WO2009018894A1

WO2009018894A1 - Method and device for determining geometric data of a measured object

Info

Publication number: WO2009018894A1
Application number: PCT/EP2008/005742
Authority: WO
Inventors: Rolf Beck
Original assignee: Carl Zeiss Industrielle Messtechnik Gmbh
Priority date: 2007-08-06
Filing date: 2008-07-15
Publication date: 2009-02-12
Also published as: DE102007038785A1

Abstract

A measured object (18) having at least one contour (19) with a defined dimension is recorded with the aid of an image recorder (12). Said image recorder (12) is located at a first known position relative to the measured object (18). The first image (44) shows the defined dimension in a first image size (48). Geometry data are determined from the image data, wherein calibration data are used to represent an imaging factor between the first image (44) and the measured object (18). According to one aspect of the invention, a second image of the measured object (18), including a second contour image (46'), is recorded at a second position of the image recorder (12) relative to the measured object (18). The calibration data are determined as a function of the first and second position and as a function of the first and second image size (48, 48').

Description

Method and device for determining geometric data of a measurement object

The present invention relates to a method for determining geometry data of a measurement object which has at least one contour with a defined dimension, with the following steps:

Receiving at least a first image of the measurement object with the aid of an image recorder which is arranged at a first known position relative to the measurement object, wherein the first image contains a first contour image which shows the defined dimension in a first view,

Determining first image data of the measurement object from the first image, and

Determining the geometry data from the first image data using calibration data representing a mapping function between the first image and the measurement object. The invention also relates to an apparatus for determining geometric data of a measurement object which has at least one contour with a defined dimension, with an image recorder for recording at least a first image of the measurement object at a first defined position, wherein the image recorder is movable relative to the measurement object and wherein the first image includes a first contour image showing the defined dimension in a first view, further comprising an image data determination unit for determining first image data of the measurement object from the first image, and a geometry data determination unit for determining the geometry data from the first image Image data using calibration data representing a mapping function between the first image and the measurement object.

Such a method and device are known, for example, from EP 0 866 308 B1.

This document describes an optical sensor for determining geometric data of a workpiece and in particular for determining the dimensions and the profile of an edge on an aircraft propeller blade. The known device has two image sensors in the form of cameras, which look from different directions on the edge of the propeller blade. A light pattern is projected onto the edge. An evaluation of the image data provided by both cameras makes it possible to determine the geometrical dimensions of the edge and its shape progression. However, this requires that the two cameras are calibrated, i. the basic relationship between the image data of the cameras and the real dimensions of a recorded object must be known. This relationship is determined in a calibration process, which precedes the measurement of a propeller blade, with the aid of a known calibration object.

The calibration object for the known device has a reference pattern with a plurality of matrix-like arranged squares, the position of which is known exactly relative to a stop. The calibration object is recorded using the cameras from varying distances. Based on the known positions of Squares can then be used to determine transformation equations describing the relationship between the image data and the real geometry data.

DE 10 2004 054 876 B3 discloses a measuring device for the 3D measurement of dental models, such as a dental prosthesis. The measuring device includes a measuring camera with which the tooth model is recorded. The model is arranged on a holder which is in a known position relative to the measuring camera. The calibration of the measuring camera also takes place here using a reference object, which in this case is a very precisely manufactured cylinder body.

According to a procedure which is described in DE 197 43 811 C2, the calibration is carried out on the basis of a plate which is positioned at different distances from a measuring camera. At each distance, the plate is illuminated with a defined pattern of light and the associated distance is determined with a calibrated measure of length.

EP 0 216 587 B1 proposes an optical measuring device in which an optically generated reference grid is to be used instead of a mechanical reference object for calibration.

