METHOD OF CALIBRATING A CAGE

Abstract

A computer implemented medical method of calibrating a cage is presented. In particular, this calibration method calculates a virtual model of the cage based on a cage tip point and a cage end point, acquired by using a pointer tip of a pointing device, and at least one axis, acquired by using a pointer shaft of the pointing device along a side of the cage. This method allows for providing a more detailed virtual model of the cage, while being in compliance with sterility restrictions.

Claims

1. A computer implemented method of calibrating a spinal cage, comprising: acquiring, by using a pointer tip of a pointing device, a cage tip point at a cage tip of the spinal cage, wherein the cage tip is disposed at a first end of the cage in a length direction of the cage; acquiring, by using the pointer tip of the pointing device, a cage end point at a cage end of the spinal cage wherein the cage end is disposed at a second end of the spinal cage, opposing to the first end, in the length direction; acquiring, by using a pointer shaft of the pointing device, at least one axis along a side of the cage; determining a calibrated virtual model of the spinal cage using the cage tip point, the cage end point and the at least one cage axis; wherein calibrating comprises determining a spatial relation between the spinal cage and the pointing device.

2. The method of claim 1, wherein acquiring the cage end point, the cage tip point and/or the at least one cage axis comprises: determining a cage-to-holder-coordinate-transformation, which describes a transformation between a holder coordinate system of a holding device and a cage coordinate system of the spinal cage.

3. The method of claim 2, wherein acquiring the cage end point, the cage tip point and/or the at least one axis comprises providing a pointer-to-holder-coordinate-transformation, which describes a transformation between the pointer coordinate system and the holder coordinate system; determining the holder-to-cage-coordinate-transformation, by using the pointer-to-holder-coordinate-transformation.

4. The method of claim 1, wherein acquiring the cage end point, the cage tip point and/or the at least one axis comprises holding the pointing device onto the spinal cage until the respective cage end point, cage tip point and/or at least one axis is acquired.

5. The method of claim 1 wherein the virtual model indicates a shape, position and orientation of the cage.

6. The method of claim 1, wherein the virtual model comprises a multi-dimensional representation of the spinal cage, in particular a 3-dimensional representation of the spinal cage.

7. The method of claim 1, wherein acquiring the cage end point comprises: acquiring a first holder point and a second holder point at opposing lateral sides of a cage holder, which holds the cage at the second end of the spinal cage, by using the pointer tip of the pointing device; determining the cage end point as a centre of a connection line between the first holder point and the second holder point.

8. The method of claim 1, further comprising the step: acquiring, by using the pointer shaft of the pointing device, at least one axis along at least one lateral side of the spinal cage in a height direction of the cage.

9. The method of claim 8, further comprising the step: acquiring, by using the pointer shaft of the pointing device, at least one axis along a top side and/or bottom side of the spinal cage in a width direction of the spinal cage.

10. The method of claim 8, further comprising the step: acquiring, by using the pointer shaft of the pointing device, at least one axis along a top side and/or bottom side of the spinal cage in a length direction of the spinal cage.

11. The method of claim 1, further comprising the steps: acquiring, by using the pointer shaft of the pointing device, a first axis along a first lateral side of the spinal cage in a height direction of the spinal cage; a second axis along a second lateral side of the spinal cage opposite of the first lateral side, in the height direction of the spinal cage; a third axis along a top side of the spinal cage in a width direction of the spinal cage; and a fourth axis along a bottom side of the spinal cage in the width direction of the spinal cage.

12. The method of claim 1, further comprising the steps: acquiring, by using the pointer shaft of the pointing device, a first axis along a first lateral side of the spinal cage in a height direction of the spinal cage; a second axis along a second lateral side of the spinal cage opposite of the first lateral side, in the height direction of the spinal cage; a fifth axis along a top side of the spinal cage in a length direction of the spinal cage; and a sixth axis along a bottom side of the spinal cage in the length direction of the spinal cage.

13. The method of claim 1, wherein, for acquiring the at least one axis in the width direction and/or height direction, the pointer shaft is held in a width axis section distant to the cage end point and the cage tip point.

