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1、精品论文A Bubble Detection Algorithm Based on Sparse andRedundant Image ProcessingTIAN Ye, ZHENG Change, KE Qiuhong5(School of Technology, Beijing Forestry University, Beijing 100083)Abstract: Deinked pulp flotation column has been applied in wastepaper recycling. Bubble size in deinked pulp flotation c
2、olumn is very important during the flotation process. In this paper, bubbleimages of deinked pulp flotation column were first caught by digital camera, and then the bubbles were detected by using a detection algorithm based on sparse and redundant image processing.10The results show the algorithms a
3、re very practical and effective on bubble detection in deinked pulp flotation column.Keywords: image processing; bubble detection; sparse and redundant0Introduction15Flotation column is mainly used in ore dressing, which adopts convection sorting principle in order to separate and recycles minerals.
4、 The speed of pulp and bubble is low, but their relative speed is very high to achieve the purpose of the mineral separation. Since the bubble size in deinked pulp flotation column determines the air surface area per unit, which directly influences the ability of bubble capturing pulp ink particles
5、and other impurities mix in pulp during the20flotation process. In addition, bubble size also affects bubbles working rising speed. So in recentyears, the bubble size measurement of floatation column gradually has become the research focus1-2.In our equipment, flotation column is composed of Cylinde
6、r made up of transparent PVCmaterial, so it is in favor of observing circumstances of cylinder and the size of the bubble when25flotation column is working. Use of a digital camera can capture dynamic bubble images directly.Because paper pulp and cylinder are translucent, we choose a back light for
7、illumination, thats also called transmitted light. Light source is LED bright-field illumination. Because the original image scontrast is poor and affected by the very large noise, classic edge extraction operators (such as Sobel , Roberts, Etc.) which are extremely sensitive to noise andimpossible
8、to apply.30This paper will realize the bubble dection by sparse and redundant image processing.1Research MethodIn the last decade, In field ofmultiresolution analysis, sparsity has been used in a wide range of image processing applications(feature extraction, denoise, restoration, and compression).
9、Differing from the traditional resentations, sparsity offers a wider range of generating elements35(called atoms). A signal is strictly or exactly sparse if most of its entries are equal to zero. if a signal is not sparse, we can sparsify itthrough an appropriate transform. for example, a sine signa
10、l is not sparse in time domain, but its Fourier transform is strictly sparse.By means carefully selected atoms (such as sinusoids, wavelets,and Gausssians), we can transforma signal to a desired form. Different transforms often are used by different purposes:340z the Fourier transform for stationary
11、 signalsz the windowed Fourier transform for locally stationary signalsz the wavelet transform for representing isotropic features, such as point ,noise基金项目：高等学校博士学科点专项科研基金（20110014120012）；国家自然基金（31200544） 作者简介：田野，（1972-），男，讲师，主要研究方向为智能检测与数据处理。 通信联系人：郑嫦娥，（1977-），女，副教授，主要研究方向：机器人技术、林火监测。 E-mail:zheng
12、change- 8 -z the ridgelet transform for perfectly straight edgesz the curvelet transform for curvilinear structures45Every transform include analysis and synthesis operations. Analysis is the operation thatassociates with each signal x a vector of coefficients attached to an atom: = T x . Synthesisi
13、s the operation of reconstructing x by superposing atoms:different linear operations 3.x = . Analysis and synthesis are1.1Two-Dimensional Decimated Wavelet Transform and bubble dection50InOne-Dimensional DWT, a scaling function (t) and a wavelet function (t) are used forobtaining approximate informa
14、tion and details informations. So One-Dimensional DWT algorithmcan be exended to two-dimension by separable products of a scaling function and a wavelet function. it will generate an approximate subimage(low-frequency subband) and the three detail subimages(high-frequency subband). They arehorizonta
15、l, vertical, and diagonal directions55details, as shown in Figure 1.2Figure 1. Image decomposition based on wavelet transformAfter two-dimensional decimated wavelet transform, A is approximation image of the60original image which contains the most information of the original image. H, V, D preserve
16、the details of the original image. H preserves the horizontal edge details. V preserves the vertical edge details .V preserves the diagonal details which are influenced by noise greatly. Using multiresolution analysis, The approximation A can be decomposed as needed. Finally, the original image will
17、 be transformed to an approximate image and a series of wavelet(detail) images at65different resolution levels, as shown in Figure 2.3-4ApproximationA2HorizontalDetails 12level j=2Horizontal Details 11level j=1VerticalDetails 2level j=2DiagonalDetails 3level j=2Vertical Details 2level j=1Diagonal De
18、tails 3level j=12211Figure 2. DWT representation of an image1.1.1Approximation image edge detecting based on canny operator70A is approximation (smoothed) image of the original image, In A, edge detecting by applying canny operator, Canny operator has the most stringent criterions of edge detecting.