The known methods and devices have in common that the calibration must be carried out before performing the actual measurement task, so that the calibration represents an additional step that delays the execution of the measurement task. This is particularly disadvantageous if the calibration has to be repeated frequently because, for example, the structure of the measuring device changes. The latter may for example be the case when the imager is provided with a zoom lens, because the calibration may vary depending on the zoom level used. If the zoom level is to be changed during the measurement of a DUT, it may be necessary to calibrate repeat before working with the new zoom level. It is easy to see that the calibration effort makes it difficult to carry out the measurement.

In view of this, it is an object of the present invention to reduce the cost of calibration in a method and a device of the type mentioned in order to simplify the determination of geometric data of a measured object with the aid of an image sensor. However, the measurement accuracy should not be affected, i. The reduced calibration effort should not be at the expense of the measurement accuracy.

This object is achieved according to a first aspect of the invention by a method of the type mentioned, in which a second image of the measurement object including a second contour image is taken at a second known position of the image sensor relative to the measurement object, wherein the second contour image of the defined dimension in a second view, and wherein the calibration data is determined in dependence on the first and the second position and in dependence on the first and second views.

According to a further aspect of the invention, this object is achieved by a device of the aforementioned type, which has a Kalibrierdatenbestimmungseinheit, which is adapted to the calibration data in dependence on the first and a second position of the image sensor relative to the measurement object and in dependence the first and second views, the second image size representing the defined dimension in a second contour image taken at the second position of the image sensor relative to the measurement object.

The new method and the new device make it possible to carry out the calibration on the basis of the measurement object itself by recording the measurement object in at least two different positions. It does not matter in principle whether the object to be measured is displaced relative to the image sensor or whether the image sensor is moved relative to the measurement object, because it depends solely on the change of the relative position of the image sensor and the measurement object to each other. The new method and apparatus utilize the fact that a real geometry feature on the measurement object remains the same when the measurement object is moved relative to the imager. In other words, the real geometry data of the measurement object is invariant with respect to a relative displacement of the measurement object and the image sensor.

Even if one does not know the absolute values of the geometry data of the measurement object before or during the execution of the measurement task, calibration data can be determined from the changed image data and the geometry data of a contour adopted as invariant, which make it possible in a subsequent step as well to determine the absolute values of the DUT. The only prerequisite is that the first and the second relative position of the image sensor and the measurement object are known and that it is ensured by means of suitable feature recognition that the first and the second contour image respectively show the same contour of the measurement object. In summary, a core idea of the new device and the new method is that a selected contour on an unknown measurement object is detected and tracked over several measurements at different measurement positions, and that the calibration data is determined from the changed contour images.

The new method and the new device have the great advantage that the calibration can be carried out in the measuring process ("online") and, if necessary, also be repeated in the measuring process. "Moreover, the device and the new method do not have a calibration object known in its properties Thus, the user of the new device can concentrate on his measurement task without having to worry about a separate calibration process without eliminating the calibration or postponing to times well before the measurement task is done significantly reduced for the user who wants to carry out a measuring task. The above task is thus completely solved.

In a preferred embodiment of the invention, the calibration data are determined independently of the defined dimension of the contour.

In this embodiment, the absolute value of the defined dimension is unknown. Only the fact is exploited that the defined dimension is invariant with respect to a change in the relative position of the object to be measured and the image sensor. Alternatively, the new device and the new method can in principle also be used in addition and / or in combination with special calibration objects whose geometry data are already known, as is typically the case in the methods and devices of the prior art. The preferred embodiment has the advantage that the calibration is performed on the real measurement object, so that the measurement can start directly. The effort for the calibration is correspondingly greatly reduced. In addition, the calibration is done here in a direct temporal context with the implementation of the measurement, so that a change in the measuring device is practically excluded by environmental influences between calibration and measurement. Therefore, this embodiment allows a particularly high measurement accuracy despite the reduced cost of calibration.

In a further embodiment, the first and the second contour image are automatically identified within the first and the second image.

As an alternative to this, it is fundamentally conceivable to identify the contour of the measurement object in each image in a user-assisted manner. In contrast, the preferred embodiment allows a fully automatic measurement including the new calibration, so that the effort for the user is further reduced.

