Self-position estimation method and self-position estimation device

Abstract

To provide a self-position estimation method and a self-position estimation device which permit a carriage moving on a surface of a three-dimensional object including a pipe to accurately estimate a self position.SOLUTION: A self-position estimation method estimates a position on a surface of a three-dimensional object of a carriage (1) moving on the surface of the three-dimensional object. The self-position estimation method includes: an initial position estimation step of photographing the surroundings of the carriage by a camera (4) provided in the carriage at an initial position of the carriage and transforming coordinates of the initial position of the carriage into coordinates on the surface of the three-dimensional object by use of a pre-calculated coordinate transformation formula; a moving amount calculation step of photographing the surroundings of the carriage by the camera at a moving position after the movement of the carriage and calculating a moving amount of the carriage through comparison between a photographed image at the initial position and a photographed image at the moving position; and a moving position estimation step of transforming coordinates of the carriage at the moving position into coordinates on the surface of the three-dimensional object based on the moving amount of the carriage by using the pre-calculated coordinate transformation formula.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present disclosure relates to a self-position estimation method and a self-position estimation device. In particular, the present disclosure relates to a self-position estimation method and a self-position estimation device for estimating the position on the surface of a three-dimensional object of a carriage that moves along the outer surface of a three-dimensional object including a cylindrical member.

Background Art

[0002] Conventionally, the following methods are known as methods for estimating the position of a carriage. For example, an encoder for detecting the rotation speed is attached to the carriage drive unit to detect the movement amount of the carriage from the rotation speed of the motor of the drive unit, and a gyro sensor is attached to the carriage to detect the traveling direction of the carriage, whereby there is a method of estimating the self-position of the carriage from the movement amount and the traveling direction of the carriage (see Patent Document 1).

[0003]

[0004] Also, there is a method of measuring the surroundings with a LIDAR or the like attached to the carriage, generating a surrounding map of the carriage, and estimating the self-position from the surrounding map (see Patent Document 2).

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0006] ​ However, the method of Patent Document 1 has problems that the deviation of the moving amount becomes large due to the slip of the driving part of the carriage, and the deviation in the traveling direction becomes large due to the turning of the carriage. In particular, in the case of a carriage that moves while adsorbing the surface of a three-dimensional object such as a pipe, for example, the deviation of the moving amount becomes large due to the slip of the driving part caused by dust on the surface, and the deviation in the traveling direction may become large due to the lowering of the carriage due to the influence of gravity.

[0007] Also, the methods of Patent Document 2 and Patent Document 3 estimate the self-position by comparing the generated surrounding map and the captured image. When the carriage travels on the surface of a three-dimensional object such as a pipe, it is necessary to compare while rotating the surrounding map in all directions. Therefore, it is actually difficult to estimate the position of the carriage by the methods of Patent Document 2 and Patent Document 3.

[0008] In view of such circumstances, an object of the present disclosure is to provide a self-position estimation method and a self-position estimation device capable of accurately estimating the self-position of a carriage moving on the surface of a three-dimensional object including a pipe.

Means for Solving the Problems

[0009] A self-position estimation method according to an embodiment of the present disclosure is a self-position estimation method for estimating the position of a carriage on the surface of a three-dimensional object moving on the surface of the three-dimensional object, an initial position estimation step of photographing the periphery of the carriage by a camera provided on the carriage at the initial position of the carriage and converting the coordinates of the initial position of the carriage into coordinates on the surface of the three-dimensional object using a previously calculated coordinate conversion formula; after the carriage moves, photograph the periphery of the carriage by the camera at the moving position, and calculate the moving amount of the carriage by comparing the captured image at the initial position and the captured image at the moving position; a moving position estimation step of converting the coordinates of the moving position of the carriage into coordinates on the surface of the three-dimensional object from the moving amount of the carriage using a previously calculated coordinate conversion formula.

[0010] The self-position estimation device according to an embodiment of the present disclosure is provided on a carriage that moves on the surface of a three-dimensional object, and includes a camera that photographs the periphery of the carriage at each of the initial position and the moving position of the carriage, and a control unit that calculates the amount of movement of the carriage by comparing the captured image of the camera at the initial position with the captured image of the camera at the moving position. The control unit converts the coordinates of the initial position of the carriage into coordinates on the surface of the three-dimensional object using a coordinate conversion formula calculated in advance, and converts the coordinates of the moving position of the carriage into coordinates on the surface of the three-dimensional object from the amount of movement of the carriage.

