Automated mask generation for PIV image analysis based on pixel intensity statistics

Particle image velocimetry (PIV) is a non-intrusive technique for measuring flow velocities by analysing successive images of seeding particles captured by specialised cameras. Images are subsequently interrogated by means of statistical operators, such as cross correlation, to infer flow velocities representative of the particle image displacements captured within the image sub-sections (Theunissen 2012). The most suitable image for PIV analyses constitutes homogeneously distributed bright particle images on a completely dark background. Unfortunately, this ideal scenario is not always possible as the flow region of interest can be occupied by objects producing artefacts (light reflections, shadow areas, local variations in seeding density, etc.) hindering the measurement quality (Westerweel et al. 2005). If the required particle image displacement measurement is in the near vicinity of a surface, special care must be taken in adequate surface preparation during the experimental phase (Paterna et al. 2013), images must be properly pre-processed by means of, e.g., background subtraction (Mendez et al. 2017), or advanced image interrogation processes are to be adopted (Ronneberger et al. 1998; Gui et al. 2003; Usera et al. 2004). Such advanced PIV analysis routines typically involve the exclusion of object regions within cross-correlation windows as to minimise distortions in the cross-correlation map, consequently limiting associated displacement bias errors (Theunissen et al. 2008). This, in turn, requires knowledge of the imaged object boundaries to enable seeded flow regions to be discerned from non-seeded object regions. The generation of such logical masks thus constitutes a critical step, independent from the PIV algorithm used.

Logical masks are typically generated manually when the geometry of the object is very simple and clearly detectable in the PIV images. However, the manual approach becomes unreliable and too time-consuming when complex aerodynamic shapes are involved or several image sets need to be analysed with many different masks. Some examples of automated mask generation have been reported in literature: in Dussol et al. (2016), strong light reflections of the object were manually detected to generate the initial mask, which was dynamically moved using the a priori knowledge of the object motion. In Sanchis and Jensen (2011), the air–water interface was successfully detected exploiting the image intensity gradients through the Radon transform. Ergin et al. (2015) dealt with the motion of a moving body by implementing a tracking method and moving to an object-fixed coordinate system, allowing the use of a manual mask to the moving object. Deen et al. (2010) applied a combination of contrast enhancement and intensity thresholding to identify bubbles in two-phase flows. However, shadows caused by the obstruction of the laser light also constitute unwanted image regions, yet these are not defined by high intensity boundaries. Moreover, experimental settings often produce complex images where objects contours are dark, vague, and blurred. Objects thus become hardly detectable even for a human observer, limiting the application of typical masking algorithms. Alternatively, the spatial coherence between image pixels is involved to filter and identify object regions by means of low-pass filtering (Willert 1999), median filtering (Scholz and Kähler 2004), etc. Due to the finite extent of the filter kernels, such operations tend to introduce inaccuracies in the localisation of the object boundaries and are influenced by noise in the grey-scale distributions. Delnoij et al. (1999) discriminated objects on the basis of inherent differences in their motion. This, however, demands objects to be identified a priori. Similarly, Honkanen and Nobach (2005) utilised the variation in flow velocities to completely remove stagnant objects. In case of temporally well-resolved PIV recordings, frequency analyses of the time-evolution in pixel intensities allow the identification of objects (Sciacchitano and Scarano 2014). This methodology is, however, only conducive for time-resolved PIV recordings involving dynamic objects.

In the current work, the authors propose a general, robust methodology for the automatic detection of static image regions containing no information relevant in the cross-correlation operation. Without any special requirement for the image regions to be excluded (shape, luminosity, or contrast), the method takes advantage of the statistical information contained within each individual pixel across several independent PIV images. A statistical test distinguishes unseeded image regions from image sections of interest with pixel accuracy. The underlying principle is the understanding that the temporal intensity variation of pixels constituting the unseeded partitions is mainly due to camera noise, producing a normal-distributed intensity histogram (Westerweel 2000). Pixels of seeded image regions on the other hand are characterized by the strong alternation of bright and dark values, producing highly skewed histograms (Westerweel 2000). A normality test is, therefore, performed on the time history of each pixel of the image to distinguish objects from particle images. Unlike filtering operations, the categorisation is performed pixel-wise and, therefore, does not incorporate neighbouring pixels. As a result of an automatic thresholding on the p value of the normality test, the proposed method is fully autonomous and independent of user input. The technique is fully assessed on synthetic images and the application to several experimental cases is proposed to show its suitability for a variety of real conditions.