In a further embodiment, the first and the second position are approximately at the defined dimension or further apart. In this embodiment, the measurement object is moved relative to the image sensor approximately as far as the dimension of the contour used for calibration is. This achieves a "significant" change in the relative position of the imager and target, which makes calibration data easier to calibrate, and in this case, the calibration data is representative of much of the measurement volume, allowing consistently high measurement accuracy regardless of the measurement location.

In a further embodiment, a plurality of first and second views are determined at a plurality of first and second positions.

In a further embodiment, the image recorder is displaced at at least three positions relative to the measurement object, wherein at least three different contour images are recorded. The calibration data will be determined several times based on different image pairs from the at least three contour images. Advantageously, the multiply determined calibration data can be averaged. The averaging makes it possible to increase the robustness of the method. Alternatively or additionally, quality factors can be determined from the plurality of data, such as a standard deviation, which is representative of the quality of the measurement and the quality of the calibration process. Advantageously, such quality factors are used to declare a measurement and calibration process valid or invalid.

In a further embodiment, a number of geometry data is determined, with associated calibration data being determined for each geometry datum.

In this embodiment, an online calibration takes place for each individual measured value on the measurement object. Alternatively, it would also be possible to perform a calibration for a large number of subsequent measured values. In contrast, the preferred embodiment allows a particularly high measurement accuracy for all Measured values independent of the order in which the measured values are recorded.

In an alternative embodiment, the calibration data are used for a large number of geometry data.

The design speeds up the performance of a measurement because the calibration steps are performed only once or a few times.

In a further embodiment, the image recorder is designed to generate a two-dimensional image of the measurement object.

In this embodiment, the imager may include a camera chip having a matrix-like arrangement of pixels. In principle, however, this embodiment can also be implemented with an image recorder which generates the two-dimensional image by scanning the measurement object line-wise and / or column by column. The advantages of the new procedure have a particularly significant effect on two-dimensional measuring devices, since the known procedures for calibrating such measuring devices are particularly complex.

In a further embodiment, the image recorder has an image plane, wherein the first and second positions lie at a constant vertical distance from the image plane.

The constant vertical distance can be predetermined by a corresponding mechanical arrangement, which ensures that the image sensor can be moved only with the constant distance relative to the measurement object. Alternatively or additionally, the constant vertical distance can also be realized by taking into account only the projection of the location change into the image plane during the relative displacement of the image recorder. In other words, only the positional change that takes place in the image plane is considered hereafter of the imager, even if the actual positional shift has a component orthogonal to the image plane of the imager. This embodiment is particularly advantageous if the image recorder is designed to produce a two-dimensional image of the measurement object, because such image sensors themselves can only recognize the position shifts in the two-dimensional image plane. The preferred embodiment leads to calibration data that allow a very accurate measured value determination.

In a further refinement, the image recorder is designed to generate a three-dimensional image of the measurement object.

In this embodiment, the imager has the ability to determine the distance to the individual measurement points on the measurement object. This can be done for example by a transit time measurement of a suitable transmission pulse or by a stereoscopic method. Another possibility is image sensors, which determine the distance to the measurement object based on auto-focus information. This embodiment has the advantage that the measurement object can be measured in three dimensions with little effort and high accuracy.

In a further embodiment, the image recorder has a zoom lens.

This embodiment is advantageous because the calibration is particularly complex when using zoom lenses. Thus, devices in which the imager has a zoom obtive jectively benefit particularly from the advantages of the invention described above, because the calibration can be repeated online with or after each new zoom level in the measurement process.

In a further embodiment, the first and the second image are recorded without distortion. This embodiment can be realized either by using at least largely distortion-free lenses and / or by a software correction of the images. This refinement has the advantage that the recognition of the contour used for the calibration is largely independent of the position of the measurement object in the measurement volume. This embodiment therefore facilitates automatic recognition of the contour. In addition, the "local" calibration data determined from a snapshot of the images can be applied to the entire image with a good approximation, making calibration even easier and faster.

