The Method of Flotation Froth Image Segmentation Based on Threshold Level Set

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Wang, Lina Zhang, Conghui Wang Departent of Software Engineering, University of Science and Technology Liaoning, Anshan, China Eail: zhaoji@ustl.edu.

1 Advances in Molecular Iaging, 5, 5, Published Online April 5 in SciRes. The Method of Flotation Froth Iage Segentation Based on Threshold Level Set Ji Zhao, Huibin Wang, Lina Zhang, Conghui Wang Departent of Software Engineering, University of Science and Technology Liaoning, Anshan, China Eail: zhaoji@ustl.edu.cn Received 3 March 5; accepted 4 April 5; published 7 April 5 Copyright 5 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Coons Attribution International License (CC BY). Abstract A novel flotation froth iage segentation based on threshold level set ethod is put forward in view of the proble of over-segentation and under-segentation which occurs when the existing ethod segented the flotation froth iages. Firstly, the proposed ethod adopts histogra equalization to iprove the contrast of the iage, and then chooses the upper threshold and lower threshold fro grey value of histogra of the iage equalization, and coplete iage segentation using the level set ethod. In this paper, the odel which integrates edge with region level set odel is utilized, and the speed energy ter is introduced to segent the target. Experiental results show that the proposed ethod has better segentation results and higher segentation efficiency on the iages with under-segentation and incorrect segentation, and it is eaningful for ore dressing industrial. Keywords Flotation Froth Iage Segentation, Active Contour Model, Histogra Equalization, Speed Function, Threshold Level Set. Introduction Flotation is a ost extensive ineral processing ethod in ineral ental refining application. Its froth surface characteristics such as shape, size and so on are the key to judge the ineral quality. In recent years, uch research has been carried out by any researchers and scholars. For exaple, Vincent [] put forward the novel ethodology based on iersion watershed in 99. Along with deeper research, Guoqing Zhao [] et al. has introduced orphological reconstruction in order to overcoe the over-segentation proble. Nowadays at hoe and broad such as Liu Jinping [3] et al. put forward a novel segentation algorith based on the characteristics of grayscale distribution of flotation froth iage by analyzing the grayscale distribution of each segent How to cite this paper: Zhao, J., et al. (5) The Method of Flotation Froth Iage Segentation Based on Threshold Level Set. Advances in Molecular Iaging, 5,

2 region to extract the features. Mohaad [4] proposed a ethod based on odified ark watershed to easure the size of flotation froth which can easure the size of froth ore accurate and autoatic. There are so any ethods for segenting iage. However, recently the level set ethod [5]-[7] in the field of iage segentation is becoing one of the ost popular and successful ethods. There are two broad categories in the existing active contour odel, such as the boundary-based active contour odel [8] and the region-based active contour odel [9]. In 997, Caselles and Sapior [] et al. put forward geodesic active contour (GAC) odel with no free paraeters which has utilized the gradient inforation of iage to akes the evolving curve to stop on the target boundary. In, Chan and Vese [] proposed the region-based odel called Chan-Vese (C-V) odel which overcoe the boundary-based odel in the sensitivity of original location. And the odel used the target and the difference of relevant pixel values to extract the targets. In order to iprove the accuracy of object edge positioning, Sagiv [] put forward the integrated active contour odel (IAC) in 5 which erges the boundary-based odel with the region-based odel. Jianin Qiao [3] cobined energy constraints with the traditional GAC ode to stabilize in nuerical calculation. In addition, in order to iprove the efficiency of segentation, Khalif [4] presented a new speed function to achieve the target segentation fro the background of the iage. Recently, flotation froth iage segentation ethod at hoe and abroad ainly concentrates edge exploration ethod and watershed segentation ethod, due to edge exploration ethod clais to the high light intensity, so the accuracy of the algorith will be greatly influenced. Although watershed segentation ethod avoids this issue, it is so easy to cause the proble of under-segentation and incorrect segentation that the accuracy of segentation decreases. In order to solve the shortcoings arising fro conventional flotation bubble iage segentation ethod, a novel flotation froth iage segentation based on threshold level set ethod is put forward in view of the proble of under-segentation and incorrect segentation which occurs when the existing ethod segented the flotation froth iages. Firstly, the proposed ethod adopts histogra equalization to iprove the contrast of the iage, and then chooses the upper threshold and lower threshold fro grey value of histogra of the iage equalization, and coplete iage segentation using the level set ethod. In this paper, the odel which integrates edge with region level set odel is utilized, and the speed energy ter is introduced to segent the target. Experiental results show the feasibility and effectiveness of threshold level set odel.. The Novel Proposed Model.. IAC Model... GAC Model Caselles [5] proposed the active contour odel which is not dependent on the free paraeters. The energy functional is as follows: EC = gs d + c gxy dd C () inside( C) Though the variational level set ethod, the above forula will be revised as functional on the ebedding function: = dd + ( ) dd () Eu g Hu xy c g Hu xy where variational level set the gradient descent of flow is as follows: u u δ ε µ div g cg = + u (3) The c is a constant speed function, g is the edge function, Hε ( z) is a Heaviside function, δ ε is a derivative of regularized Heaviside function. That is: g( z) =, K R + ( zk) (4) 39

