Iterative multigrid approach in PIV image processing with discrete window offset

 The features of an improved algorithm for the interrogation of (digital) particle image velocimetry (PIV) pictures are described. The method is based on cross-correlation. It makes use of a translation of the interrogation areas. Such a displacement is predicted and corrected by means of an iterative procedure. In addition, while iterating, the method allows a refinement of the size of the interrogation areas. The quality of the measured vectors is controlled with data validation criteria applied at each intermediate step of the iteration process. A brief section explains the expected improvements in terms of dynamic range and resolution. The accuracy is assessed analysing images with imposed displacement fields. The improved cross-correlation algorithm has been applied to the measurement of the turbulent flow past a backward facing step (BFS). A systematic comparison is presented with Direct Numerical Simulation (DNS) data available on the subject. Received: 7 October 1997/Accepted: 11 August 1998     

Intensity Capping: a simple method to improve cross-correlation PIV results

A common source of error in particle image velocimetry (PIV) is the presence of bright spots within the images. These bright spots are characterized by grayscale intensities much greater than the mean intensity of the image and are typically generated by intense scattering from seed particles. The displacement of bright spots can dominate the cross-correlation calculation within an interrogation window, and may thereby bias the resulting velocity vector. An efficient and easy-to-implement image-enhancement procedure is described to improve PIV results when bright spots are present. The procedure, called Intensity Capping, imposes a user-specified upper limit to the grayscale intensity of the images. The displacement calculation then better represents the displacement of all particles in an interrogation window and the bias due to bright spots is reduced. Four PIV codes and a large set of experimental and simulated images were used to evaluate the performance of Intensity Capping. The results indicate that Intensity Capping can significantly increase the number of valid vectors from experimental image pairs and reduce displacement error in the analysis of simulated images. A comparison with other PIV image-enhancement techniques shows that Intensity Capping offers competitive performance, low computational cost, ease of implementation, and minimal modification to the images.     

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     

Theory of non-isotropic spatial resolution in PIV

The spatial resolution of the PIV interrogation technique is discussed from an analytical standpoint and assessed with Monte Carlo numerical simulation of particle image motion. The PIV measurement error associated with lack of spatial resolution is modelled associating the cross-correlation operator to a moving average filter. The error associated with the "low-pass filtering" effect is investigated by adopting a second-order polynomial expression for the velocity spatial distribution. According to the present error analysis, the measurement error is proportional to the second-order spatial derivative of the velocity field and increases with the square of the window linear size. The strategy for the selection of the window size and properties (aspect ratio and orientation) so as to minimize the error is discussed. The principle is based on nonisotropic interrogation windows of elliptical shape, with a constant area and elongated in the direction of the largest curvature radius. The nonisotropic parameters are defined as eccentricity and orientation, which are based on the local eigenvalues/vectors of the Hessian tensor of the displacement spatial distribution. The technique is implemented in a recursive PIV interrogation method. The performance of nonisotropic interrogation technique is assessed by means of synthetic PIV images, which simulate three situations: first, a one-dimensional sinusoidal shear displacement, which allows comparison of the cross-correlation spatial response with the transfer function of linear filters. Second, the stream-wise exponential velocity decay is simulated, which simulates the particle tracers decelerating downstream of a shock wave and gives an example of a flow with main velocity differences aligned with the velocity direction. The results show that keeping the image density fixed, the error caused by insufficient spatial resolution can be reduced by a factor two when a preferential direction is found in the flow field. Finally, a Lamb–Oseen vortex flow is presented, which shows the complex pattern formed by the interrogation windows in a two-dimensional case. In this case, the improvement in interrogation performance is limited due to the isotropic nature of the velocity spatial fluctuation.     

Improvements to PIV image analysis by recognizing the velocity gradients

Two iterative PIV image processing methods are introduced, which utilize displacement and deformation of the interrogation areas to maximize the correlation. The velocity gradients used for the window deformation are iteratively estimated directly from the images and no velocity values are required from neighbouring interrogation areas, as with numerical differentiation. The improved accuracy and resolution of the velocity gradient estimation compared to numerical differentiation is shown using synthetic images. The performance in a real application is shown using experimental reference images.     

