Overlapping Particle Images Research Articles

Particle detection and size recognition based on defocused particle images: a comparison of a deterministic algorithm and a deep neural network

The systematic manipulation of components of multimodal particle solutions is a key for the design of modern industrial products and pharmaceuticals with highly customized properties. In order to optimize innovative particle separation devices on microfluidic scales, a particle size recognition with simultaneous volumetric position determination is essential. In the present study, the astigmatism particle tracking velocimetry is extended by a deterministic algorithm and a deep neural network (DNN) to include size classification of particles of multimodal size distribution. Without any adaptation of the existing measurement setup, a reliable classification of bimodal particle solutions in the size range of 1.14~upmu hbox {m}–5.03~upmu hbox {m} is demonstrated with a precision of up to 99.9 %. Concurrently, the high detection rate of the particles, suspended in a laminar fluid flow, is quantified by a recall of 99.0 %. By extracting particle images from the experimentally acquired images and placing them on a synthetic background, semi-synthetic images with consistent ground truth are generated. These contain labeled overlapping particle images that are correctly detected and classified by the DNN. The study is complemented by employing the presented algorithms for simultaneous size recognition of up to four particle species with a particle diameter in between 1.14~upmu hbox {m} and 5.03~upmu hbox {m}. With the very high precision of up to 99.3 % at a recall of 94.8 %, the applicability to classify multimodal particle mixtures even in dense solutions is confirmed. The present contribution thus paves the way for quantitative evaluation of microfluidic separation and mixing processes.

A Novel Multi-Step Multi-Exposure PTV Algorithm With Adaptive Time Separation

This work proposes a new multi-step measurement algorithm for PTV to cope with high flow velocities that do not allow time-resolved measurements. The proposed methodology relies on an iterative process, whereby a double-frame single-pulse image acquisition is followed by a multi-exposure acquisition. The novelty of the approach lies in the adaptive selection of the time separation used in the second acquisition to maximise the measurement dynamic velocity range and minimise the occurrence of overlapping particle images. The adaptive selection is performed based on the velocity field obtained by the first double-frame single-pulse acquisition and aims to obtain a rather uniform particle displacement across the measurement volume. The proposed methodology is demonstrated based on flow measurements in the near-wake of a truncated cylinder at Re=33,000. The results obtained by the presented method are then compared to those retrieved via the state-of-the-art PTV algorithm Shake-The-Box, a double-frame single-exposure strategy and a standard double-frame double-exposure strategy with a fixed pulse separation time. The increment of the particle displacement in the regions characterized by low velocity leads to a reduction of the relative uncertainty of the evaluated velocity and a consequent increase of the achievable dynamic velocity range. Among the double-frame strategies, the requirement to allow PTV measurement at a relatively high speed, the proposed methodology achieves the lowest error with respect to the reference, given by STB measurement in this case.

Particle Detection by means of Machine Learning in Defocusing PTV

The accurate measurement of a fluid flow inside a measurement volume (MV) with limited optical access poses a challenge since the view on the MV is often partially obstructed for all but one viewing angle. Defocusing particle tracking velocimetry (DPTV) can be used to determine the instantaneous threedimensional velocity field of the flow with a standard PIV setup, requiring only a single optical axis. Current detection algorithms reach an out-of-plane accuracy in an order of magnitude lower than the planar accuracy, on top of a low rate of detected particles in comparison to other PTV approaches. These drawbacks originate from the low image quality due to noise, fluctuations in illumination, reflections and overlapping particle images. It has been shown that Machine Learning (ML) based detection is more robust against these adverse effects, due to the ability to leverage a higher amount of optical features for detection than conventional algorithms (Lecun et al. (1998)). Therefore, the present work addresses the applicability of ML algorithms in the post-processing of DPTV experiments, which will be evaluated on the ground of the DPTV experiments conducted by Leister and Kriegseis (2019). The setup of these experiments can be seen in Figure 1(a) and a section of a raw image recorded during the experiments in Figure 1(b).

