GB2399165A

GB2399165A - Calibration of an optical profile scanner

Info

Publication number: GB2399165A
Application number: GB0305120A
Authority: GB
Inventors: Sandor Patko
Original assignee: AEA Technology PLC
Current assignee: Ricardo AEA Ltd
Priority date: 2003-03-06
Filing date: 2003-03-06
Publication date: 2004-09-08
Anticipated expiration: 2023-03-06
Also published as: GB2399165B; GB0305120D0

Abstract

A method of calibrating an optical profile scanner, comprising a light source arranged to define an illuminated plane on an object, and a camera to view the image, comprising the steps of: <SL> <LI>(a) using a first calibration member comprising a square or rectangular block 12 and two wings 15, and finding the three visible corners A, B, C in the image; <LI>(b) obtaining the image of a second calibration member, e.g. an object having both concave and convex curved surfaces, whose shape is accurately known; <LI>(c) estimating where the fourth corner D would be in the image; <LI>(d) from the positions of the four corners A, B, C, D determining the vanishing points P1, P2, and by projection onto a base line finding the lengths 1x, 1y representing the sides of the block 12; <LI>(e) by projecting in a similar way several points in the image of the second calibration member, finding its apparent shape; <LI>(f) calculating the difference between the apparent shape and the true shape; <LI>(g) repeating steps (c) to (f) many times to find where the fourth corner D must be to measure shapes most accurately. </SL>

Description

Calibration of Optical Profile Scanner This invention relates to a method

of calibration of an optical profile scanner, in particular a laser profile scanner.

Optical profile scanners such as laser profile scanners are known instruments. They comprise a light source such as a laser that is arranged to scan along a straight line, so defining a plane of illumination, and a camera arranged to view the shape of the line of illumination on an object, such as a wheel of a railway train. From the shape of the line seen by the camera, the shape of the object can be determined. Hitherto the calibration of such devices has required information about the locations of the light source and the camera.

According to the present invention there is provided a method of calibration of an optical profile scanner, the optical profile scanner comprising a light source arranged to define a plane of illumination, and a camera arranged to view the intersection of the plane of illumination with an object and to provide an image of it, the method comprising the steps of: a) using as a first object, a first calibration member of Wshape in plan, defining a first pair of plane surfaces that intersect at right angles and two plane surfaces that intersect with the first pair, and determining the coordinates in the image plane of the three points of intersection of the plane of illumination with the lines at which the first pair of plane surfaces intersect each other and intersect the other two plane surfaces; b) using as a second calibration member an object - 2 - whose shape is accurately known, and obtaining its image; c) from the observations in step a) estimating the coordinates in the image plane at which the plane of illumination would intersect the fourth vertex of an object of rectangular shape in plan and having the first pair of plane surfaces as two of its faces, and having the said lines of intersection as its first three vertices; d) from the estimated coordinates of the fourth vertex and the coordinates of the three points of intersection from step a) determining the vanishing points, which are the points of intersection in the image plane of lines parallel to each of the first pair of plane surfaces, hence determining the horizon line in the image plane which represents the plane of illumination at infinity, and then projecting the lengths of the first pair of plane surfaces onto a base line parallel to the horizon line in the image plane from each of the vanishing points, so as to obtain base lengths representing the lengths of those surfaces; e) projecting from each of the vanishing points a multiplicity of points in the image of the second calibration member onto the base line, and hence determining the apparent shape of the second calibration member; f) comparing the apparent shape obtained in step e) with the true shape, and obtaining a numerical measure of the difference between them; g) repeating steps c) to f) a multiplicity of times; - 3 - h) and hence determining the position of the fourth vertex that provides the smallest value of the said numerical measure.

Subsequent measurements can then be made using the optical profile scanner, on objects of unknown shape, the shape being determined in an analogous manner to steps d) and e) above, but using the position of the fourth vertex as determined in step h).

