An Apparatus and Method for Real-Time Stacked Sheets Counting

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An Apparatus and Method for Real-Time Stacked Sheets Counting With Line-Scan Cameras Tiejian Chen, Yaonan Wang, and Changyan Xiao

Abstract— To satisfy the requirement of quality control in printing and packaging industry, a sheet counting apparatus is developed, which adopts a line-scan camera to image the fringes of sheet stack and is able to provide a real-time and noncontact measurement of their quantity. With a brief introduction of the system architecture, our main work focuses on the sheet counting algorithms. The basic principle is to identify each sheet profile from the 1-D image with a robust ridge strength measurement. First, a multiscale bi-Gaussian ridge likelihood measurement and a ridge-valley descriptor are utilized to improve adjacent objects detection by increasing local contrast around sheet fringes. Then, a sheet recognition scheme, which integrates a peak detection algorithm and the ridge region criteria for verification, is proposed to discriminate true sheets from the obtained ridgeness measure. According to experiments and tests in real production lines, our apparatus can reach a very high measuring accuracy for printing papers or cards with a thickness not σ. kG(|x| + σb − σ, σb ) (3)

Fig. 4. Comparison of the different kernels (the filter refer to the second-order derivatives of the according kernel; the parameters are σ = 4, σb /σ = 0.3). (a) Normalized sheetness filter. (b) Normalized rectangle filter. (c) Normalized bi-Gaussian filter. (d) Frequency responses.

To demonstrate its performance, the Gaussian sheetness filter (2) is applied to the six representative sheet profiles in Fig. 3. We configured the parameters σmin = 3, σmax = 5, and five evenly spaced scales are used. As shown in Fig. 3(b), the ridge strength of standard sheet is positive and gets strongest at the center; it is below zero for normal gap, and around zero for the background and wide gap. It is also insensitive to the local average and sheet width variation, so both the standard sheet and broadened gap segments get acceptable responses. But undesirable results are found for the sheets marked with U1 –U5 , their ridge measure at P1 –P5 is merged with the adjacent objects and become indistinguishable in the demonstration. The main reason is that the Gaussian kernel inherently takes slowly decreasing side lobes as shown in Fig. 4(a); inappropriate background wider-than-real gaps are involved in the convolution, which will affect the contrast in case of narrow neighborhood.

Here, σ and σb are, respectively, the foreground and background scales. As analyzed in [19], a fixed ratio k = σb2 /σ 2 should be adopted to guarantee the feasibility of γ −normalized derivatives under the scale space framework. The principle of the bi-Gaussian kernel can be more obviously seen from its second-order derivative  G (x, σ ) |x| ≤ σ (4) bg (x, σ, σb ) = kG  (|x| + σb − σ, σb ) |x| > σ. Here, two Gaussian derivatives with different scale parameters are stitched together at x = ±σ . As shown in Fig. 4, its second-order derivative can be considered a combination of the Gaussian and the smoothed rectangle kernel second-order derivatives. If setting a small scale ratio ρ = (σb /σ ) < 1, the bi-Gaussian derivative operator is expected to provide more accurate ridgeness measure of the sheet fringe and its neighboring narrow gap while applied to the stack image. Simultaneously, the wide main lobe of the bi-Gaussian kernel make it still keep the same noise suppressing ability of traditional Gaussian filters, which will help to prevent multiple responses during the following sheet identification process discussed later. To improve the previous sheet ridge likelihood on adjacent objects, we directly replace the h(x, σ ) in (2) with a normalized bi-Gaussian kernel h b (x, σ, σb ) = −σ 2γ · bg  (x, σ, σb )

B. Enhancing the Sheet Likelihood by Bi-Gaussian Filter To circumvent the problem of adjacent curvilinear structure detection, a bi-Gaussian kernel was recently proposed by integrating the merits of the traditional Gaussian kernel and

(5)

and Fb =

max

σmin ≤σ ≤σmax

I (x) ⊗ h b (x, σ, σb ).

(6)

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Fig. 5. Sheet recognition results for some difficult cases. (a) Original sheet image with the true sheets location marked by . (b)–(e) Results obtained by the peak detection method, the threshold method (thr = 0), the sheet identification algorithm, and the complete counting scheme (the detector used for ridge likelihood measure, sheet identification, and verification is used to locate sheets). : detected sheet location. E1–E4: identification errors. : removed errors by verification. R: ridge region with its area and peak denoted by Ar , rm .