3 H ε ( z) z = arctan + π ε (5) δ ε ε π ε + z ( z) = The GAC odel is only suitable for the single value iage, in order to realize the vector iage segentation, Caselles and Sapiro [6] proposed a new vector iage GAC odel, the gradient descent flow of variational level set ethod is: In the forula u u δ ε µ div = g + cg u g is a function of iage edge vector. That is, where λ, λ are the two characteristic values. g = g λ λ (8)... C-V Model When the iage not only has no obvious boundary but also the lack of obvious texture feature, it is difficult to achieve a successful segentation. In the iage, the difference between object and background ay also represent the average gray value was different. The iage is divided into two parts of internal and external,, the internal and external average gray level iage exactly reflect the gray level between the object and the background of the average value, then the closed curve can be seen as the object contour. Based on the idea, C-V odel is proposed. The energy functions as follows: (,, ) = µ d + λ ( ) dd + λ ( ) dd (9) Ec c C s I c xy I c xy C It has three variables: scalar c, c, and the curve C. The first one C is the whole arc length. The second and third respectively are the square error between internal and external area s grey value with scalar c, c. In the literature the C-V odel will be extended to functional for vector iages.,, = µ d + λ ( ) dd ( ) dd C + λ () i= i= Ec c C s I c xy I c xy where c = c, c,, c, c = c, c,, c express the two diensional vector. The above forula utilizes the variational level set ethod to be revised as functional on the ebedding function: = µ δ + λ i= + λ ( ) i= Ec, c, u u udd xy I c Hudd xy I c I Hu dd xy So in the function u of fixed conditions, relative to c and c iniization can be obtained: ( i) j I ( i ) dd (6) (7) () j c =, j =,, i =,, () dd xy j That is the internal and external average vector iages in current zero level set. Under fixed c and c conditions, with respect to the u iniization can be obtained: xy 4

4 u u = δ ε µ div λ I c + λ I c u i i i= i= (3)..3. IAC Model Although the region-based C-V odel overcoes the drawback of GAC odel, it is not in favor of the contours evolving into the object boundaries quickly and accurately. However the boundary-based GAC odel lacks the ability of global segentation. So the Integrated Active Contour (IAC) Model put forward, the energy functional is as follows: ( i) i i i = µ + C λ + i λ = i= Ec, c, C g d s I c dd xy I c dd xy (4) where variational level set the gradient descent of flow is as follows: = µ δ + λ i= i= Ec, c, u ug udd xy I c Hudd xy + λ I c Hu dd xy In the function u of fixed conditions, the iniization results of c and c is the sae as forula (). And under fixed c and c conditions, the relative to u iniize type can be obtained:.. The Threshold Speed Ite u u = δ ε µ div g λ I c + λ I c i i u i= i= (5) (6) The GAC odel cannot accurate segent the object with deep low-lying regions, therefore this paper introduces a constant speed which set to c in IAC odel to guide curve evolution, the energy functional is defined the by: ( i) i i i = µ + + λ C C + λ i= i= Ec, c, C g d s c g dd xy I c dd xy I c dd xy (7) where variational level set the gradient descent of flow is as follows: u u = δ ε µ div g + cg λ I c + λ I c i i u i= i= (8) However, the paraeter by iproperly choosing will lead to edge leakage or slower convergence speed, thus a speed function is introduced V as follows: V = g βκ (9) where β is the constant paraeter which controls the soothness of active contour, and κ denotes curvature. Edge function can only reflect the local gray level change of iage rather than the actual iage edge. There is a segentation ethod called threshold segentation ethod which seeks a suitable grey value and then the two classifications are obtained by coparing it with each of iage gray level value. Finally, the iage of object and background are fored to coplete the iage segentation. The novel threshold speed function is introduced V as follows: ( ) V = αp I + α κ () The constant α is a weight nuber of curvature κ. And P I is a function of iage intensity I as follows: 4