Advantages of the Invention

[0011] According to the present disclosure, it is possible to provide a self-position estimation method and a self-position estimation device capable of accurately estimating the self-position of a carriage that moves on the surface of a three-dimensional object including piping.

Brief Description of the Drawings

[0012]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Modes for Carrying Out the Invention

[0013] Hereinafter, a self-position estimation method and a self-position estimation apparatus according to an embodiment of the present disclosure will be described with reference to the drawings.

[0014] (Overall Configuration) FIG. 1 is a diagram showing a configuration example of a self-position estimation apparatus according to the present embodiment. The self-position estimation apparatus according to the present embodiment includes a carriage 1 and a CPU (Central Processing Unit) 5. The carriage 1 is a traveling carriage (mobile carriage) that moves on the surface of a three-dimensional object, and includes a power source 2, a control / communication unit 3, and a camera 4.

[0015] The carriage 1 includes a drive unit (wheels) and is movable back and forth, left and right along the outer surface of a pipe 6 (an example of a three-dimensional object, see FIG. 2). In the present embodiment, the carriage 1 includes an adsorption means such as a magnet and moves while adsorbing the surface of the pipe 6. Here, the drive unit is not limited to wheels and may be a crawler or the like.

[0016] The power source 2 is mounted on the carriage 1 and supplies power to the control / communication unit 3 and the camera 4. The power source 2 is, for example, a battery, but is not limited to a battery as long as it supplies power to the control / communication unit 3 and the camera 4.

[0017] The control / communication unit 3 is mounted on the carriage 1, controls the camera 4, and wirelessly transmits the captured image of the camera 4 to the CPU 5. Further, the control / communication unit 3 may control the drive unit. Further, the control / communication unit 3 may control the power source 2.

[0018] The camera 4 is mounted on the carriage 1 and performs shooting and the like. The camera 4 is, for example, a stereo camera, but is not limited to a stereo camera as long as it can shoot a marker 7 and a feature point group 9 described later and measure the distance to the marker 7 and the feature point group 9 (see FIG. 4).

[0019] The CPU 5 is provided at a position away from the carriage 1 and executes calculation processing based on the captured image acquired from the carriage 1. Specifically speaking, the CPU 5 estimates (calculates) the position (coordinates) of the carriage 1 from the captured image sent wirelessly. The CPU 5 may be, for example, a control unit included in a computer capable of communicating with the carriage 1. The computer may be a process computer that manages the manufacture and inspection of the pipe 6 (see FIG. 2).

[0020] Here, as another example, the self-position estimation device may be configured such that the CPU 5 is mounted on the carriage 1. In the case where the CPU 5 is mounted on the carriage 1, the data of the self-position of the carriage 1 estimated by the CPU 5 during the running of the carriage 1 may be stored in a storage device mounted on the carriage 1 and taken out after the running of the carriage 1 is completed. Here, the storage device may be, for example, a memory card. Also, in the case where the CPU 5 is mounted on the carriage 1, the control / communication unit 3 may omit the communication part.

[0021] FIG. 2 is a diagram illustrating the carriage 1 moving on the surface of the pipe 6. In the present embodiment, as shown in FIG. 2, markers 7 are provided on the surface of the pipe 6. The marker 7 is, as an example, a two-dimensional code such as a QR code (registered trademark), and includes information on three-dimensional coordinates (hereinafter simply referred to as "three-dimensional coordinates") on the surface of a three-dimensional object. Hereinafter, although the marker 7 is described as being a two-dimensional code, the marker 7 is not limited to a two-dimensional code as long as it includes information on three-dimensional coordinates.