Here, σmin , σmax , and the scale step are configured the same as before, and a fixed scale ratio ρ ∼ 0.3 is suggested with our experiments. To compare with the previous Gaussian sheetness filter, the newly obtained sheet likelihood with the bi-Gaussian filter (6) is presented in Fig. 3(c) using the same testing data. As the ridge strength at P1 –P5 , the closely located fringes are obviously enhanced with larger positive responses and completely separated peaks are observed. C. Ridge-Valley Descriptor Although the above bi-Gaussian operator can largely improve adjacent objects detection, the abnormalities like bimodal distortion and irregular deformation, whose profiles deviate severely from the standard Gaussian shape, still get a low and indistinct response as P1 –P3 in Fig. 3(c). To compensate this, we propose to utilize the intersheet gaps, which appear as a low gray-level valley, to stretch the local contrast of the previous obtained ridge likelihood. As observed, the gap valleys seldom take irregular deformation though their width might cover a large range. Here, we directly adopt a single scale normalized second-order Gaussian kernel 2γ σv ∂/∂ x 2 G(x, σv ) to calculate the valley likelihood Fv , and σv is set to half of the mean gap width. Then, a ridge-valley descriptor is defined as F = Fb − η ∗ Fv

(7)

which stretches the contrast between the fringe and its adjacent gaps by subtracting the two likelihood measures. Here, η is a coefficient to adjust the weight of valley influence. Usually, a medium η ∈ [0.5, 1] is acceptable, and η = 0.8 is chosen in our experiments. The principle behind the descriptor is to extend the relative contrast by decreasing the value of neighboring background rather than directly increasing the ridge likelihood itself. To further understand it, we can check P1 –P3 in Fig. 3(d), which have a low Fv response at the ridges but a large one at the valleys. Consequently, the synthetic response in Fig. 3(e)

has no obvious raise on absolute peak value, but the ridgevalley magnitudes are saliently enlarged. As for the extraordinarily wide gap G, Fv actually detected the step edges, which also resulted in an unexpected enhancement of local contrast. Therefore, the ridge-valley descriptor will more benefit the subsequent sheet identification than the original ridge likelihood measures. D. Sheet Identification and Verification To achieve accurate measure of the sheets quantity, an indispensable step is to identify each sheet from the above ridge likelihood measures. According to Section III-C, this task has been largely simplified with the proposed ridge-valley descriptor, which makes it possible to discriminate a majority of sheets with a simple threshold or peak detection algorithm. However, for some difficult cases as in Fig. 5(a), complex factors like multiple ridge responses (F1), background interferences (F2), fake ridge (F3), and neighboring ridge merging (F4) make both these two algorithms inaccurate as shown in Fig. 5(b) and (c). As a remedy, we propose a general sheet identification algorithm to correctly recognize the sheets. The basic principle of sheet identification is to merge sliding window peak detection [11]–[13] with some prior knowledge. According to the previous analysis, the ridge responses of sheets are positive and strongest around its center, so all the sheets can be located around the center position by applying peak detection to the positive part of the ridgeness measure. However, as shown in Fig. 5(b), a main problem is that the multiple ridge responses and background noises are often incorrectly identified as sheet fringes. To avoid this, the following prior knowledge of the sheet stacks is utilized. 1) The space between adjacent sheet centers is above 2σmin , and the ridge response peak of sheet should be a local maximum in its neighborhood [−σmin , σmin ]. 2) The gray level around the sheet center (I p ) is higher than the average of the image. According to these constraints, the following algorithm is adopted to identify the true sheets.

