Testing applicability of image analysis for measurements of sediment concentration in laboratory experiments

. Flume experiments are typically conducted to reveal the detailed behavior of debris flows. Direct sampling at the lower end of a flume has been used to measure sediment concentrations in flume experiments; however, direct sampling measurements under non-steady or non-equilibrium conditions are difficult. In contrast, image analysis methods can acquire spatiotemporal high-resolution data in a non-contact manner. In this study, we conducted experiments in which a homogenous sediment concentration field of 0 ~ 20 % was prepared in a water tank with a depth of 10 cm using coarse and fine sediments. We filmed the experiments and verified the relationships between sediment concentrations and image features in a fixed area. As a result, the mean of pixel values for coarse sediments depends on the sediment concentration of up to 10 % and the number of mode pixels for fine sediments depends on the sediment concentration of up to 20 %. We then analyzed factors influencing image features and identified three processes. Furthermore, we analyzed the effects of the sediment grain size on image features, and the results show that both the brightness index and brightness uniformity index of images are affected. In conclusion, these findings indicate that image analysis can be used to clarify both sediment concentration and grain size.


Introduction
In previous flume experiments on debris flows and sheet flows, sediment concentrations have been measured by directly sampling sediments and water at the downstream end of a flume [1][2][3][4].
Although this method is effective under steady-state or equilibrium condition, it is difficult to measure sediment concentration under non-steady-state or nonequilibrium conditions, such as at points of slope change.
Although image analysis has been used to determine the flow depth and velocity distribution in previous flume experiments [5][6][7], few studies have estimated sediment concentrations in hydraulic experiments on debris flows and sediment sheet flows using image analysis. However, there would be numerous benefits if sediment concentrations could be measured by image analysis. For example, an image analysis system can obtain high-resolution spatiotemporal data, and images are taken from outside the experimental system.
In this study, we conducted and filmed an experiment in water tank with a uniform sediment concentration of 0 ~ 20 % for two different grain sizes of sediments, and then, we investigated the possibility of measuring the sediment concentration using image features. The causes of changes in image features depending on the sediment concentration were also analyzed.

Outline of experimental method
An acrylic tank (width: 10 cm; height: 30 cm; depth: 10 cm) was used for the experiment. The tank was covered with blue paper on two sides so that when the sediment was photographed, the background would be in uniform conditions. White sediments with grain sizes of 2 (coarse) and 0.2 mm (fine) were used, based on from previous debris flow flume experiments [1][2][3][4]. The experiment was repeated three times for each sediment and concentration. The experiment was recorded as a video using a digital camera (RX100v, Sony, Japan). Filming photographs were taken in a laboratory with the lights turned off and the light source placed in front of the tank in a room without outside light (Fig.1).

Method of controlling concentration in coarse grain
In the experiment using coarse grains, the tank was filled with water to a height of 20 cm. Dry sediment was stored in a sediment supplier whose lower mouth was sealed with a plate. Sediments were put into the tank by pulling out the plate (Fig. 1). A sieve was set between the sediment supplier and the tank for a uniform supply. The sediment concentration was controlled from 0 to 18 volumetric % by varying the size of the sediment supplier and the sieve mesh size and their combinations.
Sediments are supplied in such a way that they spread over the entire width of the tank when the sediment concentration is 0 to 10 %, and it is assumed that the sediments are uniformly supplied to the tank temporally and spatially from the start to the end of the supply. The sediment concentration C was calculated using equation (1): (1) where Wc denotes the mass of the sediment supplied by the sediment supplier (200 or 400 g); Vc is 1000 cm 3 ; t1 represents the time between when the top of the sediment passes the 15 cm height point from the bottom of the tank and when it passes the 5-cm height point (s); t2 denotes the time between when the top of the sediment passes the 15-cm height point from the bottom of the tank and when the end of the sediment passes the 15-cm height point (s).
As it was difficult to control the sediment concentration across the entire width of the tank at 14 to 18 % sediment concentration, a sieve was not installed between the sediment supplier and the tank, and the sediment was directly fed into the tank, concentrating them on one side. The sediment concentration is calculated under the assumption that the sediment concentration is uniform throughout the area where the sediments are dispersed. The area S (cm 2 ) of dispersion in an image, where dropped sediments were underwater and had not reached the bottom of the tank, was calculated by approximating it to one or more trapezoids. Furthermore, from another angle of the image, it was confirmed that the sediments were supplied uniformly from the front wall to the rear wall in the depth direction of the tank. Therefore, the volume of sediment dispersed was S multiplied by the depth of the tank, D (10 cm). Therefore, at C of 14 to 18 %, C (%) was calculated using equation (2). Fig. 1. Location of the light, the camera, and the tank in the experiment.

