Device and computer-implemented method for calibrating a system

Abstract

The invention relates to a device (10) for calibrating a system (34) for generating at least one image of an object, wherein the device (10) has a multiplicity of calibration objects (20, 22, 24) and a base body (12) with corners (14) and outer edges (16) that extend between the corners (14) and delimit surface elements (18), wherein a first subset of the calibration objects (20) is arranged on the corners (14) of the base body (12), characterized in that a second subset of the calibration objects (22) is arranged on the outer edges (16) between the corners (14) and a third subset of the calibration objects (24) is arranged between the outer edges (16) on the surface elements (18). The invention further relates to a computer-implemented method (100) that uses the device (10). The invention therefore provides a device (10) and a method (100) for calibrating a system (34) for generating at least one image of an object that can be used to determine detector parameters with high accuracy with comparatively little computing complexity.

Description

[0001] Device and computer-implemented method for calibrating a system

[0002] The invention relates to a device and a computer-implemented method for calibrating a system for generating at least one image of an object.

[0003] Systems for generating at least one image of an object can be used in a variety of areas. For example, in workpiece inspection, manufactured workpieces can be examined using optical methods to compare the surfaces of the manufactured workpiece with target parameters. Furthermore, radiographic measurements, such as computed tomography (CT), can be used to examine the manufactured workpiece, for example, for dimensional measurements.

[0004] Calibration of the imaging system is required to conduct the examinations. Especially for computed tomography scans, and especially for robotic CT, it is essential to know the geometric calibration. In the case of a computed tomography system for generating images of an object, the geometric calibration concerns the geometric positioning and orientation of the components – radiation source, detector, and measurement object – relative to each other for each individual radiographic image acquired. The geometric positioning and orientation of the components can also be referred to as the acquisition geometry. Furthermore, the individual acquired radiographic image can be referred to as a projection or projection image. In the case of optical systems, the acquisition geometry concerns the positioning and orientation of the camera and the object relative to each other.

[0005] In order to perform computed tomography reconstruction based on images, particularly radiographic images, a quantitative description of the acquisition geometry for each individual image must be available that is as accurate as possible. Especially with radiographic images, errors in geometric calibration cause image errors in the reconstructed volume data, e.g., blurred edges, double edges, distortions, and thus measurement errors when performing dimensional measurements or other analyses such as defect, pore, and porosity analysis. Geometric calibration can also be relevant for the evaluation of radiographs without tomographic reconstruction, e.g., when multiple radiographs are evaluated together to determine the spatial position of a recognized property or feature of the imaged object by viewing them from different directions.Errors in geometric calibration also cause measurement errors here.

[0006] A quantitative description of the acquisition geometry for a radiographic image is achieved, for example, by defining the nine parameters of a pinhole camera. If, in addition to a Euclidean camera reference system with the radiation source at the coordinate origin and the detector plane parallel to one of the coordinate planes, a Euclidean object reference system that is fixed across all images but arbitrary is selected, three so-called intrinsic camera parameters describe the mapping of three-dimensional coordinates of the camera reference system into the image coordinate system. The remaining six so-called extrinsic camera parameters describe the relative position and orientation of the camera and object reference systems. Three of the six extrinsic camera parameters define a translation vector that describes the relative position of the camera and object reference systems.The other three extrinsic camera parameters define a rotation that describes the relative orientation of the camera and object reference systems. The entire set of extrinsic camera parameters is referred to as the pose. The camera parameters can also be subsumed under the term detector parameters.

[0007] By specifying the intrinsic and extrinsic camera parameters, it is determined how each point of the object to be imaged, which is described by three-dimensional coordinates in the object reference system, is to be mapped to an image point in the image or radiograph. The pose, which, as explained above, comprises six of the camera parameters, describes the mapping of three-dimensional coordinates from the object reference system to three-dimensional coordinates in the camera reference system. The intrinsic camera parameters describe the mapping of these three-dimensional coordinates in the camera reference system to two-dimensional coordinates in the image, which can also be referred to as pixel coordinates.

[0008] In general, especially with complex trajectories of robotic CT, a separate set of nine camera parameters is available for each individual radiographic image. Based on the camera parameters, the object volume can then be reconstructed for this set of radiographic images of the measurement object, with the camera parameters serving as calibration parameters.