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1) The peaks of the positive ridgeness measure are detected in a sliding window with a width 2σmin + 1. If the ridge response at the window center c is the local maximum within [c − σmin , c + σmin ], take c as a sheet position and update c = c + σmin + 1, otherwise c = c + 1. 2) Remove the sheet position if the corresponding gray values I p are below the average Ir of a reference area. As shown in Fig. 3(c) and (e), the identification algorithm can achieve a full success for the typical sheets. In addition, its advantages are revealed more for the challenging cases in Fig. 5; the algorithm is obviously more effective to deal with the difficult problems F1, F2, and F4 through comparative analysis of Fig. 5(b)–(d). However, for rare extremely challenging cases, there are identification errors as labeled by E1–E4 in Fig. 5(d). For sheet recognition, if the detected location is within sheet center area, we define it as true positive (TP). The false negative (FN) error is the undetected sheet (E1), while the false positive (FP) error includes the repeatedly detected sheets (E2) and the fake ridge (E4). Another extremely rare error (E3) is that the detected location is at the gap rather than the sheet center area. These errors are closely related to the ridge detection method. The error E1 is mainly caused by neighboring ridge merging, so it occurs only when the sheetness filter is used. As for the proposed bi-Gaussian filter and descriptor, the remaining problem is the particular error E2 and common error E4, which are caused by unsmooth ridge response and the abrupt gray-level vibration separately. Considering these two exceptions, a verification step is developed as a complement to sheet identification. The verification algorithm introduces some ridge region criteria to remove the error E2 and E4 inspired by the threshold method. As shown in Fig. 5(c), the positive ridge response can be separated into different ridge regions R by the zero-crossing line. The error E2 can be removed if only one sheet is allowed in a ridge region. This is guaranteed by the advantages of the proposed ridge detection methods, which make the ridgeness measure above zero for all the sheets and below zero for the adjacent gaps. As to the fake ridge E4, the according ridge response usually appears like a low energy temporal signal, which causes the area Ar and maximum response rm of the according ridge region much smaller than the sheets. So, it can be avoided by setting thresholds on both Ar and rm . As shown in Fig. 5(e), the identification errors are effectively removed by the verification process, and all the difficult sheets counting problems are solved with our algorithms. IV. E XPERIMENTS AND S YSTEM T EST In this section, we will evaluate the apparatus performance with a series of quantitative indices, including the accuracy, counting error, robustness, measure range, and counting speed. Then, a comparison with the existing methods is presented. Finally, other applications of the apparatus are also discussed. A. Quantitative Evaluation of the Apparatus Performance The performance is evaluated from the following perspectives to verify the effectiveness of the proposed algorithms.

TABLE I Q UANTITATIVE E VALUATION OF THE A PPARATUS P ERFORMANCE

1) Counting Accuracy and Error Analysis: For the quantity measure application, it is hard to define true negative from the counting result. Instead, the precision (Pr ) and recall (Rc ) are used to investigate the counting accuracy. They are defined as TP TP Rc = . (8) Pr = TP + FP TP + FN Here, a small Pr indicates that many interferences are wrongly recognized as sheet, while a small Rc reflects that many real sheets are undetected. Obviously, for a perfect measure, it is desired both the Pr and Rc are 100%. The counting error is the main concern when the apparatus is used to count the stack flows in the product line. The apparatus detecting result is N = TP + FP and the ground truth is T = TP + FN, so the counting error e is TP + FP FP − FN N −1= −1= . (9) T TP + FN TP + FN The counting error can be divided into the systematic error and the random error. The former measures the average and inherent derivation from the ground truth, while the latter measures the random variation caused by the imaging location, the sheets stacking ways, and other uncontrollable factors. The random error also determines the repeatability of the counting result for the same stack. Due to the difficulty in discriminating the two error sources, we adopt a statistical estimation of the average error and its standard deviation σ for error analysis. In the experiments, these four indexes mentioned earlier are used for comparison. The experimental data are obtained by imaging over 200 stacks with the apparatus. From the fact that a high stack roughness also reduce the accuracy, each stack is formed by roughly stacking a random amount of sheets to find out the worst performances. To estimate the random error, each stack is measured many times at different positions. The performance statistics of the different methods is shown in Table I. As observed, when the Gaussian sheetness filter is used for ridge detection, the Pr is high and the Rc is small. The main error is the undetected sheet, which is a great limitation of the counting performance. When the bi-Gaussian filter or the descriptor is adopted, the Rc is increased up to almost 100%; on the other hand, the Pr is decreased intensively and the average counting error is enlarged. The main cause is the repeatedly detected sheet, which is due to an unexpected unsmooth ridge responses for e=

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TABLE II P ERFORMANCE D EGRADE W ITH N OISE

Fig. 7. Sheet recognition results of typical sheets with other methods. (a) Original sheet image with the true sheets location denoted by . (b)–(d) Result of the peak detection method (after smoothed by median filter), the frequency domain method, and the wavelet domain method. : identified sheet location. Fig. 6. Sheet recognition result of noisy image (μ = 50%). (a) Original image with the true sheet location denoted by . (b) Noisy image with the detected sheet location indicated by ◦. (c) Ridgeness measure of (b). : detected peaks.

