WO2012152879A1

WO2012152879A1 - Recording device, method and device for recording a surface of an object

Info

Publication number: WO2012152879A1
Application number: PCT/EP2012/058671
Authority: WO
Inventors: Bartosz Kosmecki; Andreas Reutter; Christopher ÖZBEK
Original assignee: Scopis Gmbh
Priority date: 2011-05-11
Filing date: 2012-05-10
Publication date: 2012-11-15
Also published as: DE102011053922A1

Abstract

The invention relates to a recording device for recording points of a surface of an object, comprising a scanning element (11) that is to be brought in contact with the surface for recording a point of the surface, wherein the scanning element (11) has a spatial contour (11) that is to face the surface to be recorded. Said contour can be a sphere in particular. The invention further relates to a method and to a device for recording a surface of an object using a recording device. In said method, the radius of the sphere of the scanning element is taken into consideration when recording the scanned measurement points with a reference surface. Said method is carried out in that the amount of said radius is subtracted from the distance that the scanned points have from the respective closest point on the reference surface when optimizing the recording.

Description

Registration apparatus, method and apparatus for registering a surface of an object

description

The invention relates to a registration device for registering points of a surface according to claim 1, a method for registering a surface of an object according to claim 7 and an apparatus for carrying out such a method according to claim 15.

From medical technology, clinical navigation systems are known with which z. For example, during an operation, it is possible to determine the spatial position of an instrument (for example an endoscope) and to be able to display it in the correct position in image representations (eg in the form of a CT scan) of an operating area. The positionally correct insertion requires a transformation of the spatial position of the instrument determined by the clinical navigation system into the coordinate system of the representation of the operating area. For this purpose, the operating area (eg the head of a patient) is "registered" with a registration device, ie points (or punctiform areas) of an externally accessible surface of the operating area (eg Head surface) are scanned with the registration device and in each case the spatial coordinates of the scanned points are determined. With the registration of the operating area, the actual course of a surface of the operating area in the coordinate system of the clinical navigation system can be determined and adapted to the course of the corresponding surface in the representation of the operating area. Such registration of surfaces is also used in other areas of technology, for example for the detection of surface defects, such. As described in US 5,715,166. The problem to be solved by the present invention is to provide a registration device for registering points of a surface, which enables the most reliable registration of the points and still be as easy to handle as possible. Furthermore, a method and a device for registering a surface are to be specified with which, using the registering device, a possible position-correct combination of position data in a first coordinate system with a model of the object in another coordinate system is permitted.

These problems are solved by the recording device with the features according to claim 1 or by the method with the features according to claim 7 and by the device for carrying out the method according to claim 15. Further developments of the invention are specified in the dependent claims.

Thereafter, a registration device is provided for registering points of a surface of an object, with

a scanning element to be brought into contact with the surface for registering a point of the surface, wherein

the scanning element has a spatial contour to be covered by the surface to be registered. The recording device is in particular an elongated instrument which has the scanning element at its one end. In particular, as already indicated above, the registration device according to the invention serves to prepare the use of a clinical navigation system. For this purpose, a surface of an operating area is scanned with the registration device, wherein the scanning, for example, is carried out at points follows, ie the registration device is brought pointwise in contact with the surface and determines the position of the sensing element. However, it is also conceivable that the registration device is continuously guided over the surface, wherein registration of the points of the surface touched by the registration device or the respective position of the scanning element is detected at predeterminable time intervals. The registration procedure and the further processing of the registered items will be discussed in detail below.

The fact that the scanning element has a spatial contour, in particular means that the scanning element has no sharp tip, but z. B. a curved contour, with which the sensing element is brought into contact with the surface of the object to be registered. In other words, the sensing element does not form a point-like tip, but has a certain extent in order to handle the recording device better and z. B. to avoid impressions of the surface to be registered and / or injury to a patient during the registration process.

It is conceivable that the scanning element has a spherical or elliptical shape or is generally rotationally symmetrical. In particular, the scanning element is spherical, in the form of a spherical segment (for example in the form of a hemisphere) or cylindrical. For example, the sensing element is in the form of a sphere (or sphere segment) having a radius of at least 1 mm. Of course, the sensing element does not have to be rotationally symmetrical, but may be basically of any shape, with the geometry of the sensing element being known (i.e., analytically and / or numerically defined).