[0009] A known technique is the implementation of so-called offline calibration, whereby a dedicated phantom is imaged or radiographed in advance or afterward in all required acquisition geometries. This means that for each image or radiograph of the object to be measured, an image or radiograph of the phantom is also acquired, with the acquisition geometry being as similar as possible. By analyzing the image or radiographs of the phantom, the acquisition geometry for each image or radiograph of the object to be measured is determined or estimated.

[0010] In the following, the term image also refers to a radiographic image.

[0011] US10977839B2 discloses a phantom in which individual spheres are arranged along a straight line. A numerical descriptor is calculated for each of four spheres, which is invariant even when mapped to a two-dimensional projection. The descriptor is therefore constant in every projection in which the spheres can be recognized. Therefore, correspondences can be established between the two-dimensional coordinates of the image and three-dimensional coordinates. Furthermore, the intrinsic and extrinsic camera parameters can be estimated. The estimated camera parameters can then be optimized to obtain an accurate calibration.

[0012] The object of the invention is to provide a device and a method for calibrating a system for generating at least one image of an object, with which the detector parameters can be determined with high accuracy and with comparatively little computational effort. Main features of the invention are defined in claims 1, 9, and 14. Further embodiments are the subject of claims 2 to 8 and 10 to 13.

[0013] In a device for calibrating a system for generating at least one image of an object, wherein the device has a plurality of calibration objects and a base body with corner points and outer edges which extend between the corner points and delimit surface elements, wherein a first subset of the calibration objects is arranged on the corner points of the base body, it is provided according to the invention that a second subset of the calibration objects is arranged on the outer edges between the corner points and a third subset of the calibration objects is arranged between the outer edges on the surface elements.

[0014] The invention thus provides a device with which an estimate of the detector parameters can be determined based on the known relationships between the various subsets of the calibration objects and between the calibration objects between and within the subsets. In the case of a transmission-based measurement, the calibration objects have absorption properties for the radiation of the transmission-based measurement that differ from the absorption properties of the base body. Furthermore, the calibration objects are preferably three-dimensional. The calibration objects of the first subset, which are arranged at the corner points of the surface elements, specify parameters for the general shape of the surface elements. Straight outer edges, on which the calibration objects of the second subset are arranged, preferably extend between the corner points.The contours of the surface elements are thus verifiably represented in one image by the first subset and the second subset of calibration objects. When determining or estimating detector parameters, the imaged surface elements can therefore be determined in at least one image of the device by at least considering or using the known positional relationships between the calibration objects of the first and second subsets. If the surface elements, for example,

[0015] B. triangles, all triangles formed by three imaged calibration objects in the image can be examined to see whether another calibration object is arranged on the connecting line between any two of the three imaged calibration objects, corresponding to the outer edge defined by the triangle. If this is not the case, the triangle checked in this way can be discarded. Otherwise, there is a high probability that an imaged surface element of the device is present. To decide whether an imaged surface element is present, it can be checked whether the triangle contains a calibration object from the third subset. If it is known where the calibration objects of the third subset are arranged in relation to the calibration objects of the other two subsets, this check can be simplified. Once the surface elements have been found, different test calibrations, so-calledinitial guesses are created which transfer a, e.g. calculated, test mapping of the first and second subset of the calibration objects of the device to the corners or outer edges of the imaged device. The test calibration corresponds to a mapping rule between the device and the imaged device. If a test calibration is incorrect, the calibration objects of the third subset are not transferred to the correct positions in the surface elements. Only when the correct test calibration has been found are all calibration objects correctly mapped. This test calibration can then be further optimized to obtain a precise calibration. The invention thus provides a device with which the detector parameters can be determined with high accuracy and with comparatively little computational effort.

[0016] According to one example, the arrangement of the calibration objects of the third subset relative to the calibration objects of the first subset and the second subset may differ between at least two surface elements.

[0017] In this example, the calibration objects of the third subset can encode a specific arrangement of the surface elements relative to one another. In particular, if all surface elements have the same shape or contour, a specific arrangement of the surface elements relative to one another can be identified using the third subset in an image of the device.

[0018] In a further example, each outer edge may be assigned at most one calibration object of the second subset of calibration objects and / or the second subset of calibration objects may be arranged centrally between the vertices on each outer edge.