Approximate Bayesian framework for 3D reconstruction in a volumetric PIV/PTV measurement

Non-invasive flow velocity measurement techniques like volumetric Particle Image Velocimetry (PIV) (Elsinga et al., 2006; Adrian and Westerweel, 2011) and Particle Tracking Velocimetry (PTV) (Maas, Gruen and Papantoniou, 1993) use multi-camera projections of tracer particle motion to resolve three-dimensional flow structures. A key step in the measurement chain involves reconstructing the 3D intensity field (PIV) or particle positions (PTV) given the projected images and known camera correspondence. Due to limited number of camera-views the projected particle images are non-unique making the inverse problem of volumetric reconstruction underdetermined. Moreover, higher particle concentration (>0.05 ppp) increases erroneous reconstructions or “ghost” particles and decreases reconstruction accuracy. Current reconstruction methods either use voxel-based representation for intensity reconstruction (e.g. MART (Elsinga et al., 2006)) or a particle-based approach (e.g. IPR (Wieneke, 2013)) for 3D position estimation. The former method is computationally intensive and has a lesser positional accuracy due to stretched shape of the reconstructed particle along the line of sight. The latter compromises triangulation accuracy (Maas, Gruen and Papantoniou, 1993) due to overlapping particle images for higher particle concentrations. Thus, each method has its own challenges and the error in 3D reconstruction significantly affects the accuracy of the velocity measurement. Though, other methods like maximum-a-posteriori (MAP) estimation have been previously developed (Levitan and Herman, 1987; Bouman and Sauer, 1996) for computed Tomography data, it has not been explored for PIV/ PTV 3D reconstruction. Here, we use a MAP estimation framework to model and solve the inverse problem. The cost function is optimized using a stochastic gradient ascent (SGA) algorithm. Such an optimization can converge to a better local maximum and also use smaller image patches for efficient iterations.

Automated Segmentation and Morphological Analyses of Stockpile Aggregate Images using Deep Convolutional Neural Networks

Particle size and morphological/shape properties ensure the reliable and sustainable use of all aggregate skeleton materials placed as constructed layers in transportation applications. The composition and packing of these aggregate assemblies rely heavily on particle size and morphological properties, which affect layer strength, modulus, and deformation response under vehicular loading and therefore facilitate the quality assurance/quality control (QA/QC) process. Aggregate imaging systems developed to date for size and shape characterization, however, have primarily focused on measurement of separated or slightly contacting aggregate particles. Development of efficient computer vision algorithms is urgently needed for image-based evaluations of densely stacked (or stockpile) aggregates, which requires image segmentation of a stockpile for the size and morphological properties of individual particles. This paper presents an innovative approach for automated segmentation and morphological analyses of stockpile aggregate images based on deep learning techniques. A task-specific stockpile aggregate image dataset is established from images collected from various quarries in Illinois. Individual particles from the stockpile images are manually labeled on each image associated with particle locations and regions. A state-of-the-art object detection and segmentation framework called Mask R-CNN is then used to train the image segmentation kernel, which enables user-independent segmentation of stockpile aggregate images. The segmentation results show good agreement with ground-truth labeling and improve the efficiency of size and morphological analyses conducted on densely stacked and overlapping particle images. Based on the presented approach, stockpile aggregate image analysis promises to become an efficient and innovative application for field-scale and in-place evaluations of aggregate materials.

Cut, overlap and locate: a deep learning approach for the 3D localization of particles in astigmatic optical setups