In a further embodiment, the contour is circular.

This embodiment also facilitates the automatic recognition of the contour, which is evaluated for the calibration. It is of particular advantage that a circular contour is independent of the rotational position of the test object relative to the image sensor. Therefore, the defined dimension of the contour in this embodiment can be determined particularly easily.

In a further embodiment, the contour has a defined rotational position about an axis running perpendicular to the contour. In a preferred embodiment, the contour is a rectangle with a defined length and an origin. Alternatively, the contour may be, for example, an ellipse or a non-equilateral triangle.

These embodiments also facilitate the automatic recognition of the contour and the determination of the defined dimension in the at least two contour images. This makes the calibration particularly easy and quick to perform.

In a further embodiment, the image recorder is displaced relative to the measurement object without rotation. This embodiment is another preferred way to facilitate the recognition of the defined dimension in the contour images and to accelerate the calibration process.

It is understood that the features mentioned above and those yet to be explained below can be used not only in the particular combination given, but also in other combinations or in isolation, without departing from the scope of the present invention.

Embodiments of the invention are illustrated in the drawings and are explained in more detail in the following description. Show it:

Figure 1 is a simplified representation of an embodiment of the new

Contraption,

FIG. 2 shows a first image with a first contour image of a measurement object according to an exemplary embodiment of the invention,

3 shows a second image with a second contour image of the measurement object, and

FIG. 4 shows a flowchart for explaining an exemplary embodiment of the method according to the invention.

In Figure 1, an embodiment of the new device is generally designated by the reference numeral 10. The apparatus 10 includes an imager 12, shown here in the form of a camera. In other embodiments, the imager may merely be a camera chip that provides only limited camera functionality. The image recorder 12 is here attached to a column 14, which is movable relative to a table 16. The table 16 serves to receive a measuring object 18, which has at least one recognizable contour, here in the form of a Edge 19. A drive which causes the movement of the column 14 relative to the table 16 is shown in simplified form with an arrow 20.

The relative movement of column 14 and table 16 can be done not only in the illustrated horizontal direction (x-axis) but also transversely thereto (y-axis). Furthermore, it is possible in principle that the image sensor 12 can also be moved perpendicular to the plane of the table (z-axis). Furthermore, it should be noted that for the realization of the present invention, it is only important that the image sensor 12 and the measurement object 18 can be displaced relative to one another in such a way that the views of the measurement object and in particular the position of the contour change within each image. Accordingly, the image sensor 12 may be rigidly arranged when the table 16 is movable with the measurement object 18 via suitable drives. It also does not depend on the kinematic structure of the device 10, i. For example, the imager 12 could be arranged on a gantry or a horizontal arm which are movable relative to the table 16.

The image sensor 12 here has an electronic chip 22 with a multiplicity of image points arranged in the manner of a matrix (not shown separately here). Thus, the imager 12 is capable of taking a two-dimensional image of the measurement object 18. The reference numeral 24 denotes an image plane which is defined by the position and arrangement of the pixels of the chip 22. In a preferred embodiment, the measurement object 18 is located in a τ Λn H ör ^" D i 1 r \ oKαn a OA in / -V-» O

is moved relative to the measuring object 18.

In the illustrated embodiment, the imager 12 has a zoom lens 26 that can be adjusted in the direction of arrow 28 to change the image capture area and the magnification factor. In other embodiments, the imager 12 may be provided with a fixed lens and / or with a port for replacing the lenses. The reference numeral 30 denotes a light source, which here serves to illuminate the measurement object 18 with a light pattern. In many applications, such illumination is used to facilitate the measurement image evaluation and automatic contour recognition. However, the present invention is also applicable to devices that do without additional lighting 30.

The reference numeral 32 denotes a control unit, which here includes a processor 34 and a read-only memory 36 and a main memory 38. In simple embodiments, the control unit is a PC running an operating program that performs the control of the apparatus 10 and the image evaluation.