[0019] Then, only a maximum of one calibration object from the second subset can be arranged between calibration objects from the first subset. This makes it possible to reduce the number of overlaps in an image of the calibration objects or, ideally, to avoid them altogether. The determination of the surface elements is also made easier if the calibration objects from the second subset are arranged centrally between the corner points on the outer edges. This means that the calibration objects from the second subset are at the same distance, within a tolerance, from the two corner points of the outer edge on which the calibration objects are arranged. Furthermore, the calibration objects can be arranged, for example, in at least two planes, each plane having at least four of the plurality of calibration objects, wherein preferably only some of the planes are parallel to one another.

[0020] Different planes can be defined, for example, by different surface elements. The surface elements can form different and / or opposite sides of the base body. The more calibration objects are arranged in a plane, the easier it becomes to identify the respective plane.

[0021] In another example, the planes may be non-parallel to each other. The surface elements to which the planes are assigned may, for example, have a common outer edge at the intersection of the planes. Furthermore, the base body may, for example, be designed such that the surface elements on two opposite sides may be arranged non-parallel to each other.

[0022] According to another example, each surface element can have at least two, preferably at least three, more preferably at least four, predefined positions within its surface, wherein each surface element is assigned a calibration object of the third subset of the calibration objects, which is arranged at one of the predefined positions and the other predefined positions, preferably at least two, more preferably at least three, more preferably at least four of the other predefined positions, can be free of calibration objects, wherein more preferably a subset of the predefined positions that is as large as possible or even the entire set of predefined positions can be invariant under all symmetry transformations of the surface element.

[0023] For example, four predefined positions can be the centers of four triangles, possibly equilateral except for the edges, disjoint, whose union yields exactly the surface element.

[0024] The calibration objects can thus be effectively used to encode the individual corner points of the surface elements. The distribution of the calibration objects of the third subset across the predefined positions can thus be designed such that the arrangement of the calibration objects allows a unique assignment of the surface elements. This means that each orientation of the device can have a unique distribution of the calibration objects of the third subset. This can lead to a more reliable determination of a correct test calibration. In another example, the relative arrangement of the calibration objects of the first subset and the second subset can be the same at each surface element.

[0025] The similar relative arrangement of the calibration objects of the first subset and the second subset simplifies the identification of the surface elements in the image. At the same time, the surface elements all have the same shape and size, further simplifying the identification of the surface elements in the image.

[0026] Furthermore, the surface elements can be, for example, triangular surfaces, preferably isosceles triangular surfaces, further preferably equilateral triangular surfaces, and / or the base body can be, for example, a polyhedron, preferably a regular polyhedron, further preferably a regular icosahedron.

[0027] In a perspective image, triangles are also mapped to triangles. This also simplifies the identification of surface elements in the image. In particular, triangles of the device are mapped to triangles in the image.

[0028] In another example, the base body may be an irregularly shaped body whose symmetry group only includes the identity transformation.

[0029] For example, the third subset of calibration objects may have no symmetry with respect to the ground field under Euclidean space transformations, ie, it may completely break the symmetries of the ground field.

[0030] This simplifies the determination of the alignment of the device from the image and makes the determination of a test calibration more reliable.

[0031] According to a further example, the subsets of the calibration objects may differ from each other in shape and / or size and may preferably be formed as spheres.

[0032] This makes it easier to assign images of the calibration objects to the individual subsets.

[0033] The invention further relates to a computer-implemented method for calibrating a system for generating at least one image of an object by means of a device according to the preceding description, wherein each surface element has a shape, wherein object position data of the calibration objects in the device relative to one another are known and wherein the object position data of the calibration objects of the third subset differ relative to the object position data of the calibration objects of the first subset and the second subset between at least two surface elements, wherein the method comprises the following steps: providing at least one image of the device by means of the system, wherein the calibration objects in the at least one image are mapped onto image calibration objects; determining image position data of all visible image calibration objects in the at least one image;Identifying image surface elements of the device depicted in the at least one image using the determined image position data, the shapes of the surface elements, and the object position data of at least the first subset and the second subset of the calibration objects, wherein image corner points and image outer edges are determined using the identified image surface elements; Selecting a test calibration in which, in a test image, the object position data of the first subset of the calibration objects are mapped to the image corner points and the object position data of the second subset of the calibration objects are mapped to the image outer edges; Determining test image position data of the third subset of the calibration objects using the test calibration; Comparing the test image position data with the image position data of the third subset of the calibration objects;until the test image position data and the image position data of the third subset of calibration objects are mapped to one another within a predefined tolerance range; repeating the steps: selecting a modified test calibration in which, in a test image, the object position data of the first subset and second subset of calibration objects are mapped to the image corners and the object position data of the second subset of calibration objects are mapped to the image outer edges in the image, and determining test image position data of the third subset of calibration objects and comparing the test image position data with the image position data of the third subset of calibration objects with the modified test calibration.;