severely deformed sheet profile as a coproduct of ridge likelihood enhancement. The sheet verification process is effective to reduce the above FP errors, so both a high Pr and Rc are achieved. The highest performance is achieved when we use the descriptor for ridge strength measure and the verification algorithm to remove the identification errors. 2) Robustness Analysis: For the sheets counting application, the robustness denotes the performance degradation affected by the noise, light illumination change and many other environmental changes. To assess it quantitatively, we use white noise to simulate these unexpected affects. The noise ratio is denoted by μ = σ N /Sw , where σ N is the standard deviation of the white noise, and Sw = 1/2 Smax − Smin  is half the average sheet amplitude, while Smax and Smin are the sheets local maximum and minimum separately. The performance drop with μ is given in Table II, when μ < 40% the performance degradation is very tiny. Then when μ increases, it degrades severely, the main error source is the noisy background at both ends of the image. As in Fig. 6, when μ = 50%, most of the sheets are still correctly identified. 3) Measure Range and Counting Speed Analysis: The maximum measure range R is mainly determined by the pixel count p of the camera and the minimum width w to make the sheets identifiable. In the obtained image, both the sheet width ws and gap width wg must be above certain value wt to ensure the counting accuracy. For the 0.2 mm paper sheets, ws ≈ 2wg and wt ≥ 4, so w = ws +wg ≈ 12. At both ends of the image, a total area pr is reserved to image the background, which is used as a reference in sheet detection, so the maximum measure range R = p − pr /w ≈ 600. In addition, the highest achievable resolution of the imaging module is 0.02 mm, so the measurable thinnest sheet is ∼0.16 mm. The time consumed by one counting process mainly includes the imaging time ti and the execution time t p of the counting program. The imaging speed of the line-scan camera is extremely high and ti ≈ 10 ms. The computing algorithm complexity is low, and t p < 100 ms. The counting process

is accomplished within 120 ms in the experiments. So a high counting throughout can be achieved with the apparatus. B. Comparison With Other Methods This part presents other sheet recognition approaches and the corresponding results. For a fair comparison, the sheet identification and verification algorithms are changed adaptively to achieve the best accuracy. 1) Peak Detection Algorithm: The sheet identification algorithm can be directly applied to locate the sheets [14] with the smoothed image as shown in Fig. 7(b). However, the result is very sensitive to the window width and the noise. The optimal window width varies for different stacks, and the average error with tradeoff parameter is within ±5%. 2) Optimal Threshold Algorithm: This method is widely used in various applications [15], [16]. Here, first the sheets part in the image is extracted by analyzing the histogram, and the threshold is set to its mean or median. Then, the image is binarized and the sheets are counted. The main cause of error is the varying sheet average with location as shown in Fig. 2(a). 3) Frequency Domain Algorithm: The frequency domain algorithm proposed in [4] and [10] is slightly revised to identify the sheets. In the algorithm, first the Fourier transform of the input image is calculated, then the dominant harmonic area h d is extracted. Finally, its inverse Fourier transform is taken as a feature for sheet identification. As shown in Fig. 7(c), this method fails to locate a fixed structure such as the ridge. In addition, the feature at both ends is unidentifiable from the background. The reason is that the sheet parameters vary randomly, which causes the time-varying frequency property. 4) Wavelet Domain Algorithm: To deal with the timevarying property, wavelet [31]-based algorithm is used to detect the sheets. The image is decomposed with discrete wavelet transform [12], [32], and it is observed that the sum of the third and fourth detail is an excellent feature for sheet identification. As shown in Fig. 7(d), this method is reliable and immune to the fake ridge. However, it fails to distinguish a few sheets with bimodal distortion. The data obtained in apparatus performance test are used to assess these different methods. Statistics of the systematic and random counting error are presented in Table III. From the

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TABLE III P ERFORMANCE S TATISTICS OF O THER A LGORITHMS

robustness is sufficient to satisfy the harsh industrial requirements. Moreover, the developed algorithm can be extended to other peak detection fields like spectrographic data and fringe pattern analysis. R EFERENCES

Fig. 8. Apparatus used for stacked can cover and PCB boards counting, the true location and the detected location are denoted by ◦ and  separately. (a) Can covers. (b) Apparatus counting result. (c) PCB boards. (d) Apparatus counting result.

