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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 143939, 6 pages

http://dx.doi.org/10.1155/2013/143939

## Multibubbles Segmentation and Characteristic Measurement in Gas-Liquid Two-Phase Flow

^{1}College of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China^{2}Tianjin Key Laboratory of Process Measurement and Control, Tianjin 300072, China

Received 10 July 2013; Accepted 3 September 2013

Academic Editor: Fuqiang Zhou

Copyright © 2013 Ting Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Gas-liquid two-phase flow is a typical flow, and bubble characteristic measurement is of great importance to discover flow mechanism and guide the practical fluid mechanical engineering. In this paper, a virtual stereo vision measurement system mainly consists of a high-speed camera, and two optical reflector sets was established, and bubble images in gas-liquid two-phase flow were captured by the optimized virtual stereo vision sensor. Overlapping bubbles segmentation is indispensable for the images, and an effective multibubbles segmentation method was proposed. Firstly the convexities of the overlapped area were identified based on the chain code difference, and the pseudoconcave points were removed based on the concave length constraint. According to the matching principle of concave points, the segmentation area was clarified, and the overlapping bubbles were segmented effectively. Therefore, the modality and motion feature parameters of bubbles were estimated, and three-dimensional bubble trajectories and velocity vector field were reconstructed according to the measurement model of virtual stereo vision. The experimental results show that the segmentation and characteristic measurement method of multibubbles is valid and with high precision.

#### 1. Introduction

Gas-liquid two-phase flow is a typical flow, and bubble characteristic measurement is of great importance to discover the flow mechanism and guide the practical fluid mechanical engineering [1]. With the development of computer and optoelectronic techniques, visual inspection [2, 3] based on photography has been widely used in multiphase flow measurement. However, the overlapping bubbles, which would decrease the reconstruction accuracy of modality and motion feature parameters of bubbles in gas-liquid two-phase, exist widely and cannot be recognized effectively. Many scholars have studied different methods to deal with overlapping objects in digital images, such as mathematical morphology [4], improved watershed algorithm [5], and active contour tracking algorithm [6]. However, there are some obvious disadvantages for these algorithms to detect overlapping bubbles. For example, the segmentation computation is huge, because the corrosion and expansion processes are tracked every time, which easily lead to oversegmentation. Other scholars have studied unique brightness information within the overlapping region, but the brightness difference on the surface of bubbles is an indispensable factor. Searching the edge concave points for segmenting overlapping objects is widely used in particle segmentation [7], which is faster in processing speed than other methods. In the method, extracting and matching concave points are two key steps.

Qian et al. [8] used iterated searching method to find the candidate concavities and obtained optimal splitting conic based on minimum mean square error ellipse fitting with concavities constrains, which improved the calculation accuracy of overlapping area. Heavily overlapping bubbles recognition algorithm which needs to find the local negative curvature maximum of the perimeter as connecting points was utilized by Honkanen et al. [9]. But ellipse-like bubble images with smooth outline are unavoidable in actual images. Zhang et al. [10] proposed polygonal approximation method to find dominant points and segmented ellipse fitting bubbles based on average distance deviation criterion and two constraint conditions. Similarly, it was not accurate for ellipse-like bubbles shape, and false connection points could not be recognized and removed. Yu et al. [11] utilized Normal-line Hough Transform method to detect the particle centers to segment overlapping solid particles in solid-liquid two-phase flow. But Normal-line Hough Transform is only proper for the arc detection and not effective for particles with complex outline. Moreover, the radius of solid particles must be given firstly, which limits the application considerably.

Considering the real outline of bubbles and taking the irregular bubble shapes into account, a multibubbles segmentation method based on virtual stereo vision and chain code information is proposed. It consists of three main steps, identification of candidate concave points referring to chain code difference, removal of the pseudoconcave points based on the concave length, and matching real concave points according to axial constraint. The method is fast and also suitable for more complex outline of overlapping bubbles, moreover, it can avoid oversegmentation and improve segmentation accuracy for removal of the pseudoconcave point. The proposed matching principle of concave points can improve the segmentation speed as well. Finally, three-dimensional bubble trajectories and velocity vector field are reconstructed according to the measurement model of the virtual stereo vision. The experimental results show that the segmentation and characteristic measurement method of multibubbles is valid and with high precision.