FIG. 2 shows a first image 44 of the measurement object 18, which was recorded with the image sensor 12 at a first relative position to the measurement object 18. The image 44 is shown here in a simplified manner and only shows a contour image 46 of the measurement object 18 in a first view. In this embodiment, the contour 19 and the corresponding contour image 46 are circular. The contour image 46 has an inner diameter, which is designated here by an arrow 48. Furthermore, the center 50 of the circular contour image 46 is shown. The position of the center point 50 on the surface of the table 16 is illustrated by means of two arrows 52, 54, these arrows being related here to the center 56 of a coordinate system parallel to the table surface. The first view thus shows the measurement object 18 in particular at a first position 50 and with a first image size.

FIG. 3 shows a second image 58 of the measurement object with a second contour image, which is designated by the reference number 46 'to distinguish it from the contour image from FIG. As can be seen from the illustration in FIG. 3, the center point 50 'of the contour 46' is located at a different position 52 ', 54' relative to the center 56 of the coordinate system. In addition, the diameter 48 'of the contour 46' here is virtually larger than the diameter 48 of the contour 46 of Figure 2. The second image shows the measurement object so in a second view, here a second Position and a second image size includes. The virtual size change as a result of the positional shift of the measuring object 18 relative to the image recorder 12 is exaggerated here and does not necessarily have to be present. It is also possible that despite changing the relative position between imager 12 and measurement object 18 no virtual size change occurs and only the virtual position of the contour image 46 'has changed. Calibration data can also be determined with the new method based on the virtual changed position. However, the size ratios, ie the first and the second image size, are preferably also evaluated.

In a particularly advantageous embodiment, the first and the second image are recorded and the calibration data are calculated while the image acquisition unit 12 is displaced relative to the measurement object 18. Furthermore, it is advantageous if the images are recorded when the zoom factor changes.

To explain the new method, in one exemplary embodiment it is assumed in a simplified manner that the chip 22 of the image sensor 12 has a scaling factor k that is the same in all dimensions, but that can vary from measurement to measurement. Furthermore, it is assumed that the real dimension of the contour 19 has a constant value over several measurements. In other words:

Glmetettrriisscchh -

- G vjnilmetπsch,

in which

Gl metric denotes the real size or dimension of the contour 19 when taking the first image,

G2metπsch denotes the real size or dimension of the contour 19 in the recording of the second image, and Grimetrically the real size of the contour 19 in recording the nth image referred.

In contrast, the size Glsen of the contour 19 in the first image of the size G2sens in the second image vary. Therefore, the following relationships apply:

G l metπsch = G2 = G _m etrisch etπsch _m = kl X k2 = Glsens G2sens X = kn X Gnsens 1 1 metric "

⁼ Kl X Llsens "KZ X LZsens Pl metric" Pn _me tπsch = kl X Llsens - kn X Lnsens,

wherein Plmetπsch, P2 _m etπsch, Primetπsch is the projected into the image plane 24 relative position of the image sensor 12, and Llsens, L2 _S ens, Ln _Sen s is the position of the contour 46 in the recorded images.

From these relationships, the following equations can be derived:

kl = (G2sens X (Pl metric - Pn _me tπsch) / (G2sens X Llsens "Glsens X L2sens) k2 = (Glsens X (Plmetnsch - Pn _me tπsch) / (G2sens X Llsens - Glsens X L2sens).

Thus, the scaling factors k1, k2 can be determined on the basis of the size and position of the contour 46, 46 'in the images 44, 58 and on the basis of the real positional shift of the image recorder 12 relative to the measurement object 18. Subsequently, with the scaling factors k1, k2, the diameters 48, 48 'and the position 50, 50' of the contour 46, 46 'can be calculated.