A comparative study of the MQD method and several correlation-based PIV evaluation algorithms

 The Minimum Quadratic Difference (MQD) method is compared with methods conventionally used for the evaluation of PIV recordings, i.e. correlation-based evaluation with fixed interrogation windows (auto- or cross-correlation) and correlation-based tracking. The comparison is performed by studying the evaluation accuracy achieved when applying these methods to pairs of synthetic PIV recordings for which the true displacements are known. The influence of the magnitude of the particle image displacement, evaluation window size, density of particle image distribution, and particle image size on the accuracy are investigated. In all these cases the best results in terms of a statistical error are obtained with the MQD method. The superiority of the MQD method can be explained with its potential of accounting for non-uniformities in the particle image distribution and a non-uniform illumination. It is also shown that the conventional correlation-based methods may produce principal errors that are non-existent for the MQD method. The evaluation speed achievable for the MQD method by making use of the FFT is comparable to that common for the generally used auto- or cross-correlation algorithm. Finally, a quantitative explanation is given for the often observed phenomenon that PIV velocity results tend to be smaller than the true values. Received: 15 May 1998/Accepted: 24 April 1999     

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.     

A generalized processing technique in digital particle image velocimetry with direct estimation of velocity gradients

A technique is proposed for the processing of digital particle image velocimetry (PIV) images, in one single step providing direct estimates of fluid velocity, out-of-plane vorticity and in-plane shear rate tensor. The method is based on a generalization of the standard PIV cross-correlation technique and substitutes the usual discrete cross-correlation of image pairs with a correlation of interpolated two-dimensional image intensity functions, being subject to affine transformations. The correlation is implemented by using collocation points, on which image intensity values are interpolated. The resulting six-dimensional correlation function is maximized using a general purpose optimization algorithm. The use of the method is demonstrated by application to different types of synthetically generated image pairs constructed with known particle displacement functions. The resulting errors are assessed and compared with those of a representative standard PIV method as well as with those of the present technique using no differential quantities in the search of the peak location. The examples demonstrate that significant improvements in accuracy can be obtained for flow fields with regions containing strong velocity gradients.     

A correlation-based continuous window-shift technique to reduce the peak-locking effect in digital PIV image evaluation

In this paper the peak-locking phenomenon is investigated in the evaluation of digital PIV recordings by using a correlation-based interrogation algorithm with a discrete window shift and a correlation-based tracking algorithm. Statistical analyses indicate that nonuniformly distributed bias errors are the main cause of the peak-locking effect, and the amplitude variation of the random error is also an important source of the peak locking. Simulations and experimental examples demonstrate that very strong peak-locking effects exist for the correlation-based interrogation algorithm with discrete window shift in the cases of large particle images, small interrogation windows, and very small particle images. Very strong peak-locking effects are also observed for the correlation-based tracking algorithm when the particle images are overexposed, binarized, or very small. These strong peak-locking effects can be avoided without loss of evaluation accuracy by using a continuous window-shift technique in combination with the correlation-based interrogation algorithm. Received: 2 July 2001 / Accepted: 28 November 2001     

Measurement of fully-developed turbulent pipe flow with digital particle image velocimetry

A new and unique high-resolution image acquisition system for digital particle image velocimetry (DPIV) in turbulent flows is used for the measurement of fully-developed turbulent pipe flow at a Reynolds number of 5300. The flow conditions of the pipe flow match those of a direct numerical simulation (DNS) and of measurements with conventional (viz., photographic) PIV and with laser-Doppler velocimetry (LDV). This experiment allows a direct and detailed comparison of the conventional and digital implementations of the PIV method for a non-trivial unsteady flow. The results for the turbulence statistics and power spectra show that the level of accuracy for DPIV is comparable to that of conventional PIV, despite a considerable difference in the interrogation pixel resolution, i.e. 32 × 32 (DPIV) versus 256 × 256 (PIV). This result is in agreement with an earlier analytical prediction for the measurement accuracy. One of the advantages of DPIV over conventional PIV is that the interrogation of the DPIV images takes only a fraction of the time needed for the interrogation of the PIV photographs.     