[0034] In the method according to the invention, the device according to the above description is used to calibrate a system for generating at least one image of an object. The object position data of the calibration objects here designate the positioning of the calibration objects in the device. The object position data of the calibration objects relative to one another are known. Between the various surface elements of the device, the object position data of the calibration objects of the third subset differ relative to the object position data of the calibration objects of the first subset and the second subset. This means that the object position data of the calibration objects of the first and second subsets relative to one another can be the same for each surface element.However, the object position data of the calibration objects of the third subset differ relative to the object position data of the calibration objects of the first and second subsets for different, at least two, surface elements. For example, for a first surface element, a calibration object of the third subset can be arranged centrally between the calibration objects of the first and second subsets. For a second surface element, the corresponding calibration object of the third subset can be arranged off-center, for example.

[0035] To calibrate the system, the computer-implemented method can first generate at least one image of the device and make it available, e.g., by means of a file on a storage medium, by data transfer from another computer or other methods, or even directly. The system can be used to generate the at least one image. In the at least one image, the calibration objects are mapped onto image calibration objects. The term image calibration objects is used below as a synonym for the calibration objects of the device depicted in the image. The at least one image is generally a two-dimensional image, e.g., a projection image or an optical representation of the device. However, this does not rule out the possibility that the at least one image may be a three-dimensional image.

[0036] The image position data of the visible image calibration objects are then determined in at least one image. To save computational effort, the image position data of the visible image calibration objects can initially be determined in a single image, which is then also used for the subsequent steps. However, this does not preclude the possibility that the image position data of the visible image calibration objects may also be determined in several or all of the provided images and used subsequently.

[0037] To determine the image position data, well-known image analysis methods can be used to identify the image calibration objects in the image. Furthermore, the centers of the image calibration objects can be determined with high accuracy. For example, if the calibration objects are spheres, they are mapped onto ellipses in the image. The centers of the ellipses can then be determined to estimate the position of the sphere centers in the image. The centers can then be assumed, for example, as the image points of the three-dimensional calibration objects, possibly in perspective.

[0038] In the following steps, the three-dimensional object position data of the calibration objects and the two-dimensional image position data of the image calibration objects are assigned to each other. This means that it is determined which image calibration object is the image of the corresponding calibration object from the device. The problem thus described and to be solved below is referred to here and below as the sphere correspondence problem. For this purpose, the image surface elements are identified in the image using the determined image position data. Since the relative relationships between the object position data are known, this knowledge can be used to identify image surface elements in the image. For example, ifIf the surface elements have a triangular shape, with the calibration objects of the first subset arranged at the corners of the triangles and the calibration objects of the second subset arranged between the corners on the edges of the triangles, three different image position data can be checked in the figure, for example, to see whether they satisfy these relative relationships to one another and to other image position data. If these relationships are satisfied, the three image position data are most likely located at the image corners of an image surface element. Once an image surface element has been found, the outer image edges of the image surface elements adjacent to this image surface element are also known. On this basis, the identification of further image surface elements can be simplified.At the same time as identifying the image surface elements, the image corners and outer edges can also be identified.

[0039] If the image surface elements, and thus the image corners and outer edges, are known, the image calibration objects are assigned to at least three subsets of calibration objects. The image calibration objects located at the image corners are assigned as images to the first subset of calibration objects. The image calibration objects located at the image outer edges are assigned as images to the second subset of calibration objects. The remaining image calibration objects located within the image surface elements are assigned as images to the third subset of calibration objects.

[0040] A test calibration is then selected in which, in a test mapping, the object position data of the first or second subset are mapped to the image position data of the image calibration objects assigned to the first or second subset. Through a correctly selected test calibration, the correspondences between all known image calibration objects and corresponding calibration objects are known based on assumed correspondences between a few calibration objects and image calibration objects, e.g., in the case of an assumed correspondence of a single surface element with a specific image surface element. The selection of the test calibration can be an estimate that includes the intrinsic and extrinsic detector parameters. The test mapping can then be carried out using the estimated detector parameters. The test mapping does not necessarily have to be carried out in reality, but can also be calculated orThe calibration objects of the first and second subsets can thus be used to construct the test calibration, so that for the test calibration constructed in this way, it is then checked whether the image position data of the image calibration objects can be generated by a mapping of object position data of corresponding calibration objects of the first or second subset generated by the test calibration.