[0022] In the present embodiment, the three-dimensional coordinates are coordinates in a three-dimensional coordinate system (Σ in FIG. 4) having coordinate axes corresponding to the cylindrical axis direction and the radial direction of the pipe 6, which is a three-dimensional object, and can be referred to as pipe coordinates. Here, the marker 7, which is a two-dimensional code, is provided horizontally (that is, without curving along the surface of the pipe 6). Also, the marker 7 is provided on the pipe 6 in such a direction that the coordinate axes specified by the two-dimensional code correspond to the cylindrical axis direction of the pipe 6 and the like. marker See) and can be called pipe coordinates. Here, the marker 7, which is a two-dimensional code, is provided horizontally (that is, without curving along the surface of the pipe 6). Also, the marker 7 is provided on the pipe 6 in such a direction that the coordinate axes specified by the two-dimensional code correspond to the cylindrical axis direction of the pipe 6 and the like.

[0023] The carriage 1 that travels on the outer surface of the pipe 6 captures the surrounding area at the position (initial position) at the start of travel so that the marker 7 provided on the pipe 6 can be captured by the camera 4. The CPU 5 identifies the coordinate axes of the three-dimensional coordinate system based on the marker 7 in the image captured by the camera 4. Specifically speaking, the CPU 5 may identify the coordinate axes using the finder pattern of the two-dimensional code.

[0024] The carriage 1 is used for various purposes. In this embodiment, it is used to perform flaw detection (wall thickness reduction) inspection on the pipe 6, and a flaw detection inspection device is further mounted on the carriage 1.

[0025] FIG. 3 is a diagram illustrating a two-dimensional map 8 obtained by developing the pipe surface. In order to clearly show the result of the flaw detection inspection of the pipe 6, the carriage position and the state of the defect at that position can be displayed on the two-dimensional map 8. As shown in the left figure of FIG. 3, if the carriage position is specified as the coordinates (X, Y, Z) of the three-dimensional coordinate system, it can be converted into the coordinates (X, R, θ) of the cylindrical coordinate system corresponding to the shape of the pipe 6. And in this embodiment, since the radius (R) of the pipe 6 is constant, the carriage position can be displayed on the two-dimensional map 8 using two parameters (X and θ) without increasing the processing load. At this time, if the carriage position is specified with high precision, the position of the defect measured by the carriage 1 can be specified with high precision. Therefore, the precise specification of the carriage position enables a high-precision inspection.

[0026] Here, in this embodiment, the three-dimensional object is a cylindrical pipe 6. However, the self-position estimation method described below is also applicable when the carriage 1 moves on the surface of a member other than the pipe 6 (cylindrical member), such as a member with a polygonal cross-section like a square or a triangle.

[0027] (Self-Position Estimation Method) The self-position estimation method executed by the self-position estimation apparatus according to the present embodiment will be described below. In the self-position estimation method according to the present embodiment, as shown in FIG. 7, the CPU 5 executes an initial position estimation step (step S1), a movement amount calculation step (step S2), and a movement position estimation step (step S3) in this order.

[0028] (At the start of travel: Initial position estimation step) FIG. 4 is a diagram for explaining the estimation of the self-position (at the start of travel of the carriage 1). First, at the start of travel of the carriage 1, the initial position of the carriage 1 is calculated. Σ in FIG. 4 marker (X, Y, Z) is the coordinate system of the marker 7, that is, the above-described three-dimensional coordinate system. As described above, in order to be developed as the two-dimensional map 8, the carriage position needs to be finally calculated as coordinates (coordinates in the three-dimensional coordinate system or the cylindrical coordinate system) on the surface of the three-dimensional object. Here, as shown in FIG. 4, in the present embodiment, the carriage position is the position of the center of the carriage 1. However, as another example, in order to reduce the processing load of the CPU 5, the position of the camera 4 may be treated as the same as the carriage position.

[0029] The coordinate system of the camera 4 at the start of measurement (the coordinate system from the viewpoint of the camera 4) is defined as the world coordinate system. Σ in FIG. 4 world (x w , y w , z w ) represents the world coordinate system. The world coordinates are the coordinates of the initial position of the carriage 1, and can also be referred to as the initial position coordinates or the initial camera coordinates. Hereinafter, the description will be made using the term of world coordinates.

[0030] Also, based on the positional relationship between the camera 4 and the carriage position, the CPU 5 calculates world Ro, which is the coordinates of the carriage 1 in the world coordinate system. world Ro is "the coordinates of the initial position of the carriage 1".