#### 2. Multibubbles Segmentation

##### 2.1. Selection of Candidate Concave Points

The chain code is a classical type which can be used to represent the outline of objects by the line and orientation in four or eight different directions [12], which often applied in the image to increase the computation speed and realize the segmentation more easily. Eight-direction chain code, which used in the method, can precisely describe the outline of objects because there are at most eight neighboring pixels around one pixel. The chain code value of one point refers that the previous point points to the current point, and the direction rotates anticlockwise. The relation between the two chain codes of two adjacent points, for example and , is relative and is termed relative chain codes. and are original chain code, and the value range of and is 0~7 which represents eight different directions, respectively. When their directions are the same, the relative chain code value is 0. The absolute chain code is the accumulation of the overall relative chain codes before the current point , and is defined as 0 initially. Therefore, the sum of three adjacent chain codes is And the chain code difference is defined as The chain code difference represents the angle difference of point , which is in proportion to the boundary curvature. The concave points of the outline can be easily tracked through . Figure 1 shows the schematic diagram of chain code difference.

The value of Diff with different points in Figure 1 is as shown in Table 1.

Obviously, the chain code difference is −5. The point is noted as one convex point, and the direction changes clockwise due to .

Therefore, the principle of selecting the candidate concave points can be described as follows. If value of is greater than 3, the current point is one of concave points. Otherwise, the current point is regarded as convex point. Firstly, the chain code differences of all points on the contour are calculated, and the current point is selected as candidate concave point if the value is greater than 3. That is, if some concave points are tracked on the bubble contour, these bubbles are served as candidate bubbles.

##### 2.2. Removal of the Pseudoconcave Points

All overlapping bubbles have been selected through comparison of chain code differences. However not all of them are real overlapping bubbles. It is because of the various shapes of bubbles that some selection points maybe pseudoconcave points, which may result in oversegmentation. Some constraint conditions have to be added. A new function is defined as follows The neighborhood is defined as concave cluster if the point satisfies the condition of . Then the cluster length or concave length is figured out. If the concave length is larger than the given threshold value, the cluster is regarded as matching concave point. Otherwise the clusters are not real concave points and should be removed.

##### 2.3. Matching Real Concave Points

Figure 2 shows the schematic diagram of overlapping bubbles. Figure 2(a) describes that only two bubbles are overlapped, and points A and B can be matched easily. But sometimes there are more than two bubbles overlapped together, as shown in Figure 2(b), there are 6 different matching combinations between A, B, C, and D. In order to increase the speed of calculation and improve the matching accuracy, a simple but effective method is proposed in the paper. It is based on the two principles: (1) the matching concave points must be located in the both sides of medial axis, and (2) the line between the matching pairs has only one intersection point with the medial axis.

#### 3. Three-Dimensional Reconstruction Principle

##### 3.1. Experimental Setup

A Weinberger high-speed camera whose maximum resolution is 1280*1024 @ 500 fps is used in the experiment. A laptop is used to drive the camera and acquire the RGB images. The LED panel light supplies the backlight source and the power can be adjusted discretely. In order to reconstruction the three-dimensional parameters of bubbles, virtual stereo vision measurement platform is established. The schematic diagram of measurement principle is described in Figure 3. The vision sensor consists of symmetrical reflector sets , in the middle and symmetrical reflector sets and on both sides. When bubbles are quantitatively measured, the features are imaged by real camera from the view of left and right to form stereoscopic parallax. The virtual stereo vision measurement platform does not need two severely synchronous images, which decreases the system complexity effectively, and has lower cost and relatively high speed for the particular dynamic measurement of gas-liquid two-phase flow [13, 14].

##### 3.2. Principles of Three-Dimensional Reconstruction

In order to identify the bubble pairs in the left and right half image accurately, epipolar constraint [15] based on the bubbles centroid, supplemented by the constraints of bubbles height and projection characteristics are adopted. The modality and motion parameters of bubbles can be extracted with subpixel precision. For example, the center coordinates () of one bubble are given by where and are the first moment and denotes the bubble area.

Figure 4 shows the measurement scheme of three-dimensional velocity of bubbles. () and () refer to the center coordinates of the same bubble at time and , while , , and are the displacements in horizontal, vertical, and depth direction, respectively. The same operations are performed in the adjacent frames to extract the centroid coordinates of one bubble and calculate the three-dimensional position with stereo matching and reconstruct the velocity by motion matching of different frames. The bubble velocity is defined as the displacement per unit time, and given by where , , and are velocities in the , , and direction, respectively, and time interval is .

According to the stereo and moving matching based on the motion characteristic of bubbles, the three-dimensional trajectories of bubble and velocity vector field can be accurately reconstructed based on the modality and motion feature parameters at different time.

#### 4. Characteristic Measurements

RGB bubble images of the air-water two-phase flow are taken by the virtual stereo vision sensor. Figure 5 shows the original images taken at 280 fps. Image analysis and data processing are carried out with VC++ software. The automatic multibubbles segmentation method is described in the following sections.