Preferably the lengths of the first pair of plane surfaces are equal (so the object would be square in cross-section). The points of intersection in step a) are preferably determined by fitting straight line equations to the lines in the image plane representing the intersection of the plane of illumination with each of the four plane surfaces, and determining the points of intersection from those equations. This is a more accurate way of determining the points of intersection than attempting to identify the points of intersection in the image.

To avoid problems from reflections it is preferable for the other two plane surfaces to intersect the first pair of plane surfaces at angles slightly greater than a right angle.

A preferred method of estimating the position of the fourth vertex, in step c), is firstly to perform steps c) to f) using no more than 100 different estimated positions. The estimated position that provides the smallest value of the numerical measure is then selected, and a small search area in the image plane around that estimated position is defined. The steps c) to f) are then repeated for positions randomly selected in this small search area, and if a smaller value of the numerical measure is found, then the search area is shifted so as to be centred on the position giving that smaller value before selecting the next randomly- selected position. Preferably this is repeated no more than 1000 times. This two-stage approach has been found to give accurate results, enabling the position of the fourth vertex to be determined to 0.1 pixel in an area say 40 pixels by 40 pixels. It will be appreciated that if the calculations were to be repeated for every possible position, to that accuracy, it would entail 160,000 repetitions, whereas this searching strategy can achieve accurate results with less than 1100 repetitions.

Indeed, in the preferred method, no more than 50 positions are tried in the first stage, and then the random search is repeated only 400 times, so that the results are obtained with only 450 repetitions.

The second calibration object preferably includes both concave and convex curves.

The invention will now be further and more particularly described, by way of example only, and with reference to the accompanying drawings in which: Figure 1 represents part of an image plane showing an image of a square object) Figure 2 shows a perspective view of the first calibration member; and Figure 3 shows a perspective view of a second calibration member.

An optical profile scanner comprises a light source arranged to define a plane of illumination, and a camera arranged to view the intersection of the plane of - 5 - illumination with an object and to provide an image of it. Typically the light source is a scanning laser. The laser scans to and fro so as to define the plane, which would give a straight line if it were incident on a flat surface. Alternatively the laser may be combined with lenses (line generator optics) to provide a fan-shaped planar beam. The shape of the line, as viewed by the camera, enables the cross sectional shape of the object in the plane of illumination to be determined. By way of example, such a device may be arranged between the rails of a railway line and used to check the shape of the tread of the wheels.

Referring to figure 1, the image is shown of an object which is square in plan. The points A, B and C in the image are the visible vertices of the object. The point D shows where the image of the fourth vertex would lie (for example if the object were transparent). It will be appreciated that the lines BC and AD are in reality parallel, and that in the image they converge at a point P2 on the horizon line (the horizon being the line in the image where the plane of illumination intersects objects that are very far away). Similarly the lines AB and CD are in reality parallel, so that in the image they converge at a point P1 on the horizon line. Indeed all lines that are in reality parallel to the line BC will intersect at P2, and all lines that are in reality parallel to AB will intersect at P1.

A base line Q1-Q2 is also drawn, parallel to the horizon line P1-P2. If AB is projected from P2 onto the base line it gives a characteristic length ly, while if BC is projected from P1 onto the base line it gives a characteristic length lx. It will be appreciated that any object that is of length equal to AB and is parallel to AB, if projected onto the base line from P2 will give - 6 - the same characteristic length ly, while any object that is of length equal to BC and is parallel to BC, if projected onto the base line from P1, will give the same characteristic length lx. Hence if coordinate axes x and y (in the real world) are parallel to the surfaces BC and AB of the object, then the coordinates in the real world of any other point in the image plane (such as point R) can be simply determined by projecting that point R onto the base line from P1 and from P2, and calculating in each case the corresponding multiple of the characteristic length lx or ly. For example R projected from P1 gives an intersection at 2 lx, while when projected from P2 it gives an intersection at 0.5 ly; consequently in the real world its coordinates are (2, 0.5) taking the origin of the coordinates as B. and AB and BC as units of length. The signs of the co-ordinates are determined in each case by whether the projected intersections are on the same side of B as the projection of the unit length, or on the opposite side.