14. The method of claim 1, wherein, for acquiring the at least one axis in the length direction, the pointer shaft is held in a length axis section distant to the lateral sides of the spinal cage.

15. The method of claim 1, wherein determining a calibrated virtual model comprises: determining a cage axis of the spinal cage; determining at least one nearest point of the at least one axis, being the nearest point of the at least one axis to the cage axis; and determining the virtual model using the at least one nearest point.

16. The method of claim 15, wherein determining the at least one nearest point comprises: determining a length cage axis connecting the cage tip point and the cage end point; determining a width cage axis, extending perpendicular to the length cage in the width direction through a centre of the length cage axis in the length direction; determining at least one nearest point (N1, N2, N3, N4) of the at least one axis (X1, X2, X3, X4) in the width direction (W) and/or the height direction (H), being the nearest point of the at least one axis (X1, X2, X3, X4) to the length cage axis (Al); and determining at least one nearest point of the at least one axis (X5 in the length direction (L) being the nearest point of the at least one axis (X5) to the width cage axis (Aw).

17. The method of claim 15, further comprising the steps: determining the cage coordinate system in the cage tip point, wherein the cage coordinate system comprises an x-axis, a y-axis and a z-axis, perpendicular to each other, wherein the z-axis is equal to the cage axis; determining at least one projection point, projecting the at least one nearest point into an x-y-plane, defined by the x-axis and the y-axis; determining a distance between the at least one projection point and an at least one planned projection point of a planned axis, wherein the at least one planned axis is a previously acquired axis for the spinal cage; replacing the planned axis with the acquired at least one axis; if the determined distance is smaller than a predetermined threshold; and adding the acquired at least one axis to the previously acquired axis for the spinal cage.

18. The method of claim 17, wherein replacing the planned axis with the acquired at least one axis comprises: determining a replacement likelihood score for each planned axis; and replacing the planned axis with the highest replacement likelihood score with the acquired at least one axis; wherein the replacement likelihood score is determined using a weighted replacement likelihood function, using a distance of the planned axis to the cage axis and a distance of the planned axis to the acquired axis.

19. The method of claim 1, wherein determining a calibrated virtual model comprises: determining a cage center point, representing a center of a plane determined by the at least two axis; determining at least one correction point, being an intersection of a line through the cage center point and one of the at least two axis along a cage coordinate axis of a cage coordinate system; determining the virtual model using the at least one correction point.

20. The method of claim 19, wherein determining the cage center point comprises: determining at least two intersection points, being an intersection between two of the at least two axis; determining at least one middle point, being the middle point between two intersection points along one of the at least two axis; determining the cage center point using the at least one middle point.

21. The method of claim 1, wherein determining the at least one axis comprises: acquiring at least one shaft point relating to a shaft end distant to the pointer tip and at least one pointer tip point; and determining the at least one axis by connecting the at least one shaft point and the at least one pointer tip point.

22. The method of claim 1, wherein determining the virtual model of the cage comprises: receiving a basic shape of the spinal cage; and determining the virtual model of the cage using the basic shape of the cage.

23. The method of claim 19, wherein the basic shape of the cage comprises an ellipsoid shape, a lordotic shape, a bullet shape, a round shape or a curve shape.

24. The method of claim 1, comprising the steps: receiving a diameter of the pointer shaft; determining at least one corrected nearest point by shifting the at least one nearest point of the at least one axis towards the cage axis for half of the received diameter of the pointer shaft; and determining at least one projection point, projecting the at least one corrected nearest point into an x-y-plane, defined by the x-axis and the y-axis.

25. A cage calibration system comprising a holding device with a holding device tracker, a pointing device with a pointing device tracker and a tracking device, configured for tracking the holding device tracker arranged on the holding device and the pointing device, the instrument calibration system configured for executing by at least one processor, the steps of acquiring, by using a pointer tip of a pointing device, a cage tip point at a cage tip of the spinal cage, wherein the cage tip is disposed at a first end of the cage in a length direction of the cage; acquiring, by using the pointer tip of the pointing device, a cage end point-at a cage end of the spinal cage, wherein the cage end is disposed at a second end of the spinal cage, opposing to the first end, in the length direction; acquiring, by using a pointer shaft-of the pointing device, at least one axis along a side of the cage; determining a calibrated virtual model of the spinal cage using the cage tip point, the cage end point and the at least one cage axis; calibrating the spinal cage by determining a spatial relation between the spinal cage and the pointing device.