According to a further embodiment of the invention, the sensing element is connected to a shaft of the recording device, wherein an end of the shaft connected to the sensing element has a diameter which is smaller than the maximum extent (measured perpendicular to the shaft axis) of the sensing element.

It is also possible that the registration device according to the invention comprises a marking device, via which the spatial position of the registration device can be determined. For example, the marking device comprises a plurality of marking elements (for example in the form of marking balls) which, for example, are attached to a shaft of the registration device. direction are attached. The spatial position of the marker balls can z. B. from the measuring camera of a (eg clinical) navigation system are determined so that the position (ie, the location and orientation) of the registration device in the coordinate system of the navigation system can be determined. Since the position of the scanning element (or a predetermined reference point of the scanning element) relative to the marking device (to the marking elements) is known, it is possible to determine the spatial position of the scanning element by determining the position of the marking elements. The invention also relates to a method of registering a surface of an object using a registration device as described above, comprising the steps of:

a) scanning a plurality of points of the surface of the object by contacting the sensing element of the registration device with the surface;

b) detecting each of the spatial position of a reference point of the scanning element with determination of the respective coordinates of the reference point, wherein each one position of the reference point represents an output sample point;

c) providing a model of the surface of the object;

d) adjusting the coordinates of the output sampling points determined in step b) to the shape of the model of the surface of the object, wherein

e) step d) takes place as a function of the spatial course of the contour of the scanning element.

Since the scanning of the surface extending in the space takes place via a non-point scanning element, it is not known which surface section (surface point) of the scanning element bears against the surface, so that the initial registration does not include the coordinates of the exact contact points at which the Scanning element is applied to the surface, are determined, but in each case the coordinates of the position of a reference point of the scanning element, for example a center in a spherical configuration of the scanning element. The various positions of the sensing element (ie its reference point) that it occupies during the registration process (scanning the surface) are referred to as "output sensing points". The coordinates of the output sampling points are, for example, as already mentioned above, determined by means of a (in particular clinical) navigation system, wherein the recording device has a positioning device, which is formed eg as described above.

For example, registering the surface of the object (eg, in the form of an operating area) serves to prepare the use of an instrument during an operation. The instrument has z. B. also on a marking device, with the help of the clinical navigation system can detect the position of the instrument. To change the position of the instrument into a representation, e.g. It is necessary to determine a transformation by means of which the coordinates of the instrument can be transformed into the coordinate system of the representation of the operating area, namely, a CT or MRT image or a (numerical) spatial reconstruction of the operating area in that the transformed coordinates are adapted to the orientation and the location of the representation of the operating area.

For the adaptation required for this purpose, first a numerical model (i.e., a spatial reconstruction) of the operation area and in particular the surface to be registered is provided, the model being e.g. based on recordings (such as the already mentioned CT or MRI recordings) is generated. In accordance with step d) of the method according to the invention, an adaptation of the coordinates of the output sampling points to the course of the model of the surface of the operating region, i. a transformation is determined with which the output sample points of the model-herten surface are approximated, wherein by changing the coordinates of the output sample points corrected points are generated which follow the course of the modeled surface as well as possible and in particular lie as much as possible based on the Position of the corrected points each generated (virtual) surface of the scanning element would be positioned close to the modeled surface.

The adaptation according to step d) of the method according to the invention takes place, for example, by iteratively approaching the output sampling points to the modeled surface. Of course, it is also conceivable that, conversely, the modeled surface is iteratively adapted to the surface defined by the output scanning points. The adaptation is eg terminated when the relative position of the Ausgangsabtastpunkte to the modeled surface satisfies a predetermined criterion, such as a predetermined distance. Examples of this will be explained below. With the fitting process, a transformation is thus generated which enables a positionally correct insertion of points which represent, for example, the position of an instrument in a representation of the operating area. Of course, the inventive method is not limited to medical applications. Rather, other objects (eg surfaces of workpieces) can also be registered with the method.

Specifically, the model of the surface of the object is in a (first) coordinate system different from the (second) coordinate system in which the coordinates of the output sample points are determined. It is therefore conceivable that before the adaptation according to step d) of the method according to the invention, a transformation of the coordinates of the model of the surface and / or the Ausgangsabtastpunkte takes place in a common coordinate system.

