previous findings, the measured data indicate strong axial flow components on the upper wing surface, including axial flow in the leading-edge vortex core. Collectively, color PIV is robust against mechanical misalignments, avoids laser safety issues, and computes instantaneous 3D vector fields in a fraction of the time typical for other 3D systems. Color PIV might thus be of value for volume measurements of highly unsteady flows.     

3-Component acceleration field measurement by dual-time stereoscopic particle image velocimetry

In this article, a multiplane stereo-particle image velocimetry (PIV) system was implemented and validated to measure the three-component acceleration field in a plane of turbulent flows. The employed technique relies on the use of two stereoscopic particle image velocimetry (SPIV) systems to measure pairs of velocity fields superimposed in space but shifted in time. The time delay between the two velocity fields enables the implementation of a finite difference scheme to compute temporal derivatives. The use of two synchronized SPIV systems allows us to overcome the limited acquisition rate of PIV systems when dealing with highly turbulent flows. Moreover, a methodology based on the analysis of the spectral error distribution is described here to determine the optimal time delay to compute time derivatives. The present dual-time SPIV arrangement and the proposed analysis method are applied to measure three-component acceleration fields in a cross section of a subsonic plane turbulent mixing layer.     

A scanning PIV method for fine-scale turbulence measurements

A hybrid technique is presented that combines scanning PIV with tomographic reconstruction to make spatially and temporally resolved measurements of the fine-scale motions in turbulent flows. The technique uses one or two high-speed cameras to record particle images as a laser sheet is rapidly traversed across a measurement volume. This is combined with a fast method for tomographic reconstruction of the particle field for use in conjunction with PIV cross-correlation. The method was tested numerically using DNS data and with experiments in a large mixing tank that produces axisymmetric homogeneous turbulence at \(R_\lambda \simeq 219\) . A parametric investigation identifies the important parameters for a scanning PIV set-up and provides guidance to the interested experimentalist in achieving the best accuracy. Optimal sheet spacings and thicknesses are reported, and it was found that accurate results could be obtained at quite low scanning speeds. The two-camera method is the most robust to noise, permitting accurate measurements of the velocity gradients and direct determination of the dissipation rate.