Non-contact intelligent estimation method and system for discharge port flow based on double cameras

Abstract

The invention relates to the technical field of drainage monitoring, and discloses a non-contact dual-camera-based discharge port flow intelligent estimation method, which comprises the following steps of: acquiring discharge port image data shot by a monitoring station 1 and a monitoring station 2 in real time; through image identification, obtaining a flow image width Iw1 detected by the monitoring station 1, a flow image height Iz detected by the monitoring station 1 or the monitoring station 2, and a flow image width Iw2 detected by the monitoring station 2; and estimating the flow Q of the discharge port by adopting a formula. According to the method, the deep learning technology and the physical modeling technology are fully combined, the discharge port flow scheme is systematically and fully described, and the interpretability of all links of the whole scheme is fully improved.

Description

Technical Field

[0001] The present invention relates to the technical field of drainage monitoring, and in particular to a contactless dual-camera-based intelligent method and system for estimating drainage flow. Background Art

[0002] Outlet flow monitoring plays a very important role in the field of water environmental protection. On the one hand, the management department can estimate the discharge volume of each outlet to understand the surrounding environmental precipitation conditions and organize hydrological data; on the other hand, the management department can also calculate the approximate relationship between the discharge volume and the water level to check whether there is any leakage on sunny days.

[0003] In the existing scheme, water flow detection of drain outlets is basically achieved by installing contact devices, but the installation and maintenance costs of such products are very high. During installation, due to differences in the material and pipe diameter of the drain outlet, the equipment may need to be modified and fine-tuned to adapt, making deployment difficult. During maintenance, since the drain outlet may discharge sewage and corrosive liquids in addition to rainwater, the service life of the equipment will be significantly shortened or the accuracy will be affected. Summary of the invention

[0004] The main purpose of the present invention is to solve the technical problem of low water flow detection accuracy of the drain outlet in the prior art. The non-contact dual-camera-based intelligent method for drain outlet flow estimation comprises the following steps:

[0005] The non-contact dual-camera-based intelligent method for estimating outlet flow rate is characterized by comprising the following steps:

[0006] Acquire the outlet image data taken by monitoring station 1 and monitoring station 2 in real time;

[0007] Through image recognition, the width I of the flowing water image detected by monitoring station 1 is obtained w1 , the water image height I measured by monitoring station 1 or 2 z , the width of the water image detected by monitoring station 2 w2 ;

[0008] Estimate outlet flow rate through image recognition data.

[0009] Calculate the water outlet velocity V, the formula is:

[0010]

[0011] Wherein, the flow velocity Vx in the x direction is:

[0012]

[0013] g is the acceleration of gravity, γ is the inclination angle of the outlet; the water outlet height z1 is:

[0014]

[0015] α is the angle between monitoring station 1 or 2 and the outlet section, and the parameter a of the parabola equation is:

[0016]

[0017] The water outlet height z1 is:

[0018]

[0019] Outlet height W h for

[0020]

[0021] Actual outlet width W w for

[0022]

[0023] θ1 is the radial angle between monitoring station 1 and the discharge port;

[0024] θ2 is the radial angle between monitoring station 2 and the discharge port;

[0025] Calculate the outlet cross-sectional area S 弓形 , the formula is:

[0026]

[0027] Among them, R is the inner diameter of the discharge port;

[0028] The discharge flow rate Q at the outlet is estimated using the following formula:

[0029]

[0030] Among them, V i , S 弓形i , Δ t They are instantaneous water outlet velocity, water outlet cross-sectional area, and time interval respectively.

[0031] As a preferred technical solution, the image recognition method is:

[0032] Identify pipe drains and water flows in images based on a pre-built deep learning network model;

[0033] Generate a corresponding bounding box for each identified object;

[0034] The width and height of the flowing water are obtained through the bounding box.

[0035] As a preferred technical solution, a sliding window method is used to calculate the average value of the flow data as the final flow output result;

[0036] If the valid data in the window is less than the set value, it is determined that the current state is non-drainage.

