DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION

Transcription

1 Far East Journal of Electronics and Communications Volume 3, Number 3, 2009, Pages This paper is available online at Pushpa Publishing House DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION Department of Electrical Engineering Faculty of Engineering Nagaoka University of Technology Kamitomioka Nagaoka Niigata, , Japan Abstract This paper proposes an optimization procedure of a spatial filter in a water level detection system. The water level of running water of a river is detected by applying a temporal filter and a spatial filter to a video of various river scenery. Previously, we have proposed an algorithm based on addition of frames and horizontal detection of edges. We have confirmed its superiority to the existing method based on subtraction of frames and vertical detection of edges, especially when the scenery contains rain or snow drops. However, its detection performance is limited since coefficients of the edge detector are fixed. In this paper, we propose a design method of a spatial filter as a general form of the edge detector so that the system becomes flexible to change of the river 2 scenery. Optimization criterion is proposed and the filter coefficients are determined for each of the river scenery. It is confirmed that the proposed method reduces the standard deviation of the detection error by 4.4 [%] and 7.6 [%] comparing to the conventional horizontal Prewitt filter and the horizontal Sobel filter, respectively. Keywords and phrases: water level, video, filter, detection. Received June 18, Introduction Over the past few decades, the social concern with flood disasters caused by

2 204 unusual weather condition has been growing all over the world. It is important to build environmental surveillance systems which can promptly correct information about water levels of rivers in the region via various communication channels [4]. The telemeter, which is installed by the Japanese government, collects information on the water level at several points [5]. It detects the water level by an ultra-sonic device for example. However, the observation points are limited to a few principal rivers. Recently, various types of web cameras have been installed in not only principal rivers but also in small rivers for remote video surveillance. Therefore, the water level detection based on video signal processing is becoming an issue of great importance. Takagi et al. have proposed a water level detection algorithm [7, 8, 9]. The algorithm is based on detecting a bending point of a diagonal line on a measuring board. However, their performance is sensitive to stains on the line. In addition, it is strictly controlled by an administrator to install any obstacle against water flow such as the board in the water. It is desirable to develop a video processing algorithm without setting any board in the water. A Hough transform based algorithm can detect a line which represents water surface [3]. However, it is difficult to discriminate the line to be detected from various line-like disturbances. A simple method based on the edge detection is proposed by Tsunashima et al. [11]. It detects a horizontal line as surface of the running water with a vertical detector of edges (vertical differentiator). It also employs subtraction of frames to make it robust against horizontal line-like disturbances on the wall of a channel. However, it is sensitive to moving disturbances such as snowdrops because of the frame subtraction. Recently, we have proposed a robust detection algorithm based on addition of frames and horizontal detection of edges [6]. We have confirmed its superiority to the existing method in [11], especially when the scenery contains rain or snow drops. However, its detection performance is limited since its filter coefficients are fixed. In this paper, we propose a design method of a spatial finite impulse response (FIR) filter which is a general form of the edge detector. We intend that the system becomes flexible to change of the river scenery. Optimization criterion is proposed and the filter coefficients are determined for each of the river scenery. Accuracy of the detection is examined in respect of standard deviation of the detection error of the water level.

3 DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION 205 This paper is organized as follows. The water level detection algorithm is described in Section 2. The existing edge detectors are summarized in Section 3. The optimization procedure of the spatial filter is proposed in Section 4. Superiority of the optimized filter to some conventional fixed coefficient filters is experimentally confirmed in Section 5. Conclusions are summarized in Section Water Level Detection Algorithm The water level detection algorithm, previously reported in [6], is described. It is based on addition of frames and horizontal detection of edges. The frame addition is a temporal low pass filter and the edge detection is a spatial high pass filter. The filter coefficients are fixed in the existing method. Optimization procedure of the coefficients is proposed in Section Temporal filter (Frame addition) Figure 1(a) illustrates a frame of a video signal of river scenery under snowing condition. It includes two regions - land region and water region. It is our purpose to detect the boundary between the two regions as the water level. The detection system should be robust against some moving objects such as snowdrops. Figure 1(b) shows frequency amplitude characteristics of each region. The land region in solid line contains more energy in high frequency than the water region. In the water level detection system in [6], the video signal is averaged over some consecutive frames (frame addition). Figure 1(c) illustrates a result of the frame addition over 30 frames during one second. Some moving objects such as snowdrops are almost extinguished. Since the water is running, the water region is blurred. It means the water region contains less energy in high frequency. On the contrary, non-moving textures such as concrete blocks in the land region is not blurred. Namely, high frequency components in the land region are maintained. It is confirmed by Figure 1(d) which represents frequency amplitude characteristics of each region of Figure 1(c) Spatial filter (Edge detector) A spatial filter is applied so that difference of the spectrum between the two regions is emphasized. An example of the filtered signal is illustrated in Figure 1(e). Three tap band pass filter described in Subsection 3.1 is used. It works as a horizontal detector of edges (horizontal differentiator).