19、A good effectwill be obtained adopted canny operator when processing the image containated by additive whiteGaussian noise.Applying canny operator on the approximation image, clear edges can be obtained, but some75real edges are missed, and there exist some append edges in the image. Thus the edge d
20、etails of the wavelet subimages should be used.1.1.2Denoising of the wavelet subimages based on wavelet transform.Because wavelet subimage corresponds to high-frequency component of original image, the wavelet coefficients of the wavelet subimage which have smaller amplitude present the most noise80
21、part, and the wavelet coefficients which have larger amplitude present the details of the image.Using hard or soft thresholding, reduce the noise in the wavelet subimage.Many thresholding or shrinkage rules have been proposed in the last decade. Among them, hard and soft thresholding are certainly t
22、he most well known.3-4Hard thesholding consists of setting to zero all coefficients whose magnitude is less than a85threshold t. it means the keep-or-kill rule. (i, j), (i, j) t (i, j) = HardThresh( (i, j)0, otherwiseSoft thresholding is defined as the kill-or-shrink rule:sign( (i, j) ( (i, j) t, (i
23、, j) t (i, j) = SoftThresh( (i, j)0, otherwise(1)(2) (i, j)is the wavelet coefficient.90951001.1.3Wavelet reconstructionUsing wavelet reconstruction, the resulting image will be obtained.1.2Redundant wavelet transform and bubble dectionBecause the discrete wavelet transform(DWT) leaded to the loss o
24、f the translation-invariance property, a large number of artifacts are generated when an image is reconstructed after modification of its wavelet coefficients. Byredundant wavelet transform , that problem canbe avoided. Compared to DWT, redundant wavelet transform keeped the filter bank construction
25、 and eliminated the decimation step in the DWT. So redundant wavelet transform means the undecimated wavelet transform(UWT).The isotropic undecimated wavelet transform(IUWT) algorithm is well known in the astronomical domain because it is well adapted to astronomical data, where objects are more or
26、less isotropic in most cases 5-7. The bubbles are alse the same.IUWT has motivated the following choice for the analysis scaling and wavelet functions 3 :1 D(t) =1 ( t 2 3 4 t 1 3 + 6 t 3 4 t + 1 3 + t + 2 3 ),12 (t1 , t 2 ) = 1 D (t 1)1 D (t2 )(3)1 ( t1 , t2 ) = (t , t) 1 ( t1 , t2 )42 21 242 2wher
27、e1 D (t)is the 1-D B-spline of order 3(i.e., B3-spline) and the wavelet function is105defined as the difference between two resolutions. The related pair of filters(h,g) is defined byh1 D k = 1,4,6,4,1 /16,hk , l = h1 D k h1 D lgk, l = k , l hk, lk = 2, K, 2(4)where is defined as 0,0=1 and k,l=0 for
28、 all (k, l) (0, 0).It is easy that the reconstruction is obtained by the simple coaddition of all wavelet scales andthe final smooth subband,110Ja0 k , j = a J k , j + j k , jj =12Results and Analysis(5)1152.1Wavelet Transform and bubble dectionFirst, we applied DWT to experiment using db10 wavelet.