[0037] A non-contact dual-camera-based outlet flow intelligent estimation system, characterized by comprising: a camera and an edge computer;

[0038] The camera is installed facing the pipe drain outlet and is used to collect image information of the pipe drain outlet area in real time;

[0039] The edge computer is equipped with the deep learning network model and the polynomial regression model, and is used to execute the steps of the method according to any one of claims 1 to 3 after receiving image information captured by a camera.

[0040] The second aspect of the present invention provides a contactless dual-camera-based outlet flow intelligent estimation system, comprising:

[0041] The third aspect of the present invention provides an electronic device, comprising: a memory and at least one processor, wherein instructions are stored in the memory, and the memory and the at least one processor are interconnected via lines; the at least one processor calls the instructions in the memory so that the electronic device executes the above-mentioned contactless dual-camera-based intelligent estimation method for outlet flow.

[0042] A fourth aspect of the present invention provides a computer-readable storage medium, which stores instructions. When the computer-readable storage medium is run on a computer, the computer executes the above-mentioned contactless dual-camera-based intelligent outlet flow estimation method.

[0043] The present invention has the following beneficial effects:

[0044] 1. The system is not only suitable for industrial emissions, but can also be widely used in various scenarios such as urban drainage and farmland irrigation. Whether it is a large industrial discharge outlet or a small farmland drainage outlet, it can be effectively monitored. Through the real-time video stream of the camera, the discharge situation of the outlet can be captured instantly, ensuring a rapid response to abnormal emissions, greatly improving the timeliness of environmental protection.

[0045] 2. The system can automatically and efficiently detect and analyze the emission status in the video, without manual operation, which significantly improves the processing efficiency. By using a sliding window algorithm to monitor the status of the data export, it can provide more accurate real-time information updates.

[0046] 3. The present invention fully combines deep learning technology with physical modeling technology, systematically and fully describes the outlet flow scheme, and fully increases the interpretability of each link of the entire scheme. Compared with the use of artificial intelligence technology throughout the process, this scheme will be more accurate. When encountering special circumstances or scenes with poor effects, on-site verification and theoretical analysis can be performed, thereby fully improving the applicability of the product in various fields.

[0047] Compared with traditional physical sensors, this new system only requires cameras and edge computing devices, which significantly simplifies hardware requirements and reduces installation complexity. This not only reduces initial hardware investment, but also reduces long-term operation and maintenance expenses by reducing routine maintenance and adjustment work. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Flowchart of flow estimation model detection;

[0049] Figure 2 (Water flow) Schematic diagram of outlet marking;

[0050] Figure 3 Simulation diagram of water outlet side view;

[0051] Figure 4 Camera imaging simulation diagram;

[0052] Figure 5 Schematic diagram of the river from above;

[0053] Figure 6 Schematic diagram of river channel from side;

[0054] Figure 7 Schematic diagram of the top view of the monitoring station imaging;

[0055] Figure 8 Schematic diagram of cross-sectional water flow estimation;

[0056] Fig. 9 Schematic diagram of discharge speed;

[0057] Fig.10 Schematic diagram of cross-section calculation. DETAILED DESCRIPTION

[0058] The terms "first", "second", "third", "fourth", etc. (if any) in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" or "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0059] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figure 1 The first embodiment of the contactless dual-camera-based intelligent estimation method for outlet flow in the embodiment of the present invention includes:

[0060] Acquire the outlet image data taken by monitoring station 1 and monitoring station 2 in real time;

[0061] Through image recognition, the width I of the flowing water image detected by monitoring station 1 is obtained w1 , the water image height I measured by monitoring station 1 or 2 z , the width of the water image detected by monitoring station 2 w2 ;

[0062] Estimate outlet flow rate through image recognition data.