[0041] Since the test calibration is designed such that at least part of the object position data of the calibration objects in the first and second subsets is mapped to part of the image position data of the corresponding image calibration objects, the test image position data resulting from the object position data of the calibration objects in the third subset must, in principle, be determined. These are then compared with the image position data of the image calibration objects in the third subset.

[0042] If the test image position data does not match the image position data of the calibration objects in the third subset within a predefined tolerance range, the test calibration is incorrect and is discarded. The predefined tolerance range can define a maximum permissible deviation between the test image position data and the image position data of the calibration objects in the third subset. If the surface elements are triangles, the predefined tolerance range can be defined using barycentric triangular coordinates. A modified test calibration is selected, and the test image verification described above is repeated until the test image position data matches the image position data of the calibration objects in the third subset within the predefined tolerance range.

[0043] In an alternative example of the procedure, all possible test calibrations are examined and then compared to decide which test calibration is the most accurate.

[0044] With the test calibration determined in this way, the intrinsic and extrinsic detector parameters are known with sufficient accuracy, so that the system calibration can be completed. Furthermore, at least a subset of object position data is then known, which corresponds to a subset of image position data. This solves the sphere correspondence problem.

[0045] The invention thus provides a method for calibrating a system for generating at least one image of an object, with which the detector parameters can be determined with high accuracy and with comparatively little computational effort. According to one example, if the test image position data and the image position data of the third subset of calibration objects are mapped to one another within a predefined tolerance range, the method can further comprise the following step: optimizing the test calibration using a nonlinear optimization method.

[0046] The nonlinear optimization method can be used to increase the accuracy of the test calibration or calibration itself. For the now known correspondences between the object position data and the image position data, the determined geometric error is continually reduced by adjusting the determined test calibration.

[0047] In another example, the method may further comprise the step of determining the intrinsic detector parameters using at least the image position data of the image corner points and image outer edges prior to the step of selecting a test calibration, wherein the step of selecting a test calibration may comprise the following sub-step of determining extrinsic sample detector parameters using the determined intrinsic detector parameters and the image position data of an image surface element.

[0048] In this case, the intrinsic detector parameters are determined first before the extrinsic detector parameters are determined. This is particularly advantageous when the device has a high degree of symmetry. If, for example, the base body of the device is designed as a regular icosahedron and the calibration objects of the first and second subsets are arranged identically for each surface element, the object position data of the calibration objects of the first subset form equilateral triangles. This simplifies the identification of the image surface elements. Furthermore, the determined image surface elements can be used to establish an overdetermined system of equations for the intrinsic detector parameters. This allows the intrinsic camera parameters to be determined or estimated with sufficient accuracy and with little effort.For the test calibration, only the extrinsic detector parameters need to be estimated as extrinsic sample detector parameters. The estimation of the extrinsic sample detector parameters can then be carried out in this way based on the determined intrinsic detector parameters and the image position data of a single image surface element. It is particularly advantageous that only a single image of the object can be used to determine the test calibration, instead of having to use several or all available images to determine the test calibration. This means that this method also works if the images are not acquired in a contiguous trajectory, but merely in an arbitrary sequence of images, or even if only a single image is acquired.This is a great advantage, especially when it is only possible to obtain an image of the object from very specific positions, e.g. in robotic CT.

[0049] Determining the intrinsic detector parameters and determining the extrinsic sample-detector parameters can also be performed by estimating the intrinsic detector parameters and the extrinsic sample-detector parameters, respectively.

[0050] The method may, for example, further comprise the following step: performing a bundle adjustment procedure on all images for which intrinsic and extrinsic detector parameters were determined.

[0051] The implementation of a bundle adjustment procedure allows to compensate for deviations from the expected geometry of the device, i.e. slightly shifted object position data of the calibration objects in the device, which arise during the manufacture of the device compared to the target position data or deviations due to temperature expansion.

[0052] Furthermore, the step of determining the intrinsic detector parameters using at least the image