[0031] The camera 4 captures the image of the marker 7 and measures the position and orientation of the marker 7 as seen by the camera 4. Based on the images captured by the stereo camera 4, the CPU 5 can measure (calculate) the distance from the camera 4 to the marker 7 using the principle of triangulation. The CPU 5 calculates the coordinates of the marker 7 in the world coordinate system. world The CPU 5 calculates M. The CPU 5 also calculates the coordinates of the camera 4 as seen from the marker 7. world P marker,world can be calculated using the following formula (1).

[0032]

number

[0033] The camera 4 also captures the group of feature points 9. The CPU 5 can measure (calculate) the distance from the camera 4 to the group of feature points 9 based on the principle of triangulation. The CPU 5 calculates the coordinates of the group of feature points 9 in the world coordinate system. world b x The feature point group 9 is a plurality of feature points. The feature points are stationary points in the vicinity that are not the pipes 6. The feature points may be, for example, corners of buildings in the vicinity.

[0034] CPU5 is Σ marker (X,Y,Z) and Σ world (x w ,y w ,z w ) and the transformation equation from the three-dimensional coordinate system to the cylindrical coordinate system. marker R world The CPU 5 calculates the coordinates of the carriage position in the cylindrical coordinate system at the initial position of the carriage 1 using this transformation determinant (coordinate transformation equation). marker Ro is calculated by the following formulas (2) and (3), where: marker W is the coordinate of camera 4 in the cylindrical coordinate system.

number

[0035] In this way, the CPU 5 captures the surroundings of the carriage 1 with the camera 4 provided on the carriage 1 at the initial position of the carriage 1, and executes an initial position estimation process of converting the coordinates of the initial position of the carriage 1 into the coordinates on the surface of the three-dimensional object (pipe 6) using the previously calculated coordinate conversion formula. Further, in the initial position estimation process, the CPU 5 captures the marker 7 with the camera 4 and calculates the coordinate conversion formula by comparing the position of the marker 7 with the initial position of the carriage 1.

[0036] (During travel: movement amount calculation process) FIG. 5 is a diagram for explaining the estimation of the self-position (during the travel of the carriage 1). After the initial position estimation process is executed, the carriage 1 moves on the surface of the pipe 6. The camera 4 captures the surrounding feature point group 9 during the travel of the carriage 1. The CPU 5 measures the distance to the feature point group 9, calculates the movement amount of the carriage 1 during travel from the deviation amount from the feature point group 9 as seen from the initial position, and estimates the position of the carriage 1.

[0037] The coordinate system of the camera 4 during the movement of the carriage 1 (the coordinate system from the viewpoint of the camera 4) is defined as the camera coordinate system. Σ in FIG. 5 camera (x c , y c , z c ) represents the camera coordinate system. At the initial position of the carriage 1, Σ camera (x c , y c , z c ) is the world coordinate system Σ world (x w , y w , z w ) coincided, but it is defined as a coordinate system different from the world coordinate system due to the movement of the carriage 1.

[0038] Further, based on the positional relationship between the camera 4 and the carriage position, the CPU 5 calculates camera Ro, which is the coordinate of the carriage 1 in the camera coordinate system. camera Ro is "the coordinate of the moving position of the carriage 1".

[0039] Also, the camera 4 continues to photograph the feature point group 9. The CPU 5 is the coordinates of the feature point group 9 in the camera coordinate system camera b x and calculates it.

[0040] The CPU 5 calculates the transformation determinant camera (x c , y c , z c ) and Σ world (x w , y w , z w ) for each axis deviation between them, which is the transformation determinant from the camera coordinate system to the world coordinate system world R camera and calculates it. The CPU 5 uses this transformation determinant (coordinate transformation formula) to calculate the movement amount of the carriage 1 in the world coordinate system world C by the following formula (4).

[0041]

Equation

[0042] In this way, the CPU 5 executes a movement amount calculation process of photographing the periphery of the carriage 1 by the camera 4 at the movement position after the movement of the carriage 1, comparing the photographed image at the initial position with the photographed image at the movement position, and calculating the movement amount of the carriage 1. Specifically, the CPU 5 extracts the feature point group 9 from the photographed image and calculates the distance to the feature point group 9 in the movement amount calculation process, and compares the distance to the feature point group 9 in the photographed image at the initial position and the photographed image at the movement position to calculate the movement amount of the carriage 1.