For example, the model of the surface (or points of the model of the surface) is transformed from the first to the second coordinate system in which the coordinates of the output sample points are determined (eg, the world coordinate system of a clinical navigation system). Subsequently, the adaptation (step d) of the method takes place, with which an image is provided, by means of which points (which, for example, as mentioned, represent the position of an instrument) can be imaged onto corrected (positionally correct) points in the second coordinate system. The corrected points in turn can be transformed back into the first coordinate system of the modeled surface, so that e.g. during an operation, the position of an instrument in the first coordinate system, i. into the model of the operating area (or analogously in another representation of the operating area), can be displayed in the correct position.

According to a further embodiment of the method according to the invention, the adaptation according to step d) for each output sampling point comprises determining a closest point of the model of the surface. For example, starting from the output sample points, a lot is created on the modeled surface and the intersection of the solder with the modeled surface is determined.

Using the positions of the output sample points and the nearest points of the model of the surface as well as the spatial progression of the contour of the sample, an image is then determined and points generated by applying this mapping to the coordinates of the output sample points. In particular, the mapping includes translation and / or rotation of the output sample points. For example, the output sample points are arranged rigidly to each other, i. H. the distance of the output sample points from each other is not changed by the image.

As already mentioned, the model of the surface can be generated by an SD reconstruction of the object, wherein z. B. by means of a Schwellwertverfahrens the surface of the 3D reconstruction is determined. It is conceivable here that the model of the surface is represented by a point cloud, a polygon representation (eg in the form of a triangulation representation) or analytically (in the form of a parameterized curve). The determination of the image for generating the corrected points takes place z. B. analogous to the method described in US 5,715,166, to which reference is expressly made.

After generating the corrected points, a mean distance between the corrected points and the nearest points is determined, for example, as a function of the spatial profile of the contour of the scanning element. The generation of corrected points is repeated if the average distance exceeds a predeterminable limit value, then the previously generated corrected points are used as the position of the output sampling points. In other words, a stepwise approximation of the surface represented by the output sample points to the modeled surface occurs analogously to the "Iterative Closest Point" (ICP) method (Iterative Neighbor Point Method), but instead of a punctiform sample element It is also conceivable, of course, that the mean distance already occurs before the generation of the corrected points, ie with respect to the output sampling points, and only when the average distance determined in this way exceeds the limit, the corrected points are generated at all. Determining the mean distance includes, for example, determining a size for each output sample point (or corrected point), which is the length of the distance between the output sample point (which corresponds to the respective position of the reference point of the sample element) and the corrected point Surface of the sensing element along a straight line that passes through the Ausgangsabtastpunkt (or the corrected point) and the respectively associated closest point depends. By taking into account the length of the distance between the output sample point (or the corrected dot) and the surface of the sample element, account is taken of the fact that the sample element is not dot-shaped.

For example, the sensing element is rotationally symmetrical, wherein the dependent on the length of the distance between the Ausgangsabtastpunkt (or the corrected point) and the surface of the sensing element variables are each determined in dependence on a radius of the sensing element. It is conceivable z. B. that the quantities are each formed by the square of the distance between an output sample point and the associated nearest dot, the distance being decreased by the length of the distance between the output sample point and the surface of the sample element, respectively.

The mean distance is then the sum of the squares (L2 norm). For example, the sensing element is spherical, wherein the reference point of the sensing element z. B. is the center of the sphere, so that the length of the distance between see the Ausgangsabtastpunkt (or the corrected point) and the surface of the sensing element, which is to be based on the calculation of the average distance, each reduced by the radius of the scanning element becomes.

According to a further embodiment of the invention, a check is carried out as to whether at least one of the output sampling points or the corrected points lies on an inner side of the model of the surface of the object, ie whether at least one of the corrected points in the interior z. B. a 3D reconstruction of the object is located. If so, the coordinates of the affected corrected point are changed or the affected corrected point is not considered. The invention also relates to an apparatus for carrying out a method as described above

i. a detection device for detecting in each case the spatial position of a reference point of the scanning element with determination of the respective coordinates of the

Reference point, wherein each one position of the reference point represents an output sample point;

ii. providing means for providing a model of the surface of the object providing coordinates of points of the model; and iii. fitting means for fitting the coordinates of the output sample points determined by the detection means to the course of the model of the surface of the object,

iv. the adaptation device is designed to perform the adaptation as a function of the spatial profile of the contour of the scanning element.