26. (canceled)

27. A non-transitory computer readable medium storing computer instructions which, when running on a computer or when loaded onto a computer, causes the computer to: acquire, by using a pointer tip of a pointing device, a cage tip point at a cage tip of the spinal cage, wherein the cage tip is disposed at a first end of the cage in a length direction of the cage; acquire, by using the pointer tip of the pointing device, a cage end point-at a cage end of the spinal cage, wherein the cage end is disposed at a second end of the spinal cage, opposing to the first end, in the length direction; acquire, by using a pointer shaft-of the pointing device, at least one axis along a side of the cage; determine a calibrated virtual model of the spinal cage using the cage tip point, the cage end point and the at least one cage axis; calibrate the spinal cage by determining a spatial relation between the spinal cage and the pointing device.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0197] In the following, the invention is described with reference to the appended figures which give background explanations and represent specific embodiments of the invention. The scope of the invention is however not limited to the specific features disclosed in the context of the figures, wherein

[0198] FIG. 1 schematically shows transformations and coordinate systems in a cage calibration system;

[0199] FIG. 2 shows a schematic view of a first cage according to a first embodiment;

[0200] FIG. 3 shows a schematic view of a first virtual model of a first cage of the first embodiment;

[0201] FIG. 4 is a perspective view of a second cage according to a second embodiment with a pointing device at one position;

[0202] FIG. 5 is a perspective view of the second cage of the second embodiment with a pointing device indicated at different positions;

[0203] FIG. 6 schematically shows a plurality of acquired axes of the second cage;

[0204] FIG. 7 schematically shows a second virtual model of the second cage;

[0205] FIG. 8 schematically shows a third cage according to a third embodiment;

[0206] FIG. 9 schematically shows a fourth cage according to a fourth embodiment;

[0207] FIG. 10 schematically shows a plurality of acquired axis of the fourth cage;

[0208] FIG. 11 schematically shows the consideration of the diameter of pointing device;

[0209] FIG. 12 schematically shows the cage calibration method;

[0210] FIG. 13 schematically shows a plurality of acquired axis of a fifth cage; and

[0211] FIG. 14 schematically shows a determination of correction points.

DESCRIPTION OF EMBODIMENTS

[0212] FIG. 1 describes a cage calibration system 100 for calibrating a first cage 40. The cage calibration system 100 comprises a tracking device 30, a pointing device 20 and a holding device 10. The tracking device 30 is configured for tracking objects, in particular for tracking markers disposed on the objects. In this case, the tracking device is configured for tracking the holding device 10 by tracking a holding marker 11 disposed on the holding device 10 and for tracking the pointer device 20 by tracking a pointer marker 23 disposed on the pointer device 20. The holding marker 11 and the pointer marker 23 comprise a marker array of three infrared reflecting spheres. The tracking device 30 in this case is an infrared camera capable of detecting the pointer marker 23 and the holder marker 11 disposed at the pointing device 20 and the holding device 10, respectively.

[0213] The holder marker 11 defines a holder coordinate system Holder and the pointer marker 23 defines a pointer coordinate system Pointer. The tracking device 30 defines a camera coordinate system Cam.

[0214] For tracking the holder 10, the tracking device 30 tracks the holder marker 11.