[0063] Calculate the water outlet velocity V, the formula is:

[0064]

[0065] Wherein, the flow velocity Vx in the x direction is:

[0066]

[0067] g is the acceleration of gravity, γ is the inclination angle of the outlet; the water outlet height z1 is:

[0068]

[0069] α is the angle between monitoring station 1 or 2 and the outlet section, and the parameter a of the parabola equation is:

[0070]

[0071] The water outlet height z1 is:

[0072]

[0073] Outlet height W h for

[0074]

[0075] Actual outlet width W w for

[0076]

[0077] θ1 is the radial angle between monitoring station 1 and the discharge port;

[0078] θ2 is the radial angle between monitoring station 2 and the discharge port;

[0079] Calculate the outlet cross-sectional area S 弓形 , the formula is:

[0080]

[0081] Among them, R is the inner diameter of the discharge port;

[0082] The discharge flow rate Q at the outlet is estimated using the following formula:

[0083]

[0084] Among them, V i , S 弓形i , Δ t They are instantaneous water outlet velocity, water outlet cross-sectional area, and time interval respectively.

[0085] Detailed description of the steps to construct the (station shooting (flowing water) outlet dataset:

[0086] The steps for constructing the (flowing water) outlet dataset are as follows:

[0087] 1) Build a simulated environment to collect data: Place PVC pipes of different diameters on the experimental table to simulate the outlet. During installation, a small inclination angle is constructed through the partition to prevent reverse leakage of water flow. A water storage basin is placed under the outlet of the outlet, and a water pump is placed in the basin. The outlet of the water pump is fixed at the upstream outlet of the PVC pipe to achieve circulating water supply. Set up a camera 10-30 meters away from the site to collect water flow data at different distances.

[0088] 2) Construct (flowing water) outlet dataset: Extract frames from the original video and use the Label Img annotation tool to annotate them. For outlets, the outlets need to be annotated inwards; for flowing water, the width and height of the flowing water need to be annotated separately. Figure 2As shown, red is the outlet and green is the water height. (Taking into account the gathering and diffusion of turbulence in practical applications, the position where the water width is relatively consistent should be selected when marking the water height). In the process of data set construction, data of different colors, different materials, and different distances need to be collected, and divided into training sets, validation sets, and test sets. Data enhancement is performed on the data set:

[0089] Image horizontal flip, image brightness, center zoom, etc.

[0090] 2.2.2 Outlet flow estimation algorithm

[0091] (1) Necessary Agreements

[0092] Convention 1: Assume that the actual water flow width is W w , the water outlet distance is W h , the distance from the outlet to the plane is z1. Parabola equation: Z = ax 2 +z1. Where a<0, z1 is the height to the plane, -R <y<R。

[0093] Convention 2: The radius of the outlet in the image is R, the width of the water flow detection box is Iw, and the height is Iz. Since the radius of the outlet can be obtained through actual measurement, the actual length can be calculated through the proportional relationship between R and Iw and Iz in the image, so the units of Iw and Iz in the following text are both cm.

[0094] Convention 3: From the top view of the river channel, the angle between monitoring station 1 and the outlet is θ1, and the angle between monitoring station 2 and the outlet is θ2. The width of the river channel is d (considering that d is a calibrable constant and is independent of the formula, the case where d is different when the two monitoring stations are set is not further discussed).

[0095] Convention 4: The angle between the viewing angle of the monitoring station camera and the horizontal plane is α. The height of the monitoring station is h.

[0096] (2) Algorithm Subject

[0097] In the horizontal direction, when the monitoring station is translated to the left and right sides of the outlet by a certain distance, the camera image will undergo a certain degree of rotation transformation, as shown below: Figure 7 shown. Figure 7 The rectangle in the middle is the river channel, the circle at the lower edge of the rectangle is the monitoring station, and the rectangle at the upper edge is the water flow out of the outlet. The Iw seen by the camera in the horizontal rotation angle is marked by the red line segment. For the convenience of calculation, D = d / cosθ (d is the river width, D is the straight-line distance from the monitoring station to the outlet).