29、 Table 1- Table 3 give the different decomposition levels information. Table 1 A1: Approximation MeanMedian Maximum Minimum Standard dev177.5 178.7 217.3 108.6 12.71Table2 A2: ApproximationMean Median Maximum Minimum Standard dev352.9 355.2 428.6 225.4 25.04120125Table3 A3: ApproximationMean Median
30、Maximum Minimum Standard dev89.02 89.54 106.5 56.24 6.251Because the standard dev of A2 is the biggest, which means A2 contains the most information of the original image. So we select 2 - level wavelet decomposition as shown in Figure 3.Figure 3. DWT decompositionIn Figure 3, the noises appeared in
31、 details of level 1 and level2. They can be removed by hard or soft thresholding.Figure 4 shows the result of bubble detection for the image.(a)The original image(1112x763) (b) Detecting result by Canny operator in A2 (214x301)(c)wave reconstruction (d)Thresholding130(e)Morphology processingFigure 4
32、. Bubble detecting result135In Figure 4(b), on approximation of A2 level, Edge detecting bases on canny operator, twothresholds are 0.2 and 0.4, is 1.5.To denoising, the wavelet coefficients of 1-level set zeros.After edge detecting and denoising, wave reconstruction is used. See Figure 4 (c). In Fi
33、gure 4(d),After thresholding, the binary image isobtained. Using morphologys open, close and fill hole operator8, see Figure 4 (e). The results of bubble detection are very good.2.2IUWT and bubble dectionFigure 5 shows the IUWT of the images of bubble at five resolution levels.(a) (b) (c)140145(d) (
34、e) (f)Figure 5. The IUWT of the bubble imageThe addition of these six images will reproduces the original image.The IUWT of the bubble image consist of five detail images and the smooth images. each ofthe six images is the same size oforginal image. The redundancy factor is equal to 6.In order to ac
35、quire faint feature of bubble image and denoising, the details of level 1 and level 2 are set zeros,log apply to the others, that means:5150a0 k , j = log(aJ k , j) + sign( j k , j) log( j k , j + 0.001)j =3The reconstruction image showed in Figure 6.Figure 6. the reconstruction of bubble imageFigur
36、e 7 shows the result of bubble detection.(6)(a) the reconstruction image using Equation (6) (b) Thresholding(c) the complement of (b) (d) fill hold operator(e) the answer of (d)-(c) (f) open and close operatorFigure 7. Bubble detecting result by IUWT155Using morphology processing, see Figure 7 (c)-(
37、f). The bubbles are detected. Figure 8 show the different between DWT and IUWT.（a）the original image(b) the image after DWT applyed (c) the image after IUWT applyedFigure 8. different between DWT and IUWT.160165In Figure 8(b), it stresses the dark edge of bubble, andFigure 8 (c) , it stresses the br
38、ight edge of bubble,not onlythe edge of bubble in Figure 8 (c) is more smoother than in Figure 8 (b), but alse it also consistents with the original shape.3ConclusionThis paper proposed a bubble detection algorithm based on sparse and redundant image processing, the algorithm not only reduce the noi
39、se simply and also keep the fine image edges.Finally, the bubbles are detected.References1701751801851901 Sun Liying, Li Qiongyan, Qian Hua, Tian Ye. Application of Image Enhancement Technology in BubbleDimension Measurement of deinked pulp flotation column.Advanced Materials Research. 2012; Vol (51
40、0):484-489.2 Ye Tian, Hua Qian, and Qiuhong Ke. A bubble detection algorithm based on wavelet transform and canny operator for Deinked Pulp Flotation Column. Applied Mechanics and Materials. 2013 Vols. 278-280 : 1162-1166 3 Jean-Luc Starck, Fionn Murtagh and Jalal M.Fadili. Sparse Image and Signal P
41、rocessing. New York: Cambridge University Press. 20104 Stephane Mallat. A Wavelet Tour of Signal Processing. 2nd edition. Academic Press. 19995 MALLAT S, HW ANG W L. Singularity Detection and Processing with Wavele. IEEE Trans 2002;IT-38(2):617-643.6 Starck, J.-L., and Murtagh. Image restoration wit
42、h noise suppression using the wavelet transform. Astronomy and Astrophysics, 1994; 288, 343-348.7 Starck, J.-L., and Murtagh. Astronomical Image and Data Analysis. 2nd edition. New York: Springer. 2006 8 Rafael C. Gonzalez. Digital Image Processing. 2nd edition. Pearson Education. 20059 Information on 基于稀疏与冗余算法的气泡图像提取方法田野，郑嫦娥，柯秋红（北京林业大学工学院，北京 100083） 摘要：浮选柱已经应用到废纸再利用等方面。在整个浮选过程中，气泡的大小起决定的作用。 本文首先利用高速摄影机实时捕捉浮选溶液中的气泡，然后采用基于基于稀疏与冗余算法的 气泡图像提取方法。实验证明：该方法应用在浮选柱气泡检测方面是可行的。 关键词：图像处理；浮选柱气泡；稀疏与冗余算法中图分类号：U464.172; U464.136