[0043] (During travel: Movement position estimation process) The CPU 5 uses the homogeneous transformation matrix (coordinate transformation formula) including the above marker W and world C to calculate the coordinates of the carriage position in the cylindrical coordinate system marker Ro by the following formula (5). Here, the homogeneous transformation matrix from the world coordinate system to the cylindrical coordinate system marker T world is the following formula (6). Also, the homogeneous transformation matrix from the camera coordinate system to the world coordinate systemworld T camera is given by the following formula (7).

[0044] [Number]

[0045] In this way, the CPU 5 executes a moving position estimation process of converting the coordinates of the moving position of the carriage 1 from the moving amount of the carriage 1 into the coordinates on the surface of the three-dimensional object (pipe 6) using the previously calculated coordinate conversion formula.

[0046] (Two-dimensional map creation process) The CPU 5 may further execute a two-dimensional map creation process of creating a two-dimensional map 8 obtained by developing the surface of the three-dimensional object (pipe 6) and indicating the coordinates of the carriage 1 on the surface of the three-dimensional object (pipe 6) on the two-dimensional map 8.

[0047] (Example) FIG. 6 is a diagram showing the self-position estimation accuracy of the carriage 1 in an embodiment of the present disclosure. A marker 7 which is a QR code (registered trademark) was provided on a container placed at one end of a drum can simulating the pipe 6. The marker 7 was installed horizontally and the printing surface was at the same height as the surface of the drum can. Further, the marker 7 was installed such that the X axis of the three-dimensional coordinate system was parallel to the cylindrical axis of the drum can.

[0048] A straight line was drawn on the surface of the drum can from the marker 7 parallel to the cylindrical axis to the opposite end, and a reference line was provided. Further, the circumference was measured, and lines parallel to the reference line (parallel lines) were drawn at positions shifted by 1 / 8 and 1 / 4 of the circumference from the reference line. The positions on the parallel line at a position shifted by 1 / 8 of the circumference from the reference line were set as the -45° position or the +45° position. Also, the positions on the parallel line at a position shifted by 1 / 4 of the circumference from the reference line were set as the -90° position or the +90° position.

[0049] Lines were drawn circumferentially at positions 516 mm and 916 mm along the reference line from the center of marker 7. Intersection points (10 points) of these circumferential lines with the reference line and the above parallel lines were set as measurement points. Points a to j shown in Fig. 6 are the measurement points. The carriage 1 was moved in order from point a to point j, and self-position estimation was executed at the positions of the respective measurement points, and comparison with the true value (coordinates of the measurement points) was performed.

[0050] In this embodiment, the error of self-position estimation was within the range of -5% to +5%, and sufficient accuracy was obtained. Here, in the right figure of Fig. 6, the true value is indicated by a black circle, and the range of -5% to +5% of the length in the cylindrical axis direction and the circumference of the drum can along the true value is indicated by a black line. Also, the estimated value is indicated by a triangle.

[0051] As described above, the self-position estimation method and self-position estimation device according to this embodiment can estimate the self-position of the carriage 1 without using either an encoder or a gyro sensor. Therefore, regardless of the displacement of the movement amount due to the slip of the carriage 1 during traveling, the displacement of the traveling direction due to the descent of the carriage 1, etc., the self-position can be estimated with high accuracy.

[0052] Further, according to the self-position estimation method and self-position estimation device according to this embodiment, by providing a step of converting the position (coordinates) of the carriage 1 into coordinates on the surface of a three-dimensional object using a coordinate conversion formula, even when the carriage 1 travels on a three-dimensional object rather than a flat surface such as the floor, it is possible to estimate the position (coordinates) of the carriage 1.

[0053] Furthermore, according to the self-position estimation device according to this embodiment, by adding the control / communication unit 3 and the camera 4 to a conventional traveling carriage, high-precision self-position estimation becomes possible, and complicated modification of the traveling carriage is unnecessary.

[0054] Also, when photographing the surroundings with the camera 4 attached to the carriage 1, instead of the entire photographed image, position data may be acquired by narrowing down to the coordinates of the marker 7 and the feature point group 9, and the amount of data to be stored can be reduced, and since the entire photographed image is not used for calculation, the amount of calculation can be reduced.