5 P I U L U + I L = where U, L are represent upper threshold and lower threshold, respectively. In the forula (), the intensity I is equal to the value ( U + L). The forula () akes the active contours enclose the boundary of region whose intensities are in the interval [ LU, ]. The ter P( I ) based on iage intensity I causes the odel to contract regions and expand over with gray values within the specified interval [ LU, ]. The threshold level set odel controls the active contours to capture the regions of interest by adjusting paraeters L and U..3. Cobining Threshold Speed Ite and IAC Model In this section, threshold speed ite is cobined shape priors and IAC odel. The total energy is defined by ( i) i i i = µ + + λ C C + λ i= i= Ec, c, C g d s V g dd xy I c dd xy I c dd xy () where variational level set the gradient descent of flow is as follows: u u U L U + L = δ ε µ div g + α I + α κ g λ I c + λ I c i i ( ) u i= i= 3. Algorith Ipleentation 3.. Histogra Equalization () (3) Gray histogra of the iage reflects the friendship between iage grayscale and the probability of occurrence of this kind of grayscale. In order to enhance iage contrast, this article adopts the ethod of histogra equalization [7]. Firstly, an array containing G eleent is set up, statistics of the original iage grey values, and then draw the gray-level histogra. Finally, the apping of gray-scale is realized by histogra transforation, which is written as: = =,,, h k n k G (4) k where n k is the nuber of the pixels of the sae grey value k. And the forula (4) is written as the probability of noralized expression =, =,,, P S n n S k G (5) s k k k where s k denotes the kth level of grey value of iage, and n denotes the total nuber of pixels in the iage. In addition, iage enhanceent function is shown as: a) EH ( s ) is single value increasing function, and S G akes the grayscale still fro sall to large order after equalization. b) EH ( s) G always keeps the dynaic range of grayscale unchanged. Cuulative Distribution Function (CDF) ust eet the above two requireents at the sae tie, and the unifor distribution of t transfors by the distribution of s. While the cuulative distribution functions of s is the cuulative histogra of original iage in fact, and then: k k n t = E S = = P S i (6) k H k s i i= n i= where t k is a single value increasing function of k, the dynaic range of grayscale is unchanged, and. t k 3.. Obtaining Upper and Lower Threshold According to the concrete fors of histogra and the position of peak to extract the threshold, convenience is 4

provided for the accurate segentation process. The original iage and the gray level histogra of before and after the equalization of shown as are Figure.

The gray value which is less than a and greater than b is of saller proportion in the histogra.

6 provided for the accurate segentation process. The original iage and the gray level histogra of before and after the equalization of shown as are Figure. This section will be introduced how to obtain the threshold in detail. Such as Figure (d), there are two peak valleys which are a and b ( a < b). The gray value which is less than a and greater than b is of saller proportion in the histogra. In the analysis, grayscale less than a is caused by uneven light irradiation in iage collection process and then leads to the edges of froth darker shade. While the latter is due to laplight illuinate the top of the froth. Another crest of figure shows that the nuber of gray levels between ( cd, ) is the ost and threshold should be expanded to select in order to avoid excessive under segentation in the process of segentation, a L< c, d < U b. The two values are substituted into forula (), we obtain P( I ) as follows: b a P I I b + a = (7) And then the new speed function V can be gained by substituting P( I ) into Forula () (a) (b) (c) (d) Figure. (a) Original iage; (b) The histogra of original iage; (c) After the equalization iage; (d) The histogra of after the equalization iage. 43

4. Experiental Results and Analysis In this section, we will use the novel segentation algorith proposed in

algorith and the segentation algorith based on IAC ethod to do experients. 4.