##### 4.1. Image Preprocessing

In order to extract the modality and motion features, such as the perimeter, area, circularity, and mass center coordinates of bubbles, several image preprocessing steps are necessary to be performed. Transformation from RGB images to gray images can reduce the computation data and increase the processing speed. Image difference and median filtering are intended to eliminate noises. According to the characteristics of bubble images, the improved Otsu method with dynamic threshold compression is used for image binarization subsequently. Then image morphological processing and the automatic recognition method are developed to eliminate the impurities and noise and identify the bubble feature regions [16]. The first image in Figure 5 is one typical image including overlapping bubbles. Figure 6 shows the preprocessing result for the first image in Figure 5. The image is divided into two parts, which are the left captured by the left virtual camera and the right captured by the right virtual camera. Then 8-connected area criterion is served as the rule of labeling the bubbles from the top to bottom in the two parts. There are two sets of overlapping bubbles obviously, labeled by number 10 and 26, respectively. The two sets of bubbles must be segmented first before extracting the modality parameters of bubbles.

##### 4.2. Multibubbles Segmentation

The chain code differences of all points on the outline are calculated first. If the value of the chain code differences is greater than 3, the current point is selected as candidate concave point. Accordingly, overlapping bubbles are selected. Whether the candidate overlapping bubbles are real overlapping bubbles or not is judged by the concave length. If the concave length is greater than the given threshold, the cluster is the matching concave point. Otherwise the clusters are not real concave points and the pseudoconcave points are removed. Finally real concave points are matched according to axial constraint. Take number 26 bubble for example, the outline extracted based on 8-direction chain code is shown in Figure 7(a). There are 158 chain codes in total, and the chain code difference of all points is figured out according to the criterion in Section 2.1. The chain code difference is as shown in Figure 7(b). As can be seen from Figure 7(b), there are three positions where the value of chain code difference is greater than 3. The three points are labeled by A, B, and C, respectively. So the three points are selected as candidate concave points. Among them, point A and point C are real concave points, but point B is pseudoconcave point. According to the removal criterion of the pseudoconcave points, the lengths of concave cluster of three points A, B, and C are compared with the threshold and the pseudoconcave point B is removed. Finally, the segment line can be drawn based on medial axis described in Section 2.3.

Figure 8 shows the result of multibubbles segmentation. The overlapping bubbles 10 and 26 are segmented effectively.

##### 4.3. Three-Dimensional Reconstruction of Motion Parameters

According to stereo and moving matching algorithm, three-dimensional center coordinates of each bubble in different frames are extracted. The three-dimensional trajectories of bubbles and velocity vector field can be reconstructed accurately according to three-dimensional center coordinates.

The velocity vector field is plotted in Figure 9, and arrow represents velocity vector direction, and the length of arrow lines represents the magnitude of bubble velocity. As shown in Figure 9, the maximum velocity of bubble rising is 0.235 m/s. The orientation and magnitude of bubble velocity varied continually during the rising period, resulting from combined effect of several forces such as buoyancy, surface tension, and atmospheric pressure.

The reconstruction precision can be estimated by target which is about 90 mm (length) × 80 mm (width) with *μ*m-level accuracy [13]. The spatial distance between two adjacent spheres is known precisely to simulate the bubble distribution, and the target can occupy the full field of view basically. The measurement absolute error for three-dimensional bubble position and trajectory is smaller than 0.13 mm, and the relative error is smaller than 0.49%. Through comparing the measurement value and the real value, it shows the proposed segmentation method and three-dimensional reconstruction is valid and with high precision.

#### 5. Conclusions

In this paper, a segmentation method for multibubbles in gas-liquid two-phase flow based on virtual stereo vision and chain code has been proposed, and characteristics of three-dimensional trajectory of bubbles are measured accurately. A series of reconstruction steps including image pre-processing, multibubbles segmentation, parameters extraction, and reconstruction of three-dimensional velocity field are performed during the experiment, which can lay the foundation to study the bubble dynamics, behaviors, and gas holdup in gas-liquid two-phase flow. The segmentation method is faster, more effective, and also applicable for more complex outline of overlapping bubbles. Moreover, it can decrease oversegmentation and improve reconstruction accuracy. The experimental results show that the segmentation and characteristic measurement method of multibubbles is valid and with high precision.

#### Acknowledgment

This work was funded by the National Natural Science Foundation of China (60902084, 61172120, and 61372143), and the Natural Science Foundation of Tianjin in China [12JCQNJC02200, and 13JCZDJC34800].

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