[0215] However, without calibrating the first cage 40, the navigation system using the input of the tracking device 30 is not aware of the shape, position or orientation of the first cage 40. The navigation system however is provided with the shape, position and orientation of the pointer device 20, which can be tracked using the tracking device 30 over the pointer marker 23. For calibrating the first cage 40, the pointer device 20 is held against the first cage 40 for determining different points of the first cage 40. The first cage 40 defines a cage coordinate system Cage, which is preferably set at a cage tip 41 of the first cage 40. In other words, the calibration comprises determining a transformation from the cage coordinate system Cage to other coordinate systems, in particular a cage-to-holder-coordinate-transformation CageToHolder, which describes a transformation between the holder coordinate system Holder of the holding device 10 and the cage coordinate system Cage of the first cage 40. In other words, a relationship between the different coordinate systems is determined for calibrating the first cage 40.

[0216] All transformations are invertible, so for example, if the cage-to-holder-coordinate-transformation CageToHolder is known, consequently the holder-to-cage-coordinate-transformation HolderToCage is known. Consequently, those invertible notations are also used.

[0217] The transformations define how the coordinates of one system transform into coordinates of another system. After getting the positions of the markers 11, 23 from the tracking device 30, an algorithm assigns the markers 11, 23, so the markers 11, 23 are identified and a coordinate system can be clearly defined for each marker array 11, 23. The marker positions of the marker array given by the tracking system 30 are matched (e.g. “Kabsch algorithm”) to expected positions of the marker array.

[0218] Due to the pointer marker 23 and the holder marker 11, a pointer-to-cam-coordinate-transformation PointerToCam and a holder-to-cam-coordinate-transformation HolderToCam can be easily determined. With the help of the pointing device 20, the cage-to-holder-coordinate-transformation CageToHolder is determined. This is possible, as a cage-to-pointer-coordinate-transformation CageToPointer can be determined by holding the pointing device 20 at different points on the cage 40.

[0219] The pointer device 20 comprises a pointer tip 21 and a pointer shaft 22. When holding the pointer tip 21 against the first cage 40, a single point of the first cage 40 can be acquired. However, when holding the pointer shaft 22 against the first cage 40, a whole axis, or in other words a plurality of points of the first cage 40 can be acquired.

[0220] In the following figures, different cages and virtual models of those cages are described. However, although some elements of those cages differ in particular in their position due to different shapes of the cages, those elements are indicated with the same reference sign throughout the figures. Those elements comprise in particular a cage tip point S, a cage end point E, a length cage axis Al, a width length axis Aw, a first lateral side sl1, a second lateral side 12, a top side st and a bottom side sb.

[0221] FIG. 2 describes a schematic view of the first cage 40. The first cage 40 comprises a front side 42 and an end side 44, which is disposed opposite to the front side 42. The first cage 40 is held by the holding device 10 at the end side 44 of the first cage 40. At the end side 44, the first cage 40 comprises a first cage end 43. The first cage 40 comprises a first cage tip 41 at the front side 42. The first cage tip 41 and the first cage end 43 are crucial points for calibrating the first cage 40.

[0222] FIG. 3 describes a schematic view of a first virtual model V1 of the first cage 40, determined by calibrating the first cage 40. By holding the pointer tip 21 of the pointing device 20 against the first cage tip 41, a cage tip point S can be acquired. The holding device 10 however makes the first cage end 43 inaccessible for the pointing device 20. Consequently, the pointer tip 21 is held against lateral sides of the cage holder 10, where the cage holder 10 connects with the first cage 40. Thus, a first holder point E1 and a second holder point E2 can be acquired. A cage end point E relating to the first cage end 43 is thus acquired by determining the centre of a line connecting the first holder point E1 and the second holder point E2.

[0223] A cage axis, in this case a length cage axis Al, is determined by connecting the cage end point E with the cage tip point S. The length cage axis Al is the most simple representation, in other words virtual model, of the first cage 40.

[0224] Common shapes of cages, such as shown in FIG. 3 allow for a relatively precise acquisition of the cage end point E. However the cage tip point S is relatively hard to acquire without error, keeping in mind that the user has to manually acquire the cage tip point S by holding the pointer tip 21 of the pointing device 20 against the first cage tip 41. The exact position of the first cage tip 41 on the spinal cage 40 might not be obvious for the user depending on the shape of the cage. Consequently, after determining the virtual model of the cage, a correction of the cage tip point S may be performed. The correction preferably comprises a symmetrical analysis of the determined virtual model of the cage in view of the acquired cage end point E and the acquired cage tip point S. In other words, it is determined that most likely the cage tip point S has not been acquired correctly and thus the coordinates of the cage tip point S are adjusted. This for example leads to a rotation of the virtual model of the cage to adjust the cage tip point S.

