Test Suite I (Accuracy vs. Out-of-Plane Displacement)
In test suite I the influence of the out-of-plane components of the motion on the accuracy of the displacement estimation as one of the major contributors to the PIV error is investigated. For each of 11 different out-of-plane displacements between 0 and 0.5 of the light sheet thickness a series of 100 image pairs with 128×128 pixel size is generated numerically. The displacement is uniform, the light-sheet has a top-hat profile and the particle density is 0.02 per pixel. The particle images are Airy disc functions with a random intensity between 0 and 1 and a diameter of 3 pixels given by the first zero value of the Airy disc function. The intensity is integrated uniformly over the square pixel areas with fill factor 1 and intensities from different particles are linearly superimposed. No noise is added. The images are quantised with 8 bit resolution and saved in PNG grayscale format. For all images the simulated displacement is also given.
The images and the simulated displacements can either be downloaded or generated on-the-fly by the simulation program. Pre-compiled executables are available for Windows and Mac OS X (Intel processor). The Pascal source is also available. To compile it, the Free Pascal compiler is recommended.
The images are named as ts1_xx_yya.png and ts1_xx_yyb.png, where xx is a number between 00 and 10 for the out-of-plane displacement between 0 and 0.5 of the light sheet thickness in steps of 0.05, yy is a number between 00 and 99 for the 100 realizations with varying displacements and a and b for the first and the second exposure respectively. The appropriate simulated displacements are given in the files named ts1_xx_yy.uv giving two values, which are the displacements in x and y direction.
Please, load the images or the appropriate generating programs and derive the displacement fields between the two exposures of the image pairs in pixels. Please, send back the displacement fields in text files named according to the name of the image pairs (e.g. ts1_00_00.xyuv for the displacement between ts1_00_00a.png and ts1_00_00b.png). Please, give the obtained vectors as a table of comma separated values (or any other delimiter) with four columns, namely the coordinates x and y and the two displacements u and v in x and y direction respectively, all in units of pixels. The coordinate system has its origin in the lower left corner of the lower left pixel. Please, list only validated vectors, since all given values are counted without a validation indicator. Non validated vectors can be skipped.
Positions and resolution of the derived vector fields can be chosen without restrictions. However, to achieve good performance grades in the test cases for spatial resolution the vector density should be chosen properly.
Important! Please use the same algorithm and the same parameters for the images from the different test suits even if normally you would change settings according to the flow field characteristics. The tests assess different statistical quantities of the PIV algorithm. The results of the individual tests then are combined to characterize the behaviour of a particular PIV processing algorithm with the particular settings. If you want to show the effect of different options of your algorithm, please, process all test suits with the different options and send back the results separately.
From the displacement file only one vector, namely the closest one to the center of the images, is taken into account. The difference of the estimated displacements in x and y direction are compared with the reference displacement. The root mean square of the deviations from the 100 image pairs is calculated for each case of the out-of-plane displacement.
The analyzing program reads the results from the image processing and the appropriate reference displacements. From all estimated vectors only the closest one to the center of the images is selected for comparison and for deriving the RMS error of the PIV algorithm as a function of the out-of-plane displacement. The program can be called in a shell by
ts1_contest imagedirectory prefixdirectory Algorithm1 Algorithm2 Algorithm3 ...
where imagedirectory is the directory with the images and the reference displacement files, prefixdirectory is the directory with the subdirectories Algorithm1 etc., where Algorithm1 is the name of the first algorithm, which will be used as an identifier in the generated diagrams. For example ts1_contest ..\images ..\ AnaPIV.I AnaPIV.II will look in the directory ..\images for the reference displacement files and in ..\AnaPIV.I and ..\AnaPIV.II for the estimated displacements of the algorithms AnaPIV.I and AnaPIV.II respectively. If the prefix is not necessary (algorithm directories in the present directory) .\ can be used as the prefix to use the present directory as the root of the algorithm directories. The program generates the data files and an appropriate gnuplot file for visualization.
RMS error as a function of the out-of-plane displacement in fractions of the light sheet thickness, uniform displacement, light sheet profile: top-hat, particle density: 0.02 particles per pixel. For details of the PIV algorithms follow the link on the diagram.