The detection device includes, for example, a clinical navigation system with a measuring camera, which can detect marking elements of the registration device, as already explained above. The providing device for providing a model of a surface of the object (or of the entire object) is in particular a software or a programmed device which generates a 3D reconstruction of an object or another representation of the object. The adaptation device is likewise designed in particular in the form of software or a programmed device. The invention is explained in more detail below with reference to embodiments with reference to the figures. Show it:

Figure 1 is a side view of a recording device according to a

Embodiment of the invention;

Figures 2 and 3 are perspective views of the recording device

FIG. 1;

Figure 4 is an illustration of the method according to the invention; and Figures 5 and 6, the dependence of the average distance between sampling points and a modeled surface of an object. The recording device 1 according to the invention shown in Figure 1 has at one end a scanning element 1 1, which has a contact surface 1 1 1 with a spatial contour, ie the sensing element 1 1 is not punctiform. The contact surface 1 1 1 is brought to register a point of a surface in contact with the surface.

As can be seen, in particular, in the detail enlargement A of the scanning element 1 1 contained in FIG. 1, the scanning element 11 is formed as part of a surface of a partial section of a sphere, so that the contact surface 11 is essentially spherical.

The scanning element 1 1 is (in particular in one piece) connected to a shaft 12 of the recording device 1. The shaft 12 has a tapered front portion 121 which is connected by a bend 122 to a substantially straight rear portion 123. The front end 121 of the shaft 12 tapers in such a manner that the diameter of its connected to the sensing element 1 1 end 121 1 is smaller than the maximum extent of the sensing element 1 1 perpendicular to the axis of the front shaft portion 121st In other words, the radius R _{x of} the sensing element 1 1 is greater than the radius of the end 121 1 of the front shaft portion 121st

The registration device 1 according to the invention furthermore has a marking device in the form of two marking balls 21, 22 connected to the rear shaft section 123. Using a (eg clinical) navigation system (not shown), the spatial position of the registering device 1 can be determined with the aid of the marking spheres 21, 22. In particular, since the scanning element 21 is in a fixed spatial relationship to them, the spatial position of the scanning element 11 or a reference point (eg the center point) of the scanning element 11 can be determined via the marking spheres 21, 22. When scanning (registering) the surface can thus in each case the position of the reference point of the scanning element are determined, wherein the coordinates of the reference point for different scanning positions (ie different positions of the recording device 1) are determined and stored. Thus, a set of points is generated from the respective positions of the reference point (hereinafter also referred to as "initial scanning point") following the course of the surface to be registered.

The (actual) surface of the object detected via the registration device can be adapted, for example, to a model of the surface (ie to a "virtual surface"), so that, for example, the position of an instrument, which can also be determined, for example, via the clinical navigation system The adaptation of the output scanning points to the virtual surface takes into account the spatial extent of the scanning element. <br/> <br/> The surface registration method of the present invention will be explained below with reference to FIG. A plurality of points of the (actual) surface to be registered is scanned by contacting the scanning element 1 1 of the recording device 1 with the surface, wherein the spatial position of a reference point in the form of the center of the scanning element 1 1 are detected.

In addition, a model O of the surface is provided, wherein the modeled surface O is, for example, a surface of a 3D reconstruction of the object to be examined. When scanning the surface with the aid of the registration device according to the invention, the scanning element 11 is moved to different positions, two of which (the positions P1 and P2) are shown in FIG. For each position of the scanning element 1 1, the position M1, M2 of the center of the scanning element 1 1 is recorded. The positions of the center point form a set of points (output sampling points), wherein, according to FIG. 4, the modeled surface O and the output sampling points M1, M2 are in a common coordinate system, in particular in the coordinate system (world coordinate system) of a clinical navigation system.

For example, the course of the modeled surface O first became in a coordinate system different from the coordinate system of the output sample points and the modeled surface is then transformed into the coordinate system in which the output sample points M1, M2 are present. After the modeled surface O has been transformed into the coordinate system of the output sample points M1, M2, they are spaced from the modeled surface O, with the modeled surface O rotated and / or shifted relative to a surface formed by the output sample points. In order later to be able to fade in the position of an instrument in the coordinate system of the output sample points M1, M2 in the correct position into a 3D reconstruction to which the modeled surface O belongs, it is necessary to show the course of the surface formed by the output sample points on the course of the modeled surface O, ie in particular to find an image that brings the surface formed by the Ausgangsabtastpunkte M1, M2 as parallel as possible and close to the modeled surface O.