Method of controlling concentration in fine grain
In the experiment using fine grains, sediments were spread on the bottom of the tank, water was poured to a depth of 10 cm, and a wire mesh was used to agitate and disperse the sediments in the tank. After confirming that the sediments were sufficiently dispersed in water, the wire mesh was pulled up and the amount of sediment caught in the wire mesh was measured. The initial amount of sediment placed at the bottom of the tank was varied to control the sediment concentration from 0 to 20 %.
It was assumed that the sediments were uniformly dispersed in the tank immediately after the end of agitation by the wire mesh. The water depth hf (cm) at that time was read from the image taken immediately after the end of agitation, and multiplied by the bottom area of the tank, 100 cm 2 , to obtain the volume of sediments dispersed. Assuming that the sediments are uniformly distributed within this volume, the sediment concentration C (%) was calculated using Equation (3): where Wf denotes the mass of sediment placed at the bottom of the tank; Wr denotes the mass of sediment caught in the wire mesh.

Method of image analysis
The video of the experiments was cut into RGB images per frame, and six consecutive frames (0.05 s) were extracted from the image when the sediments were uniformly dispersed, at a height of 8 to 10 cm from the bottom of the tank for coarse grains and 4 to 6 cm for fine grains, at the left side of the center of the image, with a 100 p × 100 p ratio (2 cm × 2 cm). Examples of pictures used for image analysis are depicted in Fig.2 for coarse grains and in Fig.3 for fine grains. For each extracted image, the mean, standard deviation, mode, and the number of mode pixels of the pixel value in each image were obtained as image features.   Fig. 4 depicts the relationship between the sediment concentration and the average pixel value in the R channel for coarse and fine grains. The average pixel values monotonically increased as the sediment concentration increased for coarse grains, from 0 to 10 % and for fine grains, from 0 to 1 %. For both coarse and fine grains, the average pixel value was constant when the sediment concentration was greater than the respective threshold concentration. Fig. 5 depicts the relationship between the sediment concentration and the number of mode pixels in the R channel for coarse and fine grains. For coarse grains, the number of mode pixels did not change significantly with sediment concentration. For fine grains, the number of mode pixels decreased monotonically for sediment concentrations from 0 to 2 % but increased linearly for sediment concentrations from 2 to 20 %.

Effect of sediment concentration on images
In this study, the light received by the camera is most likely either backscattered by the sediment or reflected by the background (blue paper) and then transmitted back into the tank. In addition, when the sediment concentration exceeds 2 % for coarse grains and 0.2 % for fine grains, the sediment in the image tends to appear darker in the back and brighter in the front because the light is extinct as it moves away from the light source. The background becomes darker as the sediment concentration increases due to light extinction by the sediment in the tank.
At low sediment concentrations, the background is thought to be affected by reflected light, whereas at higher concentrations above a certain level, the background is no longer reflected, and the effect of the background on the image is considered negligible. As the sediment concentration increases, the proportion of bright sediment near the camera and light source in the image is expected to increase. The above process can be represented schematically as shown in Fig. 6. Based on this assumption, in this study, there are three possible processes by which the image changes with the sediment concentration: shielding of the background by sediments, darkening of the background, and changing the brightness of the sediments.
These hypotheses were verified using images of coarse grains. For verification, it is necessary to classify pixels into sediment and background pixels. In this study, pixels with pixel values greater than 100 in the R channel are distinguished as sediment pixels, and pixels with pixel values of 100 and less than 100 are distinguished as background pixels. As a result, it is verified that the shielding of the background by sediments and the darkening of the background are effective for 0 ~ 4 % sediment concentrations and changing the brightness of sediments is effective for 4 ~ 20 % sediment concentrations.  Fig. 4 shows that the threshold, at which the average pixel value does not change with increasing sediment concentration, is greater for coarse grains than for fine grains. This is thought to be because light extinction becomes more pronounced as the product of the particle cross-section and the number concentration of grains and is inversely proportional to the particle size for the same volumetric concentration. Fig. 7 depicts the relationship between C (D/d), the value obtained by dividing the grain size d by the depth D (10 cm) of the tank, and the sediment concentration C, and the average pixel value of coarse and fine grains. In other words, the assumption in Fig. 6 holds true for fine grains as well, and this effect on the images can be expressed by C (D/d). Fig. 5 depicts that the number of mode pixels is always larger for fine grains than for coarse grains, and the relationship between the sediment concentration and the number of mode pixels differs significantly for coarse and fine grains. This is thought to be because differences in the ratio of grain size to pixel size affect the degree of uniformity of pixel values. Fig. 7. Comparison of the relationship between sediment C (D/d) and the average pixel value for coarse and fine grain in the R channel.

Conclusion
In this study, experiments were conducted to create a uniform concentration field with sediment concentration ranging from 0 to 20 % using white sediments with grain sizes of 2 and 0.2 mm. The experiments were captured with a digital camera, and the relationship between sediment concentration and image features was analyzed.
The results suggest the possibility of using image analysis to measure the sediment concentration in the range of 0 ~ 10 % using the average pixel value for coarse grains and 0 ~ 20 % using the number of mode pixels for fine grains.
The effects of sediment concentration on the image were threefold, namely, shielding of the background by sediments, darkening of the background, and changes in the brightness of the sediment, which were verified using coarse-grained images. The sediment diameter affects the average pixel value and the number of mode pixels.