AUTOMATIC BUBBLE NUCLEATION SITES IDENTIFICATION IN AN IMAGE SEQUENCE Da-chuan CHENG*, Hans BURKHARDT** * Institute of Pattern Recognition and Image Processing, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, e-mail:
[email protected] ** Institute of Pattern Recognition and Image Processing, Department of Computer Science, University of Freiburg, 79110 Freiburg, Germany, e-mail:
[email protected] Abstract. In this study, we present an algorithm which can identify the nucleation sites of vapour bubbles in an image sequence based on a template which is a bubble sub-image extracted by the user. These images are taken with a speed of one thousand images per second via a high-speed digital video camera. Our algorithm is divided into three parts: 1) the bubble position detection, 2) small bubbles identification, and 3) nucleation sites identification via tracking bubbles. We use backwards process in order to track bubbles. The advantage of this method is to avoid the problem caused by bubble merging or the identification of varying shapes of large bubbles. Afterwards, the positions of bubble nucleation sites can be identified. It is an important parameter in exploring the heat transfer in a boiling system.
1. Introduction. In order to explore the heat transfer relationship between the given liquids and the heated tubes, the identification of the nucleation sites of vapor bubbles is important. The density of the nucleation and its distribution area are some of important parameters to explore the heat transfer relationship. Based on the requirement, many experiments are made under different size, material, and the surface structure of tubes. In addition, different pressures, temperatures, heat fluxes, and tested liquids are used in the experiments. These varying experimental conditions will definitely influence the bubble appearances in the recording images. In our recent works (Cheng and Burkhardt, 2001a, 2001b, 2002), we have demonstrated the problems and difficulties of bubble tracking and identification. We solved some of the problems based on a deformable model, a circular model and our proposed method. The same problems will also appear in this study. However, the aim of this paper is to propose a method which can identify the nucleation sites of bubbles from image sequences automatically. To let the reading more conveniently, here we repeat the problems shortly. In general, the problems of bubble identification have two parts: the geometrical problem and the optical problem. In the geometrical problem: 1) the shapes of bubbles vary dependent of the given pressure, temperature and the heat flux; 2) bubbles may merge together; 3) bubbles may be covered by other flowing bubbles. In the optical problem: 1) the reflection on the surfaces of bubbles vary dependent of the given pressure, heat flux, heated tube, and testing liquid; 2) strong reflections might take place on the surface of the tube; 3) bubbles might have shadows; 4) bubbles might be in a poor-illuminated area. Many combinations of the above problems take place in our bubble image sequences. To solve all of the problem combinations at one step is nontrivial. Since our aim in this study is to identify the nucleation sites, we do not have to know the accurate boundary of every bubble. Instead, we need to know the rough size of the bubbles and their positions. In addition, we are not interested in the large bubbles and the small ones, but the intermediate size of bubbles. This is because we use the backwards tracking as the human beings use to identify the nucleation sites. In this mechanism, the large bubbles will have splitting problems and the small bubbles will be
interfered by noises. Although we have limited our interest in the intermediate bubbles, it is still nontrivial to find a good feature set to distinguish bubbles and background. One possible solution is to have a prior knowledge, i.e., a database. The database is a collection of many selected bubble and background sub-images via human beings. These sub-images in the database are the templates giving the system the bubble and background information. Based on the information, the system has the ability to distinguish the bubble and background of the image sequences with different experimental conditions. The proposed scheme is divided into six parts: 1) database set-up; 2) bubble position detection; 3) bubble centre determination; 4) bubble radius determination; 5) bubble backwards tracking; and 6) nucleation sites identification. The followings are the details of this method.
2. Method 2.1 Database setup. The system needs a prior knowledge that are given by human beings. The database is set-up by selecting some sub-images of bubbles and background via an interactive package. The number of templates in the database should not be too large but large enough to cover most of the variants of bubbles and background, respectively. This is a trade-off between the speed and robustness. All of the templates are of the same size dependent of the selected largest bubble. Notably, we select the intermediate bubbles only. 2.2 Bubble position detection. Since the system has the prior knowledge, it may distinguish the bubble and background roughly. Based on the consideration of the computation time, the image is divided into several squares (no overlaps) of the same size to the template in the database. The 2D DFT (Discrete Fourier Transform) spectrum of every square is calculated. Let S i and S i denote the square i and its 2D spectrum, respectively. The 2D spectrum of the templates in the database are calculated as well. They are denoted as B i for i-th bubble template Bi , and G i for i-th background template Gi . The spectrum of each square is compared to the spectrum of each template in the database by calculating the distances: M
M
Di ( j ) = ∑∑ | S i ( x, y ) − B j ( x, y ) | , for 1 ≤ j ≤ N B ;
(1a)
y =1 x =1 M
M
E i ( k ) = ∑∑ | S i ( x, y ) − G k ( x, y ) | , for 1 ≤ k ≤ N G ;
(1b)
y =1 x =1
where N B and N G denote the number of the templates of bubble and background, respectively. A criterion is defined to distinguish if the square belongs to the bubble class or to the background class: bubble if min (Di ) < min (E i ); S i belongs to background; otherwise. Afterwards, all squares are determined if they contain bubbles or not. Noticeably, only intermediate bubbles are expected to be detected, no matter completely or partially. Namely, some squares may share a same bubble. This is because that the Fourier transform is invariant on cyclic shift. Nevertheless, the position of bubbles are very important in our mechanism. We have to determine the correct positions of bubbles. A time-consuming but accurate method is applied.