[0098] Depend on Figure 7 From the geometric relationship, we know that: I w =W w *cosθ+W h*sinθ. (Known I w ,θ)

[0099] When two monitoring stations are set up, two independent images can be obtained. w and θ, so W can be calculated h .

[0100] I w1 =W w *cosθ1+W h *sinθ1

[0101] I w2 =W w *cosθ2+W h *sinθ2

[0102] Solving the two equations together, we get:

[0103]

[0104] In the vertical direction, during the imaging process, the angle between the height of the viewing angle and the horizontal line is α.

[0105] like Figure 6 As shown, in the actual scenario, the chord length from the outlet to the plane is L, and the angle between L and the horizontal plane is φ.

[0106] The imaging length in the vertical direction can be deduced:

[0107] I z =Lsin(α+φ)

[0108] Among them, I z For a known imaging height, α can be determined.

[0109] like Figure 6 It is easy to get the angle relationship:

[0110] tanφ=z1 / W h

[0111] cosφ=W h / L

[0112] sinφ=z1 / L

[0113] The above equations can be solved together:

[0114]

[0115] Where a is the coefficient of the parabola equation assumed in convention 1.

[0116] From the horizontal and vertical directions, solve for W h ,W w,z1, estimate the velocity. In order to ensure the generality of the outlet velocity, consider that the outlet is not horizontal. Figure 7 As shown, the outlet velocity is V, which can be decomposed into the horizontal velocity V x and vertical velocity V y . Assume that the angle between the outlet and the water outlet is γ, then And this angle can be determined in advance.

[0117] The velocity can be solved from the parabola trajectory equation:

[0118]

[0119] V y t+0.5*g*t 2 =z1

[0120]

[0121] Solving the simultaneous equations yields:

[0122]

[0123] As above Figure 8 As shown, obviously, the chord length is W w . Let the angle at the center of the circle to which the chord corresponds be ω.

[0124] According to the law of cosines:

[0125] W w =2R 2 -2R 2 cosω

[0126] That is:

[0127]

[0128] Final flow Through the ratio formula, all the units of the picture can be calculated into physical units (such as cm), for example:

[0129]

[0130] The complete derivation steps are:

[0131] Calculate the actual outlet width W w With outlet height W h

[0132]

[0133] Calculate the outlet water height z1 and the parabola equation parameter a

[0134]

[0135] Calculate the water velocity V at the drain outlet

[0136]

[0137] Calculate the outlet cross-sectional area S 弓形

[0138]

[0139] Estimated flow rate (sliding window)

[0140] At any time, the average of the previous N results is taken, where N is the window length. The flow rate is equal to the outlet cross-section (water outlet) multiplied by the area (L / s)

[0141]

[0142] Estimated traffic

[0143] The cumulative sum of the flow rates at all times from the beginning to the end of the drainage behavior is the flow rate of this outlet drainage.

[0144] Step 1: Acquire the images of two cameras at the same time and determine whether the time error of image acquisition is within the threshold. If it is within the error range and the image can be read normally, pair them and save them, otherwise re-acquire them.

[0145] Step 2: When the AI ​​regular recognition logic is triggered, the latest pair of images is selected and the target detection model is called to identify the outlet and the running water, and the detection frame and category are obtained; if the detection frame is abnormal, the abnormality includes the detection frame of the outlet target being classified as having water but no running water target; the detection frame of the running water is at other positions of the outlet instead of below, then this frame of the image is considered invalid, and the logic is repeated for the previous frame; until normal recognition is performed, Step 3 is entered. If all do not meet the requirements, the queue will be blocked to wait for new image pairs to be put in;

[0146] Step 3: If there is no water flow, insert 0 into the sliding window; if there is water flow, calculate the flow rate using the algorithm of claim 1;

[0147] Step 4: Use a sliding window to estimate the average flow rate. If it is less than the threshold or the data length in the window is insufficient, it is considered to be undrained. If and only if the window is full and the average flow rate of the values ​​in the window exceeds the threshold, it is considered to be flowing.