The procedure described here can be generalized since the position and size of the contour 46 in the first measurement in the calibrated sensor coordinate system is equal to the position transformed back by the displacement of the sensor Size of the contour 46 'must be at the second measurement. In general, one can say that the calibration data are determined here using a system of equations whose equations represent the mathematical relationship between the known positional change of the image recorder relative to the measurement object and the detected "virtual" change in the size and position of the measurement object from one image to the next. For the determination of a number of n calibration data, preferably n equations based on n image pairs are used.

FIG. 4 shows a simplified flowchart for explaining an embodiment of the new method. According to step 64, the image recorder 12 is first moved to a first position relative to the measurement object 18. In step 66, the first image 44 is then recorded. The image recording can take place during the movement if the image recording is synchronized with the respective position of the image recording unit 12. Subsequently, the first contour image 46 is identified (step 68), and a first image size 48 is determined on the basis of the contour image 46 (step 70). As shown in FIGS. 2 and 3, the image size may be, for example, the diameter 48 of a circular contour image 46. Alternatively, the area bounded by the contour 46 could be used as a measure of the image size. Furthermore, the image size could be the length of a line or another dimension.

According to step 72, the position of the contour 46 within the first image 44 is determined. This is preferably done in coordinates, as shown in Figure 2 at the Bε- zugsziffern 52, 54. All values determined in steps 64, 70 and 72 are stored in the memory 38 of the control unit 32. Subsequently, the imager 12 is moved to a second position relative to the measurement object 18 (step 74) and a second image 58 is taken (step 76). Based on the second image 58, a second contour image 46 'is identified (step 78), and its image size 48' and position 50 'are determined (steps 80, 82). In step 84, further images may be taken or the method may branch to step 86, with which the determination of the calibration data and the determination of the geometry data is initiated.

In step 86, all required data is fetched from memory 38. According to step 88, the calibration data k1, k2 are determined on the basis of the known positions of the image recorder 12 relative to the measurement object 18 and on the basis of the image sizes and contour positions.

According to step 90, an averaging can be performed by multiplying the calibration data based on several image pairs and then averaging. However, step 90 is not absolutely necessary for carrying out the method and can accordingly be dispensed with.

Furthermore, the determination of the calibration data according to step 92 can be carried out several times using different image pairs in order to determine a quality factor in the form of a standard deviation. Subsequently, the geometry data of the measurement object 18, for example, the real value of the diameter 48 and the position 50, are determined as a function of the calibration data k1, k2.

As can be seen from the above description of the new method, individual calibration data can be determined for each geometry datum to be determined on the measurement object 18. Alternatively, the calibration data determined on the basis of the contour 19 can be used for different measurements on the measurement object 18 or for measurements on another measurement object.

The new procedure makes it possible to carry out a calibration process and in particular the partial aspect of the linear scaling during the actual measurement, without having to have a calibrated reference standard available, and also without a special calibration process having to precede the actual measurement. It is only assumed that the position of the image sensor 12 relative to the measurement object 18 can be detected in exact position data, ie the movements of the image sensor 12 relative to the table 16 must be able to be detected with a calibrated measuring system. This is typically the case with coordinate measuring machines or digitizing machines in which a measuring head with an optical sensor is moved relative to a measuring table. The new method and the new device can therefore be implemented particularly easily in such coordinate measuring machines and digitizing machines.

In preferred embodiments of the invention, the identification of the contour 46, 46 'in the images 44, 58 is automatic, whereby any contour recognition algorithm can be used. Suitable algorithms have been developed for various electronic image processing applications and known to those skilled in the art, for example from US 2007/0154097 A1 or US 2007/0127821 A1.

Characterized in that in preferred embodiments of the invention, the size and position of the contour 46, 46 'is evaluated, one can assume for each measurement of the measurement series of an individual calibration factor. Deviating from this, however, one can also realize a simplified variant of the new method, which is based on the assumption that the calibration factors are constant within a measurement series. It is then possible, for example, to determine the linear scaling factor only as a function of the image size in the first and second images and as a function of the first and second positions of the image recorder relative to the measurement object.