The saple iages used for experient are shown in Figure and after histogra equalization iages are shown in

.. Watershed Segentation Method Watershed segentation ethod whose characteristics are intuitive and rapid is

Because gradient iage of any iages have a lot of local iniu, so can see the results as shown Figure 4 that

7 4. Experiental Results and Analysis In this section, we will use the novel segentation algorith proposed in this paper to do experient, at the sae tie we also use the watershed segentation algorith, the C-V segentation algorith and the segentation algorith based on IAC ethod to do experients. 4.. Experiental Results Now we choose the following four iages as the experiental iages. The saple iages used for experient are shown in Figure and after histogra equalization iages are shown in Figure Watershed Segentation Method Watershed segentation ethod whose characteristics are intuitive and rapid is chosen to segent flotation forth iage, the results are shown in Figure 4. Because gradient iage of any iages have a lot of local iniu, so can see the results as shown Figure 4 that there are a yriad of sall area boundaries. At the sae tie watershed algorith is sensitive to noise. The final segentation result is not ideal due to the proble of over and under segentations. Figure. Color saple iages. Figure 3. After the histogra equalization processing saple iages. Figure 4. Watershed segentation result. 44

(Paraeter of Heaviside function and Dirac function) and the iterations Nb_iter = 3.

8 4... Level Set Method There are results of three level set segentation ethods in the section. a) C-V odel Figure 5 shows the segentation results of the C-V which based on region, where the paraeters are set to: τ = (Step Length), ε =. (Paraeter of Heaviside function and Dirac function) and the iterations Nb_iter = 3. As is evident fro Figure 5, the results of C-V odel are better than watershed ethod, but the C-V odel is initialized again every once in a while which takes ore tie for segentation. In addition, the gray level of iage is too uneven to correct segentation. The final segentation result is not also ideal. b) IAC odel Figure 6 shows the segentation results of the IAC, where the paraeters are set to: τ =, ε =. and the iterations Nb_iter = 8. The results copared with the above two ethods are also iproved. Although all the bright spot in the whole picture can be segent and the speed is faster than C-V, the darker regions still cannot be segent. The proble of under segentation is not solved and the results are unsatisfactory. c) The novel proposed odel In this paper, the odel which integrates edge with region level set odel is utilized, and the speed energy ter is introduced to segent the target. The segentation results are shown as Figure 7, where the paraeters are set to: τ =, ε =., µ = 5 (Paraeters of Controlling the relative size of bound ter), α =.95 (A weight nuber of curvature κ ) and the iterations Nb_iter = 36. The iage contrast is enhanced by histogra equalization and then on this basis the upper and lower thresholds are selected. Finally, the speed function which contains the thresholds guides the curve evolution. The ethod proposed in this paper for the region of non-unifor gray iage has uch better segentation effect than the above ethods. Moreover, copared with C-V and IAC, the tie of segentation is also shortening The Evaluation and Analysis of Segentation Results We ainly analyze and evaluate the experiental results fro the segentation tie and accuracy. At first we copare the segentation efficiency of the segentation ethod using watershed, C-V, IAC and the proposed ethod. Figure 5. The odel of C-V segentation result. Figure 6. The odel of IAC segentation result. 45

characteristics of watershed ethod are intuitive and rapid. Next the Siilarity Index (SI) is utilized to copare the results described on above on the segentation accuracy.