[0148] Step 5: Report the results.

[0149] The present invention also relates to a contactless dual-camera-based outlet flow intelligent estimation system, comprising: a camera and an edge computer;

[0150] The camera is installed facing the pipe drain outlet and is used to collect image information of the pipe drain outlet area in real time;

[0151] The edge computer is equipped with the deep learning network model and the polynomial regression model, and is used to execute the above steps after receiving image information captured by the camera.

[0152] An embodiment of the present invention also provides an electronic device, which may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) (for example, one or more processors) and memories, and one or more storage media for storing applications or data (for example, one or more mass storage devices). Among them, the memory and the storage medium may be short-term storage or permanent storage. The program stored in the storage medium may include one or more modules, each module may include a series of instruction operations in the electronic device. Furthermore, the processor may be configured to communicate with the storage medium and execute a series of instruction operations in the storage medium on the electronic device.

[0153] The electronic device may also include one or more power supplies, one or more wired or wireless network interfaces, one or more input and output interfaces, and / or one or more operating systems, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will appreciate that the electronic device structure in this embodiment does not constitute a limitation on the electronic device, and may include more or fewer components, or combine certain components, or arrange components differently.

[0154] The structure of an electronic device provided by an embodiment of the present invention may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) (for example, one or more processors) and memories, and one or more storage media for storing applications or data (for example, one or more mass storage devices). Among them, the memories and storage media may be short-term storage or permanent storage. The program stored in the storage medium may include one or more modules, each module may include a series of instruction operations in the electronic device. Furthermore, the processor may be configured to communicate with the storage medium and execute a series of instruction operations in the storage medium on the electronic device.

[0155] The electronic device may also include one or more power supplies, one or more wired or wireless network interfaces, one or more input and output interfaces, and / or one or more operating systems, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will appreciate that the electronic device structure does not constitute a limitation on the electronic device, and may include more or less components than the aforementioned, or combine certain components, or arrange the components differently.

[0156] The present invention also provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium. Instructions are stored in the computer-readable storage medium, and when the instructions are executed on a computer, the computer executes the steps of the aforementioned method.

[0157] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the above-described system, device, or unit can refer to the corresponding process in the aforementioned method embodiment and will not be repeated here.

[0158] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including a number of instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk and other media that can store program codes.

[0159] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A non-contact dual-camera-based intelligent method for estimating outlet flow, characterized in that: The following steps are involved: Acquire the outlet image data taken by monitoring station 1 and monitoring station 2 in real time; Through image recognition, the width I of the flowing water image detected by monitoring station 1 is obtained w1 , the water image height I measured by monitoring station 1 or 2 z , the width of the water image detected by monitoring station 2 w2 , obtain image recognition data; Estimate outlet flow rate through image recognition data.

2. The contactless dual-camera-based intelligent estimation method for outlet flow according to claim 1 is characterized in that: The method of estimating the outlet flow rate through image recognition data includes the following steps: Calculate the water outlet velocity V, the formula is: Wherein, the flow velocity Vx in the x direction is: g is the acceleration of gravity, γ is the inclination angle of the outlet; the water outlet height z1 is: α is the angle between monitoring station 1 or 2 and the outlet section, and the parameter a of the parabola equation is: The water outlet height z1 is: Outlet height W h for Actual outlet width W w for θ1 is the radial angle between monitoring station 1 and the discharge port; θ2 is the radial angle between monitoring station 2 and the discharge port; Calculate the outlet cross-sectional area S 弓形 , the formula is: Among them, R is the inner diameter of the discharge port; The discharge flow rate Q at the outlet is estimated using the following formula: Among them, V i , S 弓形i , Δ t They are instantaneous water outlet velocity, water outlet cross-sectional area, and time interval respectively.