This matching of the output sampling points to the course of the modeled surface O is effected by first determining from the output sampling points M1, M2 a respective point 01, 02 of the surface O lying closest to these output sampling points. The determination of the points 01, 02 takes place, for example, in that, starting from the initial scanning points M1, M2, a respective solder is precipitated onto the surface O and the point of intersection S1, S2 of the solder with the surface O is determined. It is also conceivable that distances to a plurality of points of the surface O are determined for each output scanning point M1, M2 and then the smallest of these distances is determined in each case.

Depending on the respective distances between the output sample points M1, M2 and the nearest points 01, 02, a "mean distance" between the surface defined by the output sample points and the modeled surface O is generated and compared to a threshold value Limit value, an image (transformation) is formed using the positions of the output sample points M1, M2 and the nearest points 01, 02, where by means of the image the position of the output sample points M1, M2 is changed (approximated to the surface O) Translation and / or rotation of the set of output sample points, for example, where the output sample point M2 is converted to a corrected point M2 ', and then the average distance is again determined using the corrected points instead of the output sample points become. This process is repeated until the average distance falls below a predefinable limit.

The average distance is determined in particular as the sum of squares Q of the distances between the intersections S1, S2 and the nearest points 01, 02, i. in each case the distances of the output scanning points M1, M2 to the nearest points 01, 02 are determined and reduced by the extent of the scanning element 11 along the path M101, M202. The extent of the scanning element 1 1 along the path M101, M202 results in each case as the length of the routes M1 S1, M2S2, i. in a spherical scanning element as the radius of the scanning element.

The fitting of the surfaces is thus done by minimizing the square sum Q, it being possible for the square sum Q to have several minima, i. There are different arrangements of the output sample points or the corrected points which lead to a sum of squares Q which fall below the predefined limit value. A minimum of the sum of the squares Q may also arise because some of the output sample points and the corrected points are inside the 3D reconstruction of the object. In order to exclude such solutions, a heuristic method is used, with which such points are not considered or whose corrected position is changed.

5 shows the sum of squares for different positions x of the corrected points Μ 2 ', M2 ". The sum of squares Q then decreases both in the position T2 of the corrected point M2' shown dashed in FIG. 4 and in the position T2 ', likewise represented by dashed lines. of the corrected point M2 "to a minimum. However, the position T2 'corresponds to a position of the corrected point M2' on an inner side of the modeled surface O (within the 3D reconstruction of the object). This solution is therefore discarded and the corrected point M2 'transferred to the corrected point M2 "at the position T2', which also leads to a minimum of the sum of squares Q (Figure 6).

It should be noted that the method explained with reference to FIGS. 4-6 can of course also be carried out with a registration device designed differently than in FIG. In particular, a registration device can be used. although it also has a sensing element with a non-punctiform shape, but the sensing element is not spherically shaped (but, for example, has a differently curved contact surface). Furthermore, the method according to the invention can be carried out in arbitrarily dimensional spaces, for example, the coordinate system in which the surface to be registered is located can also be a two-dimensional coordinate system. However, higher-dimensional coordinate systems are also conceivable.

LIST OF REFERENCE NUMBERS

1 recording device

11 scanning element

12 shaft

21, 22 marker ball

111 contact surface

121 front shaft section

122 curvature

123 rear shaft section

1211 front end

0 modeled surface

01, 02 nearest point

M1, M2 output sampling point

Μ2 ', M2 "corrected point

S1, S2 intersection

P1, P2 position sensing element

T2, T2 'position corrected point

Claims

claims

1 . Registration device for registering points of a surface of an object, with

a) a sensing element (1 1) to be brought to register a point of the surface in contact with the surface, wherein

b) the scanning element (1 1) one of the surface to be registered zuwendenende spatial contour (1 1 1).

2. Recording device according to claim 1, characterized in that the spatial contour (1 1 1) has a curvature.

3. Recording device according to claim 1 or 2, characterized in that the scanning element (1 1) is rotationally symmetrical.

4. Recording device according to one of the preceding claims, characterized in that the scanning element (1 1) has a spherical or elliptical shape.

5. Recording device according to one of the preceding claims, characterized in that the scanning element (1 1) with a shaft portion (121) of the registration device (1) is connected, wherein one with the sensing element (1 1) connected end (121 1) of the shaft portion (121) has a diameter which is smaller than the maximum extent of the sensing element (1 1) measured perpendicular to the axis of the shaft portion (121).

6. Recording device according to one of the preceding claims, characterized by a marking device (21, 22), via which the spatial position of the registration device (1) can be determined.