4 206 To detect the water level, logarithm of variance of each horizontal line is used as a feature value (one dimensional feature vector). It is illustrated in Figure 1(f). Before the spatial filtering, namely in the image in Figure 1(c), there is no significant difference between the feature value in the two regions as indicated in solid line. After the filtering, the feature value in the water region becomes small as indicated in broken line. This difference in the feature value is used to distinguish the two regions. However, its performance is limited since the filter coefficients are fixed in the existing method. In this paper, we optimize the filter coefficients in Section 4 for each of the input video so that the system becomes flexible to change of the scenery Water level detection The water level is recognized as the boundary between the two regions. It is detected as follows. At first, a temporal boundary is set and the feature values are categorized into two classes. For these two classes, the mean values ml and m W of the land region class and the water region class are, respectively, calculated. 2 2 Similarly, the variances s L and s W of each class are also calculated. From these values, the Fisher s linear discrimination criterion is calculated. It is defined as the ratio of the distance between classes ( D bc ) and the variance within classes ( V wc ). It is defined by D V bc wc 2 PL PW ( ml mw ) =, (1) 2 2 P s + P s L L where P L and P W denote probability of pixels which belong to the land region class and the water region class, respectively. Varying the temporal boundary, the water level is determined as the boundary which maximizes the Fisher s linear discrimination criterion in equation (1). Figure 1(h) illustrates the criterion in the horizontal axis and the boundary in the vertical axis. The maximum point in the horizontal axis specifies the water level in the vertical axis. Finally, the water level is detected. In this paper, performance of the detection is evaluated by the detection error which is the difference between the automatically detected water level and the visually (manually) detected value. Value of the Fisher s linear discrimination criterion can be utilized as an indicator of reliability of the detection results. W W

5 DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION Existing Spatial Filters In this section, some existing spatial filters (edge detectors) with fixed coefficients are summarized Horizontal 1D edge-detectors An output pixel value of the spatial filter is produced by the filter coefficients and an input pixel value by y ( n, n ) = h x( n k, n k ) (2) 1 2 k1, k , k1, k2 where h k1, k2 is a filter coefficient and x ( n 1, n 2 ) is an input pixel value at location ( n ). Denoting a set of the coefficients by a matrix: 1, n2 some of conventionally utilized filters are given by h1,1 h0,1 h,1 F = h1, 0 h0, 0 h, 0, (3) h1, h0, h, F HPF = 1 0, FBPF = 0 1, FLAP = (4) These are one dimensional (1D) horizontal edge-detectors. F HPF, F BPF and F LAP are two tap high pass filter, three tap band pass filter and Laplacian filter, respectively D edge-detectors Two dimensional (2D) horizontal edge-detectors known as the Prewitt operator and the Sobel operator are defined by F Prewitt = 0 1, Fsobel = 2 0 2, (5)