3. The contactless dual-camera-based intelligent estimation method for outlet flow according to claim 1 is characterized in that: The image recognition method is: Identify pipe drains and water flows in images based on a pre-built deep learning network model; Generate a corresponding bounding box for each identified object; The width and height of the flowing water are obtained through the bounding box.

4. The contactless dual-camera-based intelligent estimation method for outlet flow according to claim 1 is characterized in that: The method further comprises: The sliding window method is used to calculate the average value of the flow data as the final flow output result; If the valid data in the window is less than the set value, it is determined that the current state is non-drainage.

5. The contactless dual-camera-based intelligent estimation method for outlet flow according to claim 1 is characterized in that: The specific steps of the intelligent estimation method are: Step 1: Acquire the images of two cameras at the same time and determine whether the time error of image acquisition is within the threshold. If it is within the error range and the image can be read normally, pair them and save them, otherwise re-acquire them. Step 2: When the AI ​​regular recognition logic is triggered, the latest pair of images is selected and the target detection model is called to identify the outlet and the running water, and the detection frame and category are obtained; if the detection frame is abnormal, the abnormality includes the detection frame of the outlet target being classified as having water but no running water target; the detection frame of the running water is at other positions of the outlet instead of below, then this frame of the image is considered invalid, and the logic is repeated for the previous frame; until normal recognition is performed, Step 3 is entered. If all do not meet the requirements, the queue will be blocked to wait for new image pairs to be put in; Step 3: If there is no water flow, insert 0 into the sliding window; if there is water flow, calculate the flow rate using the algorithm of claim 1; Step 4: Use a sliding window to estimate the average flow rate. If it is less than the threshold or the data length in the window is insufficient, it is considered to be undrained. If and only if the window is full and the average flow rate of the values ​​in the window exceeds the threshold, it is considered to be flowing. Step 5: Report the results.

6. Non-contact dual-camera-based intelligent estimation system for outlet flow, characterized in that: include: Cameras and edge computers; The camera is installed facing the pipe drain outlet and is used to collect image information of the pipe drain outlet area in real time; The edge computer is equipped with the deep learning network model and the polynomial regression model, and is used to execute the algorithm as claimed in claim 1 after receiving image information captured by a camera.

7. The non-contact dual-camera-based outlet flow intelligent estimation system according to claim 6, characterized in that: The algorithm steps executed by the edge computer are: Step 1: Acquire the images of two cameras at the same time and determine whether the time error of image acquisition is within the threshold. If it is within the error range and the image can be read normally, pair them and save them, otherwise re-acquire them. Step 2: When the AI ​​regular recognition logic is triggered, the latest pair of images is selected and the target detection model is called to identify the outlet and the running water, and the detection frame and category are obtained; if the detection frame is abnormal, the abnormality includes the detection frame of the outlet target being classified as having water but no running water target; the detection frame of the running water is at other positions of the outlet instead of below, then this frame of the image is considered invalid, and the logic is repeated for the previous frame; until normal recognition is performed, Step 3 is entered. If all do not meet the requirements, the queue will be blocked to wait for new image pairs to be put in; Step 3: If there is no water flow, insert 0 into the sliding window; if there is water flow, calculate the flow rate using the algorithm of claim 1; Step 4: Use a sliding window to estimate the average flow rate. If it is less than the threshold or the data length in the window is insufficient, it is considered to be undrained. If and only if the window is full and the average flow rate of the values ​​in the window exceeds the threshold, it is considered to be flowing. Step 5: Report the results.

8. An electronic device, comprising a memory and at least one processor, wherein instructions are stored in the memory; The at least one processor calls the instructions in the memory so that the electronic device executes each step of the contactless dual-camera-based intelligent estimation method for outlet flow as described in any one of claims 1-5.

9. A computer-readable storage medium having instructions stored thereon, characterized in that: When the instructions are executed by the processor, the steps of the contactless dual-camera-based intelligent estimation method for outlet flow are implemented as described in any one of claims 1 to 5.

Images