2.3 Bubble centre determination. The aim now is to detect the bubble position in a square S j . Let pi ,1 , pi , 2 denote two 1D gray-level samples (with zero mean) from the i-th bubble template in the database. See Fig. 1. One sample is vertical and another one is horizontal, they cross each other on the centre of the bubble. These samples represent the bubble instead of the whole bubble sub-image. In order to detect the correct position of the bubble in a known region, two samples (with zero mean) are taken from a local region denoted as q1, x , y and q2, x , y , where ( x, y ) ∈ S j
represents the centre of the testing sample. They are of the same size and direction to pi ,1 and
pi , 2 . The centre point is shifted and every point in S j is taken to calculate the cross-correlation. Noticeably, we use cross-correlation since we definitely know there is a bubble in the square S j .
∑∑p
C (i , x , y ) =
x∈S j y∈S j
i ,1
∑∑p
⋅ q1, x , y
si ,1t1, x , y
+
x∈S j y∈S
i,2
⋅ q2, x , y
si , 2 t 2, x , y
,
(2)
where si ,1 and si , 2 denote the standard deviation of pi ,1 and pi , 2 , respectively. The t1, x , y and t 2, x , y represent the standard deviation of q1, x , y and q2, x , y , respectively. Since every point in S j is compared to every bubble template in the database, the bubble centre ( x 0 , y 0 ) should appear in the place where C ( k , x 0 , y 0 ) is largest, 1 ≤ k ≤ N B . After the searching, some squares might contain the same bubble. A process is used to remove those coincidental squares containing the same bubble.
Fig. 1: A bubble template in the database. Two 1D samples that contain the gray level information of the bubble are extracted to be the features.
2.4 Bubble radius determination. To determine the radii of bubbles is non-trivial if there are strong reflections and shadows accompanied with bubbles. This is because the strong contrast resulted from reflections or shadows causes the contour vague. However, with the help of the prior knowledge of database makes this task easier. Via the resizing of the templates and the comparison between the templates and the bubbles of unknown size, the radii of the bubbles can be determined accurately. As the same, we take the 1D samples as features instead the whole bubble sub-image. Let pi′,1 and pi′, 2 be the original samples from the i-th bubble template. { pi′,(1n ) } and { pi′,(2n ) } are their n-variants of different size. Here we simulate the bubbles of different size by resizing the samples. Their corresponding zero-mean features are denoted as { pi(,n1) } and { pi(,n2) } . A cross-correlation process is repeated:
C (i , r ) =
pir,1 ⋅ q1r
+
pir,2 ⋅ q2r
, (3) sir,1t1r sir, 2 t 2r For every template, there are n C (i, r ) values corresponding to the variants. The radius r ′ of the bubble can then be determined if C (k , r ′) is the largest value among them where 1 ≤ k ≤ N B .
2.5 Bubble backwards tracking. The aim of this process is to track the intermediate bubbles which are detected somewhere in the image sequence and might not be detected after several subsequent images owing to the fact that they become smaller. This process is principally a combination of bubble centre determination and bubble radius determination. However, the searching region of the bubble is dependent of the size of the bubble to be tracked. This is based on the fact that the bubble moving speed is dependent of its volume. Nevertheless, this searching region is designed to be changeable according to the experimental demand. 2.6 Nucleation site identification. After the identification of all intermediate and small bubbles, the identification of their nucleation sites is trivial. A simple threshold is given, if the radius of a bubble is less than this threshold and the bubble is not moving, then we assume there is a nucleation site at this position.
3. Results. In this paper, we use an image sequence as an illustration. In this sequence, it is a bottom view of a tube, the conditions are: tube diameter 25 mm, p s = 4.74 bar, q = 3000W / cm 2 , sandblasted surface type, 2-Propanal. There are two to three lamps for the illumination, the distance between the tube and the lamps is about 20 cm. Figure 2 demonstrates the process of database set-up. Figure 2(a) is the image from where the bubble and background templates are selected manually. The templates are shown in Fig. 2(b) and 2(c).
(a) (b) Fig. 2: Two bubbles and six background sub-images are selected as templates.
(c)
Afterwards, every image is divided into several squares as shown in Fig. 3(a). Figure 3(b) is a result of the bubble position detection. A rough detection indicates where the bubbles might be.