9 The statistical graph of the tie efficiency of four kinds of segentation ethod is shown in Figure 8 through experients and analysis. As you can see in Figure 8, the segentation tie of the proposed ethod is uch faster than that of C-V and IAC ethods, but which is slower than watershed ethod and the result is that the characteristics of watershed ethod are intuitive and rapid. Next the Siilarity Index (SI) is utilized to copare the results described on above on the segentation accuracy. In Figure 9, the statistical situation of the SI is shown, respectively. As you can see in Figure 9, the segentation accuracy of the proposed ethod is superior to that of watershed ethod, C-V ethod and IAC ethod. 5. Conclusion This paper utilizes the Histogra Equalization to enhance iage contract to see the size and shape of froth easily, and chooses the upper threshold and lower threshold fro grey value of histogra of the iage equalization, and coplete iage segentation using the level set ethod. The threshold speed function is introduced in the odel which integrates edge with region level set odel is adopted to solve the proble of over segentation and under segentation. Via the coparison of several groups of experients, it is proved that the segentation precision and efficiency of the novel level set segentation ethod are iproved. Figure 7. The odel of the present paper segentation result. 8 6 Tie used for iage segentation (s) Watershed C-V IAC The proposed odel Figure 8. Tie efficiency contrast. 46

10 (SI) Acknowledgeents. Watershed C-V. IAC The proposed odel Figure 9. Segentation accuracy contrast. This research is funded by the Education Departent of Liaoning Province Foundation grant Nuber LJQ433 and University of Science and Technology Liaoning Foundation grant Nuber 3RC8. References [] Vincent, L. and Soille, P. (99) Watersheds in Digital Spaces: An Efficient Algorith Based on Iersion Siulations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3, [] Zhao, G.Q., Gu, Y.Y., et al. (7) A Classification of Flotation Froth Based on Geoetry. Mechatronics and Autoation, Harbin, [3] Liu, J.P., Gui, W.H., Chen, Q., et al. (3) An Unsupervised Method for Flotation Froth Iage Segentation Evaluation Base on Iage Gray-Level Distribution. IEEE Control Conference (CCC), Xi an, [4] Massinaei, M. (4) Developent of a New Algorith for Segentation of Flotation Froth Iages. Minerals and Metallurgical Processing, 3, [5] Wirthgen, T., Lepe, G. and Zipser, S. () Ulrich Grünhaupt Level-Set Based Infrared Iage Segentation for Autoatic Veterinary Health Monitoring. Coputer Vision and Graphics, [6] Wirthgen, T., Zipser, S., Franze, U., et al. () Autoatic Segentation of Veterinary Infrared Iages with the Active Shape Approach. Lecture Notes in Coputer Science. Proceedings of 7th Scandinavian Conference on Iage Analysis, [7] Li, P.H., Bagci, U., Aras, O., et al. () A Novel Spinal Vertebrae Segentation Fraework Cobining Geoetric Flow and Shape Prior with Level Set Method. IEEE International Syposiu on Bioedical Iaging, Barcelona, [8] Li, C.M., Xu, C.Y., Gui, C.F., et al. (5) Level Set Evolution without Re-Initialization: A New Variational Forulation. IEEE Conference on Coputer Vision and Pattern Recognition, San Diego, [9] Paragios, N. and Deriche, R. () Geodesic Active Regions and Level Set Methods for Supervised Texture Segentation. International Journal of Coputer Vision, 46, [] Caselles, V., Kiel, R. and Sapiro, G. (997) Geodesic Active Contours. International Journal of Coputer Vision,, [] Vese, L. and Chan, T. () A Multiphase Level Set Fraework for Iage Segentation Using the Muford and Shah Model. International Journal of Coputer Vision, 5, [] Sagiv, C., Sochen, N.A. and Zeevi, Y.Y. (6) Integrated Active Contours for Texture Segentation. IEEE Transac- 47

11 tions on Iage Processing, 5, [3] Qiao, J.M. () The Iproveent of Iage Segentation Based on GAC Model and C-V Model. Harbin Institute of Technology, Harbin. [4] Khalifa, F., El-Baz, A., Ouseph, R., et al. () Shape-Appearance Guided Level-Set Deforable Model for Iage Segentation. IEEE International Conference on Pattern Recognition, Istanbul, [5] Chung, D.H. and Sapiro, G. () On the Level Lines and Geoetry of Vector-Valued Iage. IEEE, Signal Processing Letters, 7, [6] Sapiro, G. () Geoetric Partial Differential Equations and Iage Analysis. Cabridge University Press, Cabridge. [7] Wang, B. () The Iproveent of Iage Segentation Based on Level Set Method. Xidian University, Xi an. 48

Novel Image Representation and Description Technique using Density Histogram of Feature Points

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