A method of registering a surface of an object using a recording apparatus according to any one of the preceding claims, comprising the steps of: a) scanning a plurality of points of the surface by contacting the surface thereof

Scanning element (1 1) of the registration device (1) with the surface; b) detecting respectively the spatial position of a reference point of the scanning element by detecting the respective coordinates of the reference point, wherein in each case a position of the reference point represents an output scanning point (M1, M2);

c) providing a model (O) of the surface of the object;

d) adapting the coordinates of the output sampling points (M1, M2) determined in step b) to the course of the model (O) of the surface of the object, where e) step d) in dependence on the spatial profile of the contour (1 1 1) of the Scanning element (1 1) takes place.

8. The method according to claim 7, characterized in that step d) comprises:

Transforming the coordinates of the output sample points (M1, M2) and / or the model (O) of the surface of the object into a common coordinate system; and

for each output sample point (M1, M2) detected according to step b), determining a nearest point (01, 02) of the model (O) of the surface in the common coordinate system;

9. The method according to claim 8, characterized in that prior to generating the corrected points (Μ2 ', M2 ") in dependence on the spatial profile of the contour (1 1 1) of the scanning element (1 1) a mean distance between the Ausgangsabtastpunkten ( M1, M2) and the nearest points (01, 02) is determined, and if the average distance exceeds a predeterminable limit value:

i. Determining an image as a function of the coordinates of the initial scanning points (M1, M2) and the nearest points (01, 02) of the model (O) of

Surface for generating corrected points (Μ2 ', M2 "); and

ii. Generating corrected points (Μ2 ', M2 ") by mapping the coordinates of the output sample points (M1, M2) using the map determined in step i).

10. The method according to claim 9, characterized in that the corrected points (Μ2 ', M2 ") replace the output sample points (M1, M2), an average distance between the corrected points (M1, M2) and the points closest to them is determined and, if the mean distance exceeds the predefinable limit, steps i) and ii) are repeated.

1 1. A method according to claim 9 or 10, characterized in that the determining of the mean distance comprises determining a size for each output sample point (M1, M2) or each corrected point (Μ2 ', M2 "), which is the length of the segment between the output sample point (M1, M2) or the corrected point (Μ2 ', M2 ") and the contour (1 1 1) of the scanning element (1 1) along a straight line through the Ausgangsabtastpunkt (M1, M2) or the corrected point (Μ2' , M2 ") and the respectively associated nearest point (01, 02) runs, depends.

12. The method according to claim 1 1, characterized in that the scanning element (1 1) is rotationally symmetrical, so that the of the length of the distance between the Ausgangsabtastpunkten (M1, M2) or the corrected points (Μ2 ', M2 ") and the contour (1 1 1) of the sensing element (1 1) dependent variables in dependence on a radius (Rx) of the sensing element (1 1) are determined.

13. The method according to any one of claims 10 to 12, characterized in that the of the length of the distance between the Ausgangsabtastpunkten (M1, M2) or the corrected points (Μ2 ', M2 ") and the contour (1 1 1) of the sensing element (1 1) are each formed by the square of the distance between an output sampling point (M1, M2) or a corrected point (Μ2 ', M2 ") and the associated nearest point (01, 02), the distance in each case by the length of the distance between the Ausgangsabtastpunkt (M1, M2) or the corrected point (Μ2 ', M2 ") and the contour (1 1 1) of the sensing element (1 1) are reduced.

14. The method according to any one of claims 9 to 13, characterized in that a check is made whether at least one of the Ausgangsabtastpunkten (M1, M2) or the corrected points (Μ2 ', M2 ") on an inner side of the model (O) of the surface of the object and, if so, the coordinates of the output sample point (M1, M2) or the corrected point (Μ2 ', M2 ") or the affected output sample point (M1, M2) or the affected corrected point ( Μ2 ', M2 ") is not considered.

15. Apparatus for carrying out a method according to one of claims 7 to 14, with a) detecting means for detecting each of the spatial position of a reference point of the scanning element (1 1) by detecting the respective coordinates of the reference point, wherein each one position of the reference point represents an output sampling point (M1, M2);

b) providing means for providing a model (O) of the surface of the object providing coordinates of points of the model; and

c) matching means for fitting the coordinates of the output sample points (M1, M2) determined by the detection means to the course of the model (O) of the surface of the object,

d) the adjusting device is designed to perform the adaptation in dependence on the spatial course of the contour (1 1 1) of the scanning element (1 1).