This is helpful for the subsequently accurate identification. The desired detection is only the intermediate bubbles, somehow, small or large bubbles may be detected sometimes as shown in Fig.3(b). After the bubble centre identification, the accurate bubble centre can then be determined as illustrated in Fig. 4. 1
2
3
(a) (b) Fig. 3: (a) The image is divided into several non-overlap squares. (b) The result of bubble position detection. The intermediate, large and small bubbles are of the size indicated by arrow 1, 2 and 3, respectively.
(a) (b) Fig. 4: (a) is the result of bubble centre determination from Fig.3(b). (b) is the result from another image where the coincidental squares are demonstrated by three arrows. Some coincidental squares which have lower cross-correlation values are removed. Only one square is retained to represent a bubble.
Figure 5 shows the results of nine subsequent images in a backwards tracking phase. The squares denote the result of bubble centre determination and the four points surrounding the bubbles indicate the radii of the corresponding bubbles. See Fig. 5(e), there is a bubble which has no square containing it. This is because this bubble is not detected in this image, however, the bubble tracking phase stated in section 2.5 has compensated this error and all of the intermediate
bubbles are detected. Repeated, once a bubble is detected, it will not be lost till it vanishes. The disappearance of a bubble has two possibilities: either vanishes in a nucleation site or goes downwards outside the scene. In this sequence, the disappearance takes place only in the nucleation site since it is a bottom view of the tube.
(a)
(b)
(c)
(d)
(e)
(f)
(g) (h) (i) Fig. 5: The system starts in (a), therefore only few bubbles are detected. The bubbles are tracked in a backwards phase. More and more bubbles are then detected and tracked.
Figure 6 is an example that two nucleation sites are detected via the bubble tracking phase. As mentioned before, if the radius of a bubble is smaller than a threshold, then a nucleation site is detected since the bubble does not move any more. Figure 7 is a demonstration that a bubble is splitting. It is split because the sequence is in a backwards phase. The system can identify the bubbles after split, separately. Notably, the small bubbles in the relative low illumination area cannot be detected in Fig. 5. However, they can be tracked as shown in Fig. 7. This is due to the fact that once the bubble is detected, it will not be lost until it vanishes.
(a) (b) (c) Fig. 6: (b) A small bubble, indicated by an arrow, is not detected, but it is discovered in (c). Two nucleation sites are detected and indicated by arrows (c).
(a) (b) Fig. 7: (a) The bubble is splitting, its major part is identified and marked as four points. (b) After the split, since two bubbles are similar to the templates in the database, they can be detected separately.
4. Discussion. There are three limitations in this proposed scheme. Figure 8(a) illustrates a detected large bubble but its radius is not correct. This is owing to the radius of the bubble exceeds the searching range in the phase of bubble radius determination. In addition, there are no such large bubble in the database. Figure 8(b) shows the second limitation. The square indicated by an arrow contains two small bubbles, however, the system can not identify anyone of them since there are not small bubble templates in the database. Therefore, the system fails to
identification. The third limitation is the system needs lots of computations. If the number of templates increases, the computation time also increases.
5. Conclusion. We have proposed a scheme that can identify and track the bubbles in an image sequence, furthermore, to identify the nucleation sites. Four hundred images are tested and most of the results are reliable, except the cases take place as mentioned in section 4. After the tracking, the radii, speeds, positions of bubbles and the positions of the nucleation site are easily identified. They are very important parameters for our cooperating research group (Gorenflo 2000 and Luke 2000) to explore the heat transfer in a boiling system. The future work is to solve the limitations, especially in reducing the computation time.
(a)
(b)
Fig. 8: Two limitations of this scheme. (a) One can not identify the large bubble. (b) Another one fail to identify the small bubbles.
6. Acknowledgement. The authors thank Prof. D. Gorenflo and Dr. A. Luke, University of Paderborn, for providing the bubble images and the financial support by the grants of Deutsche Forschungsgemeinschaft (DFG). References [1] Cheng D.C and Burkhardt H., Bubble recognition from image sequences, Inverse Problems and Experimental Design in Thermal and Mechanical Engineering, EUROTHERM Seminar N° 68, 5-7, March, 2001a, Poitiers, France. [2] Cheng D.C. and Burkhardt H., Tracking bubbles in high-speed image sequences, International Conference of Thermalphysical Properties and Transfer Processes of New Refrigerants, B5.4, 3-5 October, 2001b, Paderborn, Germany. [3] Cheng D.C. and Burkhardt H., Bubble tracking in image sequences, to appear in the International Journal of Thermal Science, 2002. [4] Gorenflo D., Fust W., Luke A., Danger E., and Chandra U., Pool Boiling Heat Transfer from Tubes with Basic Surface Modifications for Enhancement, Proceedings of the 3rd European Thermal Sciences Conference, Sept., 2000, pp. 743-748, Heidelberg, Germany. [5] Luke A., New Methods of Characterization for the Microstructure of Heated Surfaces in Boiling, Proceedings of the 3rd European Thermal Sciences Conference, Sept., 2000, pp. 737-742, Heidelberg, Germany.