comparison, the performance of the existing algorithms is far behind that of the proposed method. The main reason is that these methods cannot model the complex sheets adaptively. C. Other Applications of the Apparatus The apparatus can also be used to count other stacked items, such as can cover and the printed circuit board (PCB). Their corresponding 2-D images shown in Fig. 8 are obtained with a web camera, from which we can see the stacked can covers are highly reflective and the PCB board edges are very blurry. For the can cover, with 4 ≤ σ ≤ 8 and ρ = 0.3, all the 0.5-mm-thick items are correctly identified as shown in Fig. 8(b). For the PCB board, the obtained image is very noisy, the gap between the boards is narrow and the contrast is ambiguous. However, with 50 ≤ σ ≤ 60 and ρ = 0.1, the 5-mm-thick boards are still correctly recognized, as shown in Fig. 8(d). V. C ONCLUSION In this paper, we have presented a low-cost sheet-counting apparatus using line-scan cameras. Its real-time performance is ascribed to a fast image acquisition speed and our efficient counting algorithms. A multiscale bi-Gaussian ridge likelihood measurement and a ridge-valley descriptor are utilized to improve adjacent object detection by increasing local contrast around sheet fringes. Then, a peak detectionbased identification algorithm and the ridge region criteria are combined to recognize the true sheets from the ridgeness measure. After more than one year’s test in production line, our apparatus can achieve a very high accuracy for various sheetlike stacks with a thickness >0.2 mm. Its accuracy and

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[26] A. F. Frangi, W. J. Niessen, K. L. Vincken, and M. A. Viergever, “Multiscale vessel enhancement filtering,” in Medical Image Computing and Computer-Assisted Interventation. Berlin, Germany: Springer-Verlag, 1998. [27] K. Krissian, G. Malandain, N. Ayache, R. Vaillant, and Y. Trousset, “Model-based detection of tubular structures in 3D images,” Comput. Vis. Image Understand., vol. 80, no. 2, pp. 130–171, 2000. [28] C. Xiao, M. Staring, D. Shamonin, J. H. Reiber, J. Stolk, and B. C. Stoel, “A strain energy filter for 3D vessel enhancement with application to pulmonary CT images,” Med. Image Anal., vol. 15, no. 1, pp. 112–124, 2011. [29] M. W. K. Law and A. C. S. Chung, “An oriented flux symmetry based active contour model for three dimensional vessel segmentation,” in Computer Vision. Berlin, Germany: Springer-Verlag, 2010. [30] R. A. Grothe, Jr., and D. A. Wright, “Methods of automated spectral peak detection and quantification without user input,” U.S. Patent 7 983 852, Jul. 19, 2011. [31] J.-L. Starck, F. D. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach. Cambridge, U.K.: Cambridge Univ. Press, 1998. [32] G. Karagiannis, D. S. Alexiadis, A. Damtsios, G. D. Sergiadis, and C. Salpistis, “Three-dimensional nondestructive ‘sampling’ of art objects using acoustic microscopy and time–frequency analysis,” IEEE Trans. Instrum. Meas., vol. 60, no. 9, pp. 3082–3109, Sep. 2011. Tiejian Chen received the B.Eng. and M.S. degrees in control engineering from Hunan University, Changsha, China, in 2008 and 2011, respectively, where he is currently pursuing the Ph.D. degree. His current research interests include imaging instrument and image processing.

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Yaonan Wang received the B.S. degree in computer engineering from East China Science and Technology University, Shanghai, China, in 1981, and the M.S. and Ph.D. degrees in electrical engineering from Hunan University, Changsha, China, in 1990 and 1994, respectively. He was a Senior Humboldt Fellow in Germany from 1998 to 2000 and Visiting Professor with the University of Bremen, Bremen, Germany, from 2001 to 2004. He has been a Professor with Hunan University since 1995. His current research interests include intelligent control, image processing, and computer vision system for industrial applications.

Changyan Xiao received the B.Eng. and M.S. degrees in mechanical and electronic engineering from the National University of Defense Technology, Changsha, China, in 1994 and 1997, respectively, and the Ph.D. degree in biomedical engineering from Shanghai Jiao Tong University, Shanghai, China, in 2005. He was a Visiting Post-Doctoral Researcher with the Division of Image Processing, Leiden University Medical Center, Leiden, The Netherlands, from 2008 to 2009. Since 2005, he has been with the College of Electrical and Information Engineering, Hunan University, Changsha. His current research interests include medical imaging and instruments. He is the coresponding author of the paper.