[0055] Although the embodiments according to the present disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art can easily make various modifications or corrections based on the present disclosure. Therefore, it should be noted that these modifications or corrections are included in the scope of the present disclosure. For example, the functions included in each component or each step can be rearranged so as not to be logically contradictory, and a plurality of components or steps can be combined into one or divided. Although the embodiments according to the present disclosure have been described mainly centered on the device, the embodiments according to the present disclosure can also be realized as a method including the steps executed by each component of the device. The embodiments according to the present disclosure can also be realized as a method, program, or storage medium recording the program executed by a processor included in the device. It should be understood that these are also included in the scope of the present disclosure.

[0056] In the above embodiment, the CPU 5 uses the coordinate conversion formula from the world coordinate system to the cylindrical coordinate system, but it may first convert from the world coordinate system to the three-dimensional coordinate system and then convert the three-dimensional coordinate system to the cylindrical coordinate system.

[0057] In the above embodiment, the CPU 5 estimated the three-dimensional coordinate system of the carriage 1 by the camera 4 reading the marker 7 and calculated the coordinate conversion formula. Here, for example, when the coordinates of the three-dimensional coordinate system of the initial position of the carriage 1 are known in advance, the CPU 5 may estimate the coordinates (three-dimensional coordinate system) of the carriage 1 without using the marker 7.

Explanation of Reference Numerals

[0058] 1 Carriage 2 Power supply 3 Control / communication unit 4 Camera 5 CPU 6 Pipe 7 Marker 8 Two-dimensional map 9 Feature point group

Claims

1. A self-position estimation method for estimating the position of a cart moving on the surface of a three-dimensional object on the surface of the three-dimensional object, comprising: The three-dimensional object is provided with markers containing information on the coordinates on the surface of the three-dimensional object, and the orientation of the markers is associated with the direction of the three-dimensional object. An initial position estimation step of taking a picture of the periphery of the cart and the marker by a camera provided on the cart at the initial position of the cart, calculating a transformation determinant by comparing the position and orientation of the marker identified by the picture with the initial position of the cart, and using the transformation determinant to transform the coordinates of the initial position of the cart into coordinates corresponding to the shape of the three-dimensional object; After the cart moves, a moving amount calculation step of taking a picture of the periphery of the cart by the camera at the moving position, and calculating the moving amount of the cart by comparing the picture taken at the initial position with the picture taken at the moving position; A moving position estimation step of using a pre-calculated homogeneous transformation matrix to transform the coordinates of the moving position of the cart into coordinates corresponding to the shape of the three-dimensional object from the moving amount of the cart. The self-position estimation method includes these steps.

2. In the moving amount calculation step, a feature point group is extracted from the captured image to calculate the distance to the feature point group, and the moving amount of the cart is calculated by comparing the distances to the feature point group in the captured image at the initial position and the captured image at the moving position. The self-position estimation method according to Claim 1.

3. The self-position estimation method according to Claim 1 or 2 further includes a two-dimensional map creation step of creating a two-dimensional map by unfolding the surface of the three-dimensional object and indicating the coordinates of the cart on the surface of the three-dimensional object on the two-dimensional map.

4. The three-dimensional object is a cylindrical member. The self-position estimation method according to any one of Claims 1 to 3.

5. A self-position estimation device for estimating the position of a cart moving on the surface of a three-dimensional object on the surface of the three-dimensional object, comprising: The three-dimensional object is provided with markers containing information on the coordinates on the surface of the three-dimensional object, and the orientation of the markers is associated with the direction of the three-dimensional object. A camera provided on the cart for taking pictures of the periphery of the cart at the initial position and the moving position respectively, and the marker at the initial position of the cart; A control unit for calculating the moving amount of the cart by comparing the captured image of the camera at the initial position with the captured image of the camera at the moving position. The control unit calculates a transformation determinant by comparing the position and orientation of the marker specified by imaging with the initial position of the carriage, converts the coordinates of the initial position of the carriage into coordinates corresponding to the shape of the three-dimensional object using the transformation determinant, and converts the coordinates of the movement position of the carriage from the movement amount of the carriage into coordinates corresponding to the shape of the three-dimensional object using a previously calculated homogeneous transformation matrix, a self-position estimation device.

Images