[0225] FIG. 4 describes a perspective view of the second cage 140 according to a second embodiment, with a second cage tip 141 and a second cage end 143. The second cage 140 has a basic shape of a kidney or “banana” with a constant height in a height direction H. The length of the second cage 140 extends in a length direction L from the second cage tip 141 to the second cage end 143. Consequently, the second cage 140 has a width in a width direction W. The second cage 140 further comprises a first lateral side sl1 and a second lateral side sl2. The second cage 140 further comprises a top side st and a bottom side sb. FIG. 4 indicates the pointing device 20. In fact, FIG. 0.4 indicates the pointer tip 21 and the pointer shaft of the pointing device 20. In order to determine a more detailed virtual model of the second cage 140, the pointer shaft 20 is held against the first lateral side sl1 to acquire an axis of the second cage 140. Using the acquired axis, together with holding the pointer tip 21 against the second cage end 143 and the second cage tip 141 as described above, a more detailed virtual model of the second cage 140 can be determined.

[0226] FIG. 5 describes the perspective view of a cage of FIG. 4 with the pointing device 20 being indicated at different positions. In order to achieve a good 3D estimate virtual model of the second cage 140, four axes are acquired. This is executed by holding the pointer shaft 21 against the first lateral side sl1 in the height direction, against the second lateral side sl2 in the height direction, against the top side st in the width direction and against the bottom side sb in the width direction. In should be noted that FIG. 5 does not indicate four pointing devices 20, but only one pointing device 20 that is disposed at four different positions after another to acquire the four axes X1, X2, X3, X4.

[0227] FIG. 6 schematically shows the plurality of acquired axes X1, X2, X3, X4, namely the first axis X1 relating to the first lateral side sl1, the second axis X2 relating to the second lateral side sl2, the third axis X3 relating to the bottom side sb and the fourth lateral side relating to the top side st. In addition, FIG. 6 shows a cage tip point S relating to the second cage tip 141 and an end point E relating to the second cage end 143. The cage axis, in this case the length cage axis Al, is determined by a connection between the cage tip point S and the end point E. At the cage tip point S, the cage coordinate system Cage is disposed. The cage coordinate system comprises an x-axis, a y-axis and a z-axis, perpendicular to each other, wherein the z-axis runs along the length cage axis Al.

[0228] For each axis, X1, X2, X3, X4 a nearest point N1, N2, N3, N4, being the nearest point of the axis X1, X2, X3, X4 to the length cage axis Al is determined. The nearest points N1, N2, N3, N4 are determined by a connection between the respective axis X1, X2, X3, X4 to the length cage axis Al being perpendicular to the length cage axis Al and the respective axis X1, X2, X3, X4.

[0229] Furthermore, FIG. 6 shows a first projection point P1, being the projection along the Z-axis of the cage coordinate system Cage of the first nearest point N1 into the X-Y plane of the cage coordinate system Cage. Also a second projection point P2 is shown, being the projection along the Z-axis of the cage coordinate system Cage of the second nearest point N2 into the X-Y-plane of the cage coordinate system Cage.

[0230] The first projection point P1 and the second projection point P2 are used in a function, deciding of the acquired first axis X1 and/or the acquired second axis X2 are newly introduced axes or new measurements of an already planned axis.

[0231] The acquired axes X1, X2, X3, X4 are determined by acquiring a plurality of points along the respective axes X1, X2, X3, X4. In this case, the first axis X1 is defined by an acquired first shaft point H1 and by an acquired first pointer tip point T1. The second axis X2 is defined by an acquired second shaft point H2 and by an acquired second pointer tip point T2. The third axis X3 is defined by an acquired third shaft point H3 and by an acquired third pointer tip point T3. The fourth axis X4 is defined by an acquired fourth shaft point H4 and by an acquired fourth pointer tip point T4. The shaft points H1, H2, H3, H4 relate to an end of the pointer shaft 22 distant to the pointer tip 21, when holding the pointing device 20 in the respective position of acquiring the respective axis X1, X2, X3, X4. The pointer tip points T1, T2, T3, T4 relate to the pointer tip 21, when holding the pointing device 20 in the respective position of acquiring the respective axis X1, X2, X3, X4.