6 208 respectively, [1, 10]. The diagonal band pass filters defined by F 0 0 0, BPF = F =, BPF (6) are also examined. It should be noticed that, in our discussion, the maximum number of tap is limited to three. This is because no significant improvement by more than four tap is confirmed [2] Vertical edge-detectors The filters in equation (4) horizontally detect edges in an image. In this paper, vertical edge-detector is also examined by applying transpose of the matrix in the equation. For example, the vertical versions of the F HPF and F BPF are defined by T T F, HPF = F =. BPF (7) Optimization of the Spatial Filter In this section, an optimization procedure of the filter coefficients in equation (3) is proposed. Denoting the matrices of the spatial filter by F OPT _3Tap = h1, 0 h0, 0 h, 0, (8) h1,1 h0,1 h,1 F OPT _3 3 = h1, 0 h0, 0 h, 0, (9) h1, h0, h, the coefficients in equations (8) and (9) are adaptively renewed depending on each input video of the river scenery. Here, equation (8) is a 1D horizontal filter. Its transpose is the 1D vertical filter. Equation (9) is the 2D filter.

7 DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION 209 In equation (1), given an input video, the variance within classes V wc is determined. There is no way to control this value. On the contrary, the distance between classes D bc can be controlled by the filtering as indicated in Figure 1(f). Therefore, we determine a set of the coefficients such that it maximizes the distance between classes. Assuming that the probability density function of the feature values is uniform in each region and the video contains the two regions half and half, the distance between classes becomes proportional to the ratio of variance in the land region 2 and that of the water region v W. Using the method of Lagrange multipliers, the optimum coefficients are determined as a solution which minimizes the equation: 2 v L 2 2 L = v W λ( vl 1). (10) For example, in case of the 1D horizontal filter in equation (8), the optimum coefficients are determined by where L W T, 0 ( ϕ ϕ λi )[ h h h ] = 0, (11) 1, 0 0, 0 ϕ R θ = θ θ 0, R 1, R 2, R θ θ θ 1, R 0, R 1, R θ θ θ 2, R 1, R 0, R, 1 I = , 1 x( n1 + k, n2 ) x( n1, n2 ), N R { L, W} θk, R =, ( n n ) R R 1, 2 and N R is the number of pixels in the region R. As a result, the optimum coefficients are given as the eigen-value problem in equation (11). 5. Experimental Results In this section, significance of the proposed optimization procedure described in Section 4 is examined comparing to the existing fixed coefficient filters summarized in Section 3.

8 Video examples for analysis Figure 2 summarizes all the fifteen video samples for the experiment. These videos are with pixels and 30 frames per sec. under different scenery. Figure 3 summarizes four images for analysis in details. Sample A and sample B are the same location but different weather conditions. Model A and model B are AR(1) model with different signal to noise ratio. The models emulate the land region and the water region after the frame addition Results for model A Figure 4(a) indicates the feature value of each line after the frame addition and the spatial filtering for the model A. The horizontal 1D filters in Subsection 3.1 are applied. When the filter is not applied, there is no significant difference between the two regions as indicated in the label ORG. After applying the filters, the distance between the classes is increased (the feature value in the water region is decreased). In this case, it is confirmed that the three tap optimized filter OPT_3tap and the Laplacian filter LAP is the same and the best. Figure 4(b) indicates results of the vertical 1D filters in Subsection 3.3. No significant difference among those filters is observed. However, the variance within the water region class is increased comparing to Figure 4(a). In respect of the Fisher s linear discrimination criterion, namely the reliability of the system, the horizontal filters are better than the vertical filters. Figure 4(c) indicates results of the 2D filters. Comparing to the 1D filters, the variance within the class is reduced and the distance between the classes is increased. It is confirmed that the optimized 2D filter labeled as OPT_ 3 3 is better than any of the 2D filters in Subsection Results for models A, B, samples A, B Figure 5(a) indicates the distance between classes for model A, model B, sample A and sample B in Figure 3. The horizontal 1D filters and the vertical 1D filters are applied. When the filter is not applied, the distance is almost unity as indicated in ORG. After applying the filters, the distance is increased. For model B, the distance is not so increased by any filters. For sample A and sample B, the horizontal filters labeled as _H is better than the vertical filters labeled as _V. For model A, it is opposite.