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.     

A digital mask technique for reducing the bias error of the correlation-based PIV interrogation algorithm

 In this paper the bias phenomenon in the evaluation of PIV recordings by using the correlation-based interrogation algorithm is discussed, and a digital mask technique, that can effectively reduce the bias error, is introduced. The correlation-based interrogation algorithm, when masked with a Gaussian window function, can achieve a higher evaluation accuracy not only for PIV recordings of flows with small velocity gradients, but also for that of flows with large gradients. Received: 14 October 1998/Accepted: 20 July 1999     

The fully digital evaluation of photographic PIV recordings

The performance of a purely digital evaluation system for photographic PIV recordings is described. High resolution digital images are obtained from the 35 mm negatives using a commonly available slide scanner. Together with the continually improving capabilities of standard computers, this evaluation system is a cost effective alternative to the traditional analog optical/digital (Young's fringe method) and purely optical PIV interrogation systems. Compared to the optical systems the fully digital evaluation can provide a higher spatial resolution while maintaining a similar measurement uncertainty. Using actual PIV recordings absolute measurement uncertainties are obtained and further predictions toward optimal displacement data recovery are made with the aid of Monte-Carlo simulations. Measurement uncertainties are minimized for particle image diameters on the order of 2 pixels while the reduction of the image depth (i.e. bits/pixel) has little effect. The overall performance of the described digital evaluation is compared to two types of optical evaluation systems.Affiliated with DNW-NWB, DLR-Braunschweig.     

Robust evaluation of the dissimilarity between interrogation windows in image velocimetry

Image velocimetry techniques, which extract motion information by comparison of image regions, typically make use of cross-correlation to measure the degree of matching. In this work, a novel measure of the dissimilarity between interrogation windows is proposed which is based on a more robust estimator than cross-correlation. The method is validated on synthetic images and on two experimental data sets obtained from a periodically pulsed jet and a backward-facing step. The former is a basically laminar flow, whereas the latter is fully turbulent. Both of them are characterized by regions of high velocity gradients. The efficiency of the robust image velocimetry (RIV) is compared with a cross-correlation algorithm (PIV). The analysis of results shows that the RIV is less sensitive to the appearance and disappearance of particles, and to high velocity gradients and, in general, to noise, generating less spurious velocity vectors. As a consequence RIV resolves better the vorticity peaks at the center of the vortex rings generated by the pulsed jet, obtaining, for a given interrogation window size, a higher spatial resolution. Moreover, in the analysis of the flow field generated by the backward-facing step, the RIV performs better in the shear layer at the border of the recirculation region, leading to a more reliable estimation of Reynolds shear stress and horizontal velocity component.     

Theory of cross-correlation analysis of PIV images

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.For the direct cross-correlation method of single-exposure, double-frame systems which model video array detector interrogation and of double-exposure single-frame systems which generalize earlier direct auto-correlation methods of interrogation of photographic recordings, optimal system parameters are recommended for a range of velocity fields in order to eliminate signal bias and to minimize loss of signal strength. The signal bias resulting from velocity gradients in auto-correlation analysis can be eliminated in cross-correlation interrogation by appropriate choice of the optimal parameters. Resolution, detection rate, accuracy and reliability are compared with direct auto-correlation methods for double- and multiple-pulsed systems.     