[0232] Based on the acquired axes X1, X2, X3, X4, the cage tip point S and the cage end point E, a bounding box can be determined approximating a virtual model of the cage 40 that also is calibrated.

[0233] FIG. 7 schematically shows a second virtual model V2 of the second cage 140, as it is determined based on the acquired axes X1, X2, X3, X4, the cage tip point S and the end point E. For comparison, the acquired axes X1 and X2 are also indicated next to the second virtual model V2.

[0234] FIG. 8 schematically shows a third cage 240 according to a third embodiment; The third cage 240 comprises a top side st that is inclined in the width direction W. In addition, the third cage 240 comprises a first lateral side sl1 and a second lateral side sl2, as well as a bottom side sb. For each acquired side, a position of the pointing device 20 held against the respective side st, sl1, sl2, sb is indicated. The third cage 240 is held by a second holding device 210.

[0235] FIG. 9 schematically shows a fourth cage 340 according to a fourth embodiment. The fourth cage 340 comprises a top side st that is inclined in the length direction L. In addition, the fourth cage 340 comprises a first lateral side sl1 and a second lateral side sl2, as well as a bottom side sb. For each acquired side, a position of the pointing device 20 held against the respective side st, sl1, sl2, sb is indicated.

[0236] FIG. 10 schematically shows a schematic view of acquired axis relating to the fourth cage 340. Compared to the third cage 240 of FIG. 8, instead of the fourth axis X4, a fifth axis X5 defined by an acquired fifth shaft point H5 and by an acquired fifth pointer tip point T5 is acquired by holding the pointer shaft 21 against the top side st in the length direction L. Consequently, when determining a fifth nearest point N5, the reference axis is not the length cage axis Al, but a width cage axis Aw extending in the width direction W, being perpendicular to a length cage axis Al.

[0237] FIG. 11 schematically shows the consideration of a diameter of the pointing device 20. In FIG. 11, a pointing device model Vp, being a virtual model of the pointing device 20, is indicated. A nearest point N to the cage axis A is indicated. However, as the pointing device 20 has a certain diameter, an error is introduced that can be omitted, as the shape of the pointing device 20 is already known. Thus, a correction vector C is determined extending from the nearest point N towards the cage axis A. The correction vector C has a length equal to the diameter of the pointing device 20 in the nearest point N. Thus, a corrected nearest point N′ is determined by applying the correction vector C to the corrected nearest point N′.

[0238] FIG. 12 schematically shows the cage calibration method. In a first step S10 by using a pointer tip 21 of a pointing device 20, a cage tip point S is acquired at a cage tip 41 of the cage 40, wherein the cage tip is disposed at a first end 42 of the cage in a length direction L of the cage. In a second step S20, by using the pointer tip 21 of the pointing device 20, a cage end point E is acquired at a cage end 43 of the cage 40, wherein the cage end 43 is disposed at a second end 44 of the cage 40, opposing to the first end 42, in the length direction L. In a third step S30, by using a pointer shaft 22 of the pointing device 20, at least one axis X1, X2, X3, X4 along a side Sl1, Sl2, St, Sb of the cage 40 is acquired. In a fourth step S40, a calibrated virtual model V1, V2 of the cage is determined using the cage tip point S, the cage end point E and the at least one cage axis X1, X2, X3, X4. Calibrating comprises determining a spatial relation between the cage and the pointing device.