Astigmatic optical systems encode the depth location of spherical objects in the defocus blur of their images. This allows the simultaneous imaging of 3D positions of a large number of such objects, which can act as tracer particles in the study of fluid flows. The challenge lies in decoding the depth information, as defocused particle images might be overlapping or have low maximum intensity values. Current methods are not able to simultaneously detect and locate overlapping and low-intensity particle images. In addition, their cost of computation increases with particle image density. We show how semi-synthetic images of defocused particle images with proximate center point positions can be employed to train an end-to-end trainable particle image detector. This allows for the detection of low-intensity and overlapping particle images in a single pass of an image through a neural network. We present a thorough evaluation of the uncertainty of the method for the application of particles in fluid flow measurements. We achieve a similar error in the depth predictions to previous algorithms for non-overlapping particle images. In the case of neighboring particle images, the location error increases with decreasing particle image center distances and peaks when particle image centers share the same location. When dealing with actual measurement images, the location error increases by approximately a factor of two when particle images share the same center point locations. The trained model detects low-intensity particle images close to the visibility limit and covers 91.4% of the depth range of a human annotator. For the employed experimental arrangement, this increased the depth range along which particle images can be detected by 67% over a previously employed thresholding detection method (Franchini et al. in Adv Water Resour 124:1–8, 2019).Graphic abstract

Measuring droplet size distributions from overlapping interferometric particle images.

Interferometric particle imaging provides a simple way to measure the probability density function (PDF) of droplet sizes from out-focus images. The optical setup is straightforward, but the interpretation of the data is a problem when particle images overlap. We propose a new way to analyze the images. The emphasis is not on a precise identification of droplets, but on obtaining a good estimate of the PDF of droplet sizes in the case of overlapping particle images. The algorithm is tested using synthetic and experimental data. We next use these methods to measure the PDF of droplet sizes produced by spinning disk aerosol generators. The mean primary droplet diameter agrees with predictions from the literature, but we find a broad distribution of satellite droplet sizes.

Higher order multi-frame particle tracking velocimetry

Particle tracking velocimetry methods (PTV) have a great potential to enhance the spatial resolution compared to spatial correlation-based methods (PIV). In addition, they are not biased due to inhomogeneous seeding concentration or in-plane and out-of-plane gradients so that the measurement precision can be increased as well. The possibility to simultaneously measure the velocity with the temperature, ph-value, or pressure of the flow at the particle location by means of fluorescent particles is another advantage of PTV. However, at high seeding concentrations, the reliable particle pairing is challenging, and the measurement precision decreases rapidly due to overlapping particle images and wrong particle image pairing. In this paper, it is shown that the particle image information acquired at four or more time steps greatly enhances a reliable particle pairing even at high seeding concentrations. Furthermore, it is shown that the accuracy and precision can be increased by using vector reallocation and displacement estimation using a fit of the trajectory in the case of curved particle paths. The improvements increase the PTV working range as reliable and accurate measurements become possible at seeding concentrations typically used for PIV measurements.

A vision-based hybrid particle tracking velocimetry (PTV) technique using a modified cascade correlation peak-finding method

A novel technique for particle tracking velocimetry is presented in this paper to overcome the issue of overlapping particle images encountered in the flows with high particle density or under volumetric illumination conditions. To achieve this goal, algorithms for particle identification and tracking are developed based on current methods and validated with both synthetic and experimental image sets. The results from synthetic image tests show that the particle identification algorithm is able to resolve overlapped particle images up to 50 % under noisy conditions, while keeping the root mean square peak location error under 0.07 pixels. The algorithm is also robust to the size changes up to a size ratio of 5. The tracking method developed from a classic computer vision matching algorithm is capable of capturing a velocity gradient up to 0.3 while maintaining the error under 0.2 pixels. Sensitivity tests were performed to describe the optimum conditions for the technique in terms of particle image density, particle image sizes and velocity gradients, also its sensitivity to errors of the PIV results that guide the tracking process. The comparison with other existing tracking techniques demonstrates that this technique is able to resolve more vectors out of a dense particle image field.

Optical microscopy measurement of pair correlation functions

We studied the pair correlation function g(r) of silica particles with a fluorescent core and a nonfluorescent shell which were confined between two glass plates by optical video microscopy. To investigate the possible role of optical artifacts due to overlapping particle images, we compared experiments, where, first, the whole particle (white image) and then, only the fluorescent core (fluorescent image) was used for determining particle positions. While under white-image conditions the observed g(r) exhibits a main peak at about 1.2 times the particle's diameter; under fluorescent image conditions the obtained g(r) resembles a short-ranged repulsive system where the main peak is close to contact. This discrepancy points towards artifacts of video microscopy, leading to erroneous g(r) and in turn to erroneous effective-pair potentials.