On the other hand, one can introduce further calibration factors which take into account, for example, the correction of distortions or a tilting of the contour during a displacement of the image recorder relative to the measurement object when more than two measurements of the contour are carried out.

Claims

claims

A method of determining geometry data of a measurement object (18) having at least one contour (19) with a defined dimension, comprising the steps of:

Receiving (66) at least a first image (44) of the measurement object (18) by means of an image sensor (12) arranged at a first known position relative to the measurement object (18), the first image (44) being a first image Contour image (46) showing the defined dimension in a first view (48)

Determining first image data (70, 72) of the measurement object (18) from the first image (44), and

Determining the geometry data (94) from the first image data using calibration data representing a mapping function between the first image (44) and the measurement object (18),

characterized in that a second image (58) of the measurement object (18) including a second contour image (46 ') is taken at a second known position of the image recorder (12) relative to the measurement object (18), the second contour image (46'; ) shows the defined dimension in a second view (48 '), and wherein the calibration data is determined as a function of the first and the second position and in dependence on the first and second views (48, 48').

2. The method according to claim 1, characterized in that the calibration data are determined independently of the defined dimension of the contour (19).

3. The method of claim 1 or 2, characterized in that the first and second contour image (46, 46 ') within the first and the second image (44, 58) are automatically identified.

4. The method according to any one of claims 1 to 3, characterized in that the first and the second position are approximately in the defined dimension or further apart.

A method according to any one of claims 1 to 4, characterized in that a plurality of first and second views (48, 48 ') are determined (84) at a plurality of first and second positions.

6. The method according to any one of claims 1 to 5, characterized in that a plurality of geometric data are determined, wherein for each geometry datum associated calibration data are determined.

7. The method according to any one of claims 1 to 5, characterized in that the calibration data are used for a plurality of geometry data.

8. The method according to any one of claims 1 to 7, characterized in that the image sensor (12) is adapted to produce a two-dimensional image (44, 58) of the measuring object (18).

9. The method according to any one of claims 1 to 7, characterized in that the image sensor (12) is adapted to generate a three-dimensional image of the measurement object.

10. The method according to any one of claims 1 to 9, characterized in that the image sensor (12) has an image plane (24), wherein the first and second positions in a constant vertical distance (D) to the image plane (24).

11. The method according to any one of claims 1 to 10, characterized in that the image sensor (12) has a zoom lens (26).

12. The method according to any one of claims 1 to 11, the first and second image (44, 58) are recorded without distortion.

13. The method according to any one of claims 1 to 12, characterized in that the contour (19) is circular.

14. The method according to any one of claims 1 to 12, characterized in that the contour (19) has a defined rotational position about a perpendicular to the contour (19) extending axis.

15. The method according to any one of claims 1 to 14, characterized in that the image sensor (12) relative to the measurement object (18) is rotated without rotation.

16. An apparatus for determining geometric data of a measuring object (18), which has at least one contour (19) with a defined dimension, with

an image recorder (12) for recording at least a first image (44) of the measurement object (18) at a first defined position, wherein the image recorder (12) is movable relative to the measurement object (18), and wherein the first image ( 44) includes a first contour image (46) showing the defined dimension in a first view (48),

an image data determination unit (32, 68-72) for determining first image data of the measurement object (18) from the first image (44), and

a geometry data determination unit (32, 94) for determining the geometry data from the first image data using calibration data rier data representing a mapping function between the first image (44) and the measurement object (18),

characterized by a calibration data determination unit (32, 90) which is designed to display the calibration data in dependence on the first and second positions of the image recorder (12) relative to the measurement object (18) and on the first and second views ( 48 '), the second view (48') representing the defined dimension in a second contour image (46 ') taken at the second position of the imager (12) relative to the measurement object (18).

A computer program with program code adapted to perform a method according to any one of claims 1 to 15 when the program code is run on a computer serving as a control unit for a device according to claim 16.