[0239] FIG. 13 schematically shows a plurality of acquired axis of a fifth cage 440. A sixth axis X6, a seventh axis X7, an eighth axis X8 and a ninth axis X9 is acquired. The ninth axis X9 is inclined compared to the opposing eighth axis X8. With the already described method, the ninth axis X9 and the length cage axis Al is used to determine a ninth nearest point N9. The ninth nearest point N9 will consequently lead to a side area A9 of the virtual model of the cage. As indicated by FIG. 13, the inclination of the ninth axis X9 leads most likely to a virtual model that does not approximate the real shape of the fifth cage 440 very well. In order to include the inclination of the ninth axis X9 into the virtual model, in the case described in FIG. 13, the virtual model, in this case the determined box with the right side area A9 is inclined accordingly. However, this would rather lead to a false ninth axis X9′ with the same inclination of the ninth axis X9 through a side area middle point MA9 of the indicated right side area A9. The side area middle point MA9 is defined by the point on the right side area A9 that has the same distance to the sixth axis X6 and the seventh axis X7. In other words, the false ninth axis X9′ would be a parallel axis to the ninth axis X9, shifted to the left side.

[0240] FIG. 14 schematically shows a determination of correction points for the fifth cage 440. In a first step, a cage center point C is determined. Therefore, intersection between the acquired axis are determined. Thus, a sixth intersection point I6 is determined at an intersection of the sixth axis X6 and the eighth axis X8. A seventh intersection point I7 is determined at an intersection of the seventh axis X7 and the eighth axis X8. An eighth intersection point I8 is determined at an intersection of the sixth axis X6 and the ninth axis X9. A ninth intersection point I9 is determined at an intersection of the seventh axis X7 and the ninth axis X9.

[0241] Between the intersection points, a middle point is determined. Between the sixth intersection point I6 and the eighth intersection point I8, a sixth middle point M6 is determined. Between the seventh intersection point I7 and the ninth intersection point I9, a seventh middle point M7 is determined. Between the seventh intersection point I7 and the sixth intersection point I6, an eighth middle point M8 is determined. Between the eighth intersection point I8 and the ninth intersection point I9, a ninth middle point M9 is determined.

[0242] Based on the intersection points I6, I7, I8, I9 the cage center point C of the fifth cage 440 can be defined. For example, the cage center point C is determined by adding the interaction points I6, I7, I8, I9 and divide the accumulated coordinates by four.

[0243] Alternatively the determined middle points M6, M7, M8, M9 thus define the cage center point C of the fifth cage 440 in this plane, namely by determining the intersection between a connection of the sixth middle point M6 and the seventh middle point M7 with a connection of the eighth middle point M8 and the ninth middle point M9. In other words, the cage center point C is determined by the point, where a distance to opposing acquired axis along the cage coordinates are equal. In general, two opposing middle points, in particular the sixth middle point M6 and the seventh middle point M7 as well as the eight middle point M8 and the ninth middle point M9, are sufficient to determine the cage center point C by finding an equidistant point on a connection of said middle points.

[0244] Using the center point C, correction points K6, K7, K8 and K9 are determined using the cage coordinate axis. The cage coordinates of FIG. 14 comprise two visible axis, an x-axis along the acquired seventh axis X7 and an y-axis along the acquired eighth axis X8. The sixth correction point K6 is determined by an intersection of the y-axis through the cage center point C with the sixth axis X6. The seventh correction point K7 is determined by an intersection of the y-axis through the center point C with the seventh axis X7. The eighth correction point K8 is determined by an intersection of the x-axis through the cage center point C with the eighth axis X8. The ninth correction point K9 is determined by an intersection of the x-axis through the cage center point C with the ninth axis X9.

[0245] FIG. 14 indicates the ninth nearest point N9 as determined in FIG. 13. When determining the virtual model of the fifth cage 440, instead of using the ninth nearest point N9, the ninth correction point K9 would lead to a corrected side area A9′. This corrected side area A9′ leads to a more accurate approximation of the dimensions of the fifth cage 440. Consequently, when determining the dimensions, namely length, width and height, of the fifth cage 440 for the corresponding virtual model, the determined correction points K6, K7, K8,K9 lead to a better approximation of the dimension of the fifth cage 440 than using the nearest points N6, N7, N8, N9.