The application of the normality test explained in the previous section leads to the generation of a mask based solely on the time history of each pixel and as such independent of the spatial coherence between image pixels. The spatial information can be used in a post-detection phase to enhance the quality of the mask, especially when insufficient images are available. In such cases, spurious random pixels might be excluded producing pixel-sized holes in the binary mask generated. To increase the robustness of the mask, morphological operations can be included to simplify the binary image preserving the characteristics of the shape and eliminating irrelevancies (Haralick et al. 1987). While the reader may require alternative operations when dealing with special geometries, the morphological operations of closing and filling proposed in this work are fundamental. All morphological operations can be performed using the MATLAB routines bwmorph and imfill. The closing process allows to smoothen contours and to eliminate small holes, whereas the process of filling allows to close every area of the binary mask that cannot be reached by filling in the background from the edge of the image. The majority process allows a final cleansing of the mask by recursively setting a pixel to 1 when more than half of the pixels in the immediate neighbourhood are 1. Figure 5 illustrates the achievable improvements by means of the morphological operations where an example mask is artificially perturbed with noise and holes (Fig. 5a). After the closing process, pixel-sized holes have disappeared (Fig. 5b). The bigger hole inside the mask is removed as a result of the filling process (Fig. 5c) and the recursive application of majority (Fig. 5d) filters out smaller pixel-sized structures without altering the main shape of the mask.

The reader should note that the adoption of morphological operations, despite being beneficial from a general point of view, may cause unwanted effects on the smallest scale of the geometry (8 by 8 pixels). Operations like majority would reduce the size of every sharp corner of the mask by one pixel.² Although the advantages of using morphological operations may well outweigh smaller issues on this scale, its use should, therefore, be considered as a facultative addition to the main methodology.

To assess the validity of the proposed masking methodology and investigate the minimum number of images required for the approach to be reliable, Monte Carlo simulations involving synthetic PIV images were performed. Cylinders of three different diameters of 100, 200, and 400 pixels, occupying 3, 13, and 50% of the entire image area, respectively, served as object. Pixel intensities within the cylinders were randomly drawn from a Gaussian distribution with a mean normalized intensity of 0.12 and standard deviation of 0.03. Images were 500 by 500 pixels in size, discretized in 16 bits, with randomly distributed particles in the flow regions having a diameter of 3 pixels and a seeding density of 0.1 ppp (Fig. 6).

For each cylinder, 200 independent images were generated a total of 100 times to obtain statistically meaningful average results. For each size of the set, the error ε in the estimation of the mask area was evaluated as:where W and H are the width and height of the image in pixels, M is the ideal mask, and M̂ is the estimated mask. Results for the error ε are presented in Fig. 7 and show a similar behaviour for all cylinders.

When fewer than 20 images are used for the mask detection, the outcome of the algorithm is erroneous due to an insufficient number of independent occurrences to distinguish normally distributed pixels from highly skewed pixels in flow regions. However, increasing the number of images analysed, the mask error quickly drops to 10⁻¹ or less for a set of 40 images. After this value, the error reaches a constant level as increasing the number of images does not affect the normality test anymore. This number of images is further confirmed by the theoretical estimation of Eq. (7), where 40 images with a seeding density of 0.1 ppp yield a probability of 98% of pixels being occupied at least by a particle image throughout the PIV sequence.

A detail of the resulting mask detected for a cylinder of 100 pixels in diameter using 200 PIV images is shown in Fig. 8, demonstrating a near perfect agreement with the imposed mask.