It will thus be appreciated that, by using this approach, once the positions in the image plane of the corners A, B. C and D of a square object have been located, the coordinates in the real world of any other point in the image plane can be determined. In practice there will clearly be a difficulty in accurately determining the position of the corner D, because with a real object that corner will usually be hidden.

Referring now to figure 2, a first calibration object 10 consists of an aluminium block 12 which is square in cross-section, to which are attached two plates 14; the sides of the square are of known lengths. Each plate 14 is machined so it defines a plane surface 15 which is at 100 to the adjacent surface of the block 12, and parallel lines 16 are scribed on the surfaces of the 7 - block 12 and the plane surfaces 15, so each line 16 defines a plane that is perpendicular to the vertices.

In use the object 10 is arranged so as to be intersected by the plane of illumination with the vertices perpendicular to the plane of illumination, so that the laser beam generates a line 18 across its surface which, in the image, is W-shaped and is parallel to the lines 16. The coordinates in the image plane of the vertices of the block 12 are determined accurately by first fitting an equation to each straight section of the line 18. The calculated intersections of those straight lines provide the positions of the vertices (A, B and C as shown in figure 1). Because the surfaces 15 are not at right angles to the adjacent surface of the block 12, there is less inaccuracy arising from the reflection of a section of line 18 in the adjacent plane surface.

To determine the position in the image of the hidden vertex (D as shown in figure 1), a second calibration object 20 is used, this object 20 being of accurately known shape, and including both convex and concave curves. Again, parallel lines 22 are scribed along its surface. This is placed so as to be intersected by the plane of illumination, so the laser beam generates a line 24 across its surface which in the image is a curve (and is parallel to the lines 22). The position of the hidden vertex D is found by a repeated trial and error procedure, in which a position of D is assumed, the transformation described in relation to figure 1 is performed for a multiplicity of points along the curved line 24, and the discrepancy between the true shape of the object 20 and the deduced shape is characterized by a numerical measure (for example this may be the mean square distance between the true curve and the calculated curve) referred to as a checksum. - 8

In a first stage, a search area is centred on the fourth corner of a parallelogram whose other sides are AB and BC; a search area 40 pixels by 40 pixels is centred on that vertex, and 50 points are selected at random that lie within both the parallelogram and the search area.

In this first stage, each point has coordinates which are integer numbers of pixels. The position in the image of the hidden vertex D is assumed in turn to be at each of these randomly selected points. The point that gives the least value of the checksum is then selected for use for the next stage. In the next stage a search area 3 pixels by 3 pixels is centred on this optimum point. A point is selected at random in this search area (in this stage coordinates are not restricted to integer values of pixels), and the calculation is performed assuming that point to be the position of the hidden vertex D. If the checksum gives a lower value, the search area is re- centred to that new point before the next point is selected. This procedure is repeated 400 times.

Having ascertained the position of the hidden vertex D in the image plane, it is then possible as explained in relation to figure 1, to determine the coordinates in real space of any point in the image plane. Consequently when an object of unknown shape is intersected by the illumination plane, the resulting curve in the image plane can be transformed to determine the true shape of that cross-section of the object.

It will be appreciated that the term horizon line refers to the plane of illumination where it intersects objects at infinity, and so need not be horizontal, so that the line P1-P2 in practice may have any orientation.

It will also be appreciated that the base line need not pass through the image of the vertex B. The searching strategy for ascertaining the position in the image plane - 9 - of the hidden vertex D may differ from that described above. For example, in the first stage, the number of points that are selected might for example be 100 rather than 50. The searching strategy might, as a second stage, consider a search area say 8 pixels by 8 pixels centred on the optimum point found in the first stage, and then select say 50 points at random in this second search area (working to tenths of a pixel); and then move on as a third stage to consider a search area say 2 pixels by 2 pixels centred on the optimum point found in the second stage. And in some or each of these stages the points might be selected in a regular geometric array, rather than being selected at random.