PIV measurements of turbulent flow in planar mixing layer

A turbulent mixing layer consists of two different flow types, i.e. shear layer (shear-flow turbulence) and free stream regions (nearly homogeneous turbulence). The inherent non-uniform seeding tracer distributions observed around the interfaces between the shear layer and two free stream regions usually lead to a difficulty in particle image velocimetry (PIV) measurements. A parametric study on the application of PIV to the measurement of velocity field in a planar mixing layer is made by means of six factors, including interrogation window size, aspect ratio of interrogation window, interrogation window offset, threshold of data validation, sharpening spatial filters (Prewitt and Sobel masks), and smoothing spatial filter (median mask). The objective of this study is to obtain accurate turbulent measurements in both mean and fluctuating velocities using PIV under an appropriate parametric setting. The optimal levels, which are trade-off in between the accuracy and fine spatial resolution of velocity field measurements, are determined with the aid of the Taguchi method. It is shown that the PIV measurements made with this optimal set of parameters are in good agreement with the measurements made by a two-component hot-wire anemometer. Case independency of the proposed optimal set of parameters on the flow condition of the mixing layer is validated through the applications to two additional tests under the different experimental conditions in changing solely either velocity ratio of high-speed to low-speed free stream velocities or Reynolds number.     

Fundamentals of multiframe particle image velocimetry (PIV)

A sophisticated strategy for the evaluation of time-resolved PIV image sequences is presented which takes the temporal variation of the particle image pattern into account. The primary aim of the method is to increase the accuracy and dynamic range by locally adopting the particle image displacement for each interrogation window to overcome the largest drawback of PIV. This is required in order to resolve flow phenomena which have so far remained inaccessible. The method locally optimizes the temporal separation between the particle image pairs by taking first and second order effects into account. The validation of the evaluation method is performed with synthetically generated particle image sequences based on the solution of a direct numerical simulation. In addition, the performance of the evaluation approach is demonstrated by means of a real image sequence measured with a time-resolved PIV system.     

A combination correlation-based interrogation and tracking algorithm for digital PIV evaluation

A combination of the correlation-based interrogation algorithm and the correlation-based tracking algorithm is proposed for digital PIV evaluation. A zero-padding interrogation algorithm is adopted in which the interrogation windows differ in size and in which the number of pixels in the side length of the smaller window is not restricted to a power of 2. This greatly improves the algorithm's accuracy and measurement range. The correlation-based tracking algorithm is employed when the already-measured vector can serve as a good predictor of the next vector to be measured. In this case, only a very small searching scope is required and computation can be fast. Computational intensity analysis shows that, using the same-sized sampled window, the correlation-based tracking algorithm is more efficient than the conventional correlation-based interrogation algorithm if the searching scope is less than 4. Compared with some of the other correlation-based algorithms, the proposed combination method is faster, is more accurate, has a larger measurable range, and can utilize a sampled window of any size.     

Simultaneous measurements of velocity and density in buoyancy-driven mixing

A variant of the particle image velocimetry (PIV) technique is described for measuring velocity and density simultaneously in a turbulent Rayleigh-Taylor mixing layer. The velocity field is computed by the usual PIV technique of cross-correlating two consecutive images, and deducing particle displacements from correlation peaks of intensity fields. Different concentrations of seed particles are used in the two streams of different temperature (density) fluids, and a local measure of the density is obtained by spatially averaging over an interrogation window. Good agreement is reported between the first- and second-order statistics for density obtained from this technique and from a thermocouple. Velocity-density correlations computed by cross-correlating individual time series are presented. The errors in the density measurements are quantified and analyzed, and the issue of spatial resolution is also discussed. Our purpose for this paper is to introduce the PIV-S method and validate its accuracy against corresponding thermocouple measurements.     

Fast and accurate PIV computation using highly parallel iterative correlation maximization

Our contribution deals with fast computation of dense two-component (2C) PIV vector fields using Graphics Processing Units (GPUs). We show that iterative gradient-based cross-correlation optimization is an accurate and efficient alternative to multi-pass processing with FFT-based cross-correlation. Density is meant here from the sampling point of view (we obtain one vector per pixel), since the presented algorithm, folki, naturally performs fast correlation optimization over interrogation windows with maximal overlap. The processing of 5 image pairs (1,376 × 1,040 each) is achieved in less than a second on a NVIDIA Tesla C1060 GPU. Various tests on synthetic and experimental images, including a dataset of the 2nd PIV challenge, show that the accuracy of folki is found comparable to that of state-of-the-art FFT-based commercial softwares, while being 50 times faster.