Three-dimensional particleimage tracking for dilute particle-liquid flows in a pipe

A three-dimensional (3D) particle image tracking techniquewas used to study the coarse spherical particle-liquid flows in apipe. The flow images from both the front view and the normal sideview, which was reflected into the front view by a mirror, wererecorded with a CCD camera and digitized by a PC with an imagegrabber card. An image processing program was developed to enhanceand segment the flow image, and then to identify the particles. Over90% of all the particles can be identified and located from thepartially overlapped particle images using the circular Houghtransform. Then the 3D position of each detected particle wasdetermined by matching its front view image to its side view image.The particle velocity was then obtained by pairing its images insuccessive video fields. The measurements for the spherical expandedpolystyrene particle-oil flows show that the particles, like thespherical bubbles in laminar bubbly flows, tend to conglomerate nearthe pipe wall and to line up to form the particle clusters. As liquidvelocity decreases, the particle clusters disperse and more particlesare distributed in the pipe centre region.

Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics

The interferometric particle imaging and the global phase Doppler techniques for multi-dimensional particle sizing are based on out-of-focus images of the particles illuminated in laser light sheets of finite width. For a given optical arrangement, an increase in particle number concentration will eventually lead to overlapping particle images on the recording medium, and this in turn will degrade or even prohibit the correct processing of individual particle images for size. The probability of overlapping images should therefore be minimized, which places constraints on the design of the optical system. These constraints are rigorously derived, using Poisson statistics to describe the particle spatial distribution in the flow. The main result consists of an overlap probability coefficient as a function of number density and the optical parameters of the system. However, the resolution of the third position coordinate normal to the laser sheet and the measurement size range also result from this analysis. These results are a prerequisite for designing such systems.

A method for recognizing particles in overlapped particle images

This paper describes a new method to divide a planar curve into circular arcs in order to recognize the overlapped particles in an image. The segmentation is based on a new breakpoint detection method. An area correlation coefficient for two arcs is introduced to identify and cluster the arcs belonging to the same circle. The Least-Squares Method is applied to estimate the center of a circle and its radius. The present method is evaluated using a computer-generated sample image and real coal-ash images with heavily overlapped particles taken by an electron microscope. All the results showed that the present method is effective in recognizing the overlapped circles with high accuracy.

A Method for Measuring Particle Size in Overlapped Particle Images.

This paper describes a new method to measure the sizes of particles and their probability distribution function by image processing. In the present research, an image with heavily overlapped particles was processed. The edges of the particles in the image are detected by Canny's method, and the contours are linked from the pixels in the edges by using chain-coding. The contours are subsequently segmented according to the curvature. Constant curvature segments are clustered according to some relations among contour segments which are likely to represent the same circle. The Least Squares Method which provides an accurate parameter estimation is performed to find out the parameters of a circle. The present method can recover most of particles even in a heavily overlapped particle image. It provides a useful way of investigating the structure of material or counting particles in many fields of engineering. Another advantage of the present method is its short computational time. All the computations in this paper were carried out on a personal computer, and the computational time of processing one image was between 4–10 sec on the personal computer (Pentium II, 300 MHz), which depended on the number of particles in the image. It is clear that the present research can be extended to the real-time processing of particle-detecting and particle-measuring in the future.

Recognition of partially overlapped particle images using the Kohonen neural network

A neural network is proposed for the recognition of partially overlapped particle images in the analysis of Particle Tracking Velocimetry (PTV) frames. The Kohonen neural network is an approximation to an optimum classifier. In this work it allows single particle images to be distinguished from overlapped particle images by shape analysis: it classifies 99.1% of the spots correctly (in test images). If a spot has an almost circular shape, the barycenter co-ordinates are extracted. If the spot shape is far from being circular, it is believed to be a particle overlap, and a procedure to find more centroids is activated.