It will be appreciated that this method of calibration requires the use of optical components that are of low distortion, so the formation of the image can be modelled as that from an ideal pinhole camera. It will also be appreciated that the procedure described above specified positions of points in the image in terms of pixel coordinates, which effectively assumes the pixels to be square. If the pixels in the camera are rectangular then the pixel coordinates must be corrected accordingly; for example if the pixels are rectangular with an aspect ratio 1:1.2 (so the y side of each pixel is 20% bigger than the x side), then all y pixel coordinates should be multiplied by 1.2 before performing the calculations. - 10

Claims

Claims 1. A method of calibration of an optical profile scanner, the

optical profile scanner comprising a light source arranged to define a plane of illumination, and a camera arranged to view the intersection of the plane of illumination with an object and to provide an image of it, the method comprising the steps of: a) using as a first object, a first calibration member of W-shape in plan, defining a first pair of plane surfaces that intersect at right angles and two plane surfaces that intersect with the first pair, and determining the coordinates in the image plane of the three points of intersection of the plane of illumination with the lines at which the first pair of plane surfaces intersect each other and intersect the other two plane surfaces; b) using as a second calibration member an object whose shape is accurately known, and obtaining its image; c) from the observations in step a) estimating the coordinates in the image plane at which the plane of illumination would intersect the fourth vertex of an object of rectangular shape in plan and having the first pair of plane surfaces as two of its faces, and having the said lines of intersection as its first three vertices; d) from the estimated coordinates of the fourth vertex and the coordinates of the three points of intersection from step a) determining the vanishing points, which are the points of intersection in the image plane of lines parallel to each of the first pair of plane surfaces, hence determining the horizon line in the image plane which represents the plane of illumination at infinity, and then projecting the lengths of the first pair of plane surfaces onto a base line parallel to the horizon line in the image plane from each of the vanishing points, so as to obtain base lengths representing the lengths of those surfaces) e) projecting from each of the vanishing points a multiplicity of points in the image of the second calibration member onto the base line, and hence determining the apparent shape of the second calibration member; f) comparing the apparent shape obtained in step e) with the true shape, and obtaining a numerical measure of the difference between them; g) repeating steps c) to f) a multiplicity of times; h) and hence determining the position of the fourth vertex that provides the smallest value of the said numerical measure.
2. A method as claimed in claim 1 wherein the lengths of the first pair of plane surfaces are equal in the first calibration member.
3. A method as claimed in claim 1 or claim 2 wherein the points of intersection in step a) are determined by fitting straight line equations to the lines in the image plane representing the intersection of the plane of illumination with each of the four plane surfaces, and determining the points of intersection from those equations. - 12
4. A method as claimed in any one of the preceding claims wherein, in the first calibration member, the other two plane surfaces intersect the first pair of plane surfaces at angles slightly greater than a right angle.
5. A method as claimed in any one of the preceding claims comprising firstly performing steps c) to f) using no more than 100 different estimated positions selected in a search area in the image plane; then selecting the estimated position that provides the smallest value of the numerical measure, and then defining a smaller search area in the image plane around that estimated position; and then as a second stage repeating steps c) to f) for positions selected in this smaller search area.
6. A method as claimed in claim 5 wherein, in the second stage, the positions are selected randomly within the smaller search area and if a smaller value of the numerical measure is found, then the smaller search area is shifted so as to be centred on the position giving that smaller value before selecting the next randomly- selected position.
7. A method as claimed in any one of the preceding claims wherein the second calibration object includes both concave and convex curved surfaces.
8. A method of calibration of an optical profile scanner substantially as hereinbefore described with reference to, and as shown in, the accompanying drawings.

15763 MdDe P.T. Mansfield

Chartered Patent Agent Agent for the Applicants