9 DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION 211 Figure 5(b) indicates results of the 2D filters. It is confirmed that the optimized 2D filter labeled as OPT_ 3 3 is the best comparing to other 2D filters. For model A and sample B, the distance is better than that of the 1D filters Results for samples of various scenery Figure 6(a) indicates the standard deviation (SD) of the water level detection errors for fifteen kinds of video signals in Figure 2. The mean value of the error is zero. The 1D filters are applied. It is confirmed that the horizontal 1D filters can reduce the error than the vertical 1D filters. In case of 1D filtering, the optimized horizontal OPT_3Tap filter is the best but almost same as the horizontal Laplacian filter labeled as LAP_3tap. These are better than the horizontal band bass filter labeled as BPF_3tap. Figure 6(b) indicates results of the 2D filters. It is confirmed that the optimized 2D filter is the best in respect of reducing the SD of the water level detection errors. The SD is reduced by 4.4 [%] and 7.6 [%] comparing to the conventional horizontal Prewitt filter and the horizontal Sobel filter, respectively. Comparing the 1D optimized filter and the 2D optimized filter, there is no significant difference between them. As a conclusion, the optimized 1D horizontal filter is the best in respect of detection performance and simplicity of the digital signal processing. 6. Conclusions In this paper, we proposed a design method of the spatial filter in the water level detection system so that the system becomes flexible to change of the river scenery. The distance between the class of land region and the water region is used as the optimization criterion. The spatial filter coefficients are determined for each of the river scenery. It is confirmed that the proposed method reduces the standard deviation of detection error by 4.4 [%] and 7.6 [%] comparing to the conventional horizontal Prewitt filter and the horizontal Sobel filter, respectively. Relation between the number of pixels and the variance within classes should be investigated in the future. Acknowledgment This research was partially supported by the Ministry of Internal Affairs and Communications, Japan as a SCOPE-C research project.

10 212 References [1] R. C. Gonzalez and R. E. Woods, Digital Image Processing, Prentice-Hall Inc., [2] M. Iwahashi and S. Udomsiri, Optimum filter design for water level detection, IEICE Tech. Report, SIP2007-3, IE (22) (2007), [3] S. Kobayashi, S. Muramatsu, H. Kikuchi and M. Iwahashi, Water level tracking with condensation algorithm, International Workshop on Advanced Image Technology (IWAIT), no. P7-43, 2007, pp [4] Ministry of international affairs and communications, Japan, [5] Ministry of land, infrastructure and transport, Government of Japan, [6] A. Saito and M. Iwahashi, Water level detection algorithm based on synchronous frame addition and filtering, IEICE Circuits and Systems Karuizawa Symposium, 2006, pp [7] Y. Takagi, A. Tsujikawa, M. Takato, T. Saito and M. Kaida, Development of a noncontact liquid level measuring system using image processing, Water Science and Technology 37(12) (1998), [8] Y. Takagi, T. Yoneoka, H. Mori, M. Yoda, A. Tsujikawa, T. Saito and M. Kaida, Development of a non-contact liquid level measuring system using image processing, International Workshop on Instrumentation, Control and Automation of Water and Waste Water Treatment and Transport Systems, 1996, pp [9] Y. Takagi, T. Yoneoka, H. Mori, M. Yoda, A. Tsujikawa and T. Saito, Development of a water level measuring system using image processing, The 1st IWA Conference on Instrumentation, Control and Automation, 2001, pp [10] A. Tinku and Ajoy K. Ray, Image Processing, John Wiley & Sons, Inc., [11] N. Tsunashima, M. Shiohara, S. Sasaki and J. Tanahashi, Water level measurement using image processing, Information Processing Society of Japan, Research Report, Computer Vision and Image Media 121(15) (2008),

11 DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION 213 Figure 1. Procedure of the water level detection.

12 214 Figure 2. Fifteen video samples in various scenery. Figure 3. Four samples for analysis in details.

13 DESIGN OF SPATIAL FILTER FOR WATER LEVEL DETECTION 215 (a) Horizontal 1D filter (b) Vertical 1D filter (c) 2 D filter Figure 4. Feature value of Model A.

14 216 (a) Horizontal 1D filters and vertical 1D filters. (b) 2D filters. Figure 5. The distance between classes. (a) 1D filters. (b) 2D filters. Figure 6. Water level detection error.