To validate the performances of the automatic mask detection in experimental conditions, three experimental test cases are proposed: (a) a micro-channel flow; (b) a transparent acrylic aerofoil, and (c) a pipe junction simulating a lung. The first test case comprises 600 PIV images of a micro-channel flow driven by 200 bar of pressure, constituting Case A of the 4th International PIV Challenge (Kähler et al. 2016). The resulting mask is presented in Fig. 9a, where a sample of the original PIV images is superimposed with the estimated mask shown in red. In addition to the mask, Fig. 9b, c, respectively, shows a histogram of the grey levels in time for pixels belonging to the masked area and flow region. The plots are in agreement with the observation that masked regions are characterized by normally distributed histograms, whereas seeded image regions present a strongly skewed distribution in grey levels. For the histograms presented in Fig. 9b and c, values of skewness are, respectively, 5.1 × 10⁻³ and 2.0.

The second test case comes from an experiment performed in the low turbulence wind tunnel of the University of Bristol. PIV experiments were performed using a 200 mJ Nd:Yag laser and 4MP FlowSense EO camera on an NACA0024 airfoil at a chord-based Reynolds number of 1.4 × 10⁵. The airfoil was manufactured out of acrylic to reduce light reflections in vicinity of the surface. A total of 400 images were acquired in 16 bits image depth. The final mask is presented in Fig. 10a and illustrates how both aerofoil and light shadow area are detected by the masking algorithm. Both regions are characterized by the lack of information due to the absence of particles and present normally distributed grey levels. Figure 10b, c shows two histograms for a pixel belonging to the aerofoil and a pixel belonging to the shadow, respectively; as already mentioned, both the histograms are normally distributed and contribute to the masked region; however, the histogram for the aerofoil region (Fig. 10b) has a mean value which is higher than the shadow area (Fig. 10c), confirming that the suitability of the method is independent from the brightness and the contrast of the masked region.

The reader should notice that the shadow areas produced by the aerofoil are not entirely detected as masks; due to the transparent material used to manufacture the object, the casted shadows are not as dark as those produced by an opaque object, but they gradually fade from dark to bright (see detail of Fig. 10a). This implies that particle images also disappear progressively as they cross the shadow: those areas where the particle image intensity is on par with the random noise are detected as mask, while the regions that may contain valuable information about the displacements are maintained as flow regions, producing the pattern observed in Fig. 10a.

The final test case involves 534 images of a flow bifurcation simulating a lung at Re = 2.24 (Theunissen and Riethmuller 2008). The 8 bit discretization renders the test case challenging as sporadic noisy areas within the seeded flow region do not produce significant skew in the PDFs. Figure 11b, c, respectively, shows the histograms of pixels belonging to the boundary region and noisy flow area. Both present a normal distribution. This strong image noise in the flow region, coupled with the bright intensity of the particles and the low bit discretization, produces small regions within the flow area to be masked out. Overall, the geometry of the object is correctly retrieved and the occurrence of these additional masked regions is restricted to very small domains. As mentioned in the previous section, these regions can be easily cleaned through the application of additional morphological operations. It is, however, important to note that the mask is based on statistical information of the PIV images and the exclusion of those masked regions from a PIV analysis does not affect the cross-correlation results as those pixels do not contain information from a statistical point of view.

The automatic mask detection proposed in this paper requires objects in PIV images to be stationary. With the analysis based on the time history of each pixel, vibrations or deformations of the regions to be masked would combine time history of objects with time history of flow regions, hampering the correct classification of the pixels. Conditions like rigid motion and vibrations can be easily tackled by implementing a tracking method and moving the analysis to an object-fixed coordinate system (Ergin et al. 2015). The presence of ghost particles on reflective surfaces constitutes a more complex case. If the experimental settings were such that particle images were reflected within the objects to be masked, the mask detection will not be able to discern real particles from reflected ones. These regions will subsequently be characterized on the basis of pixels containing (reflected) particle images and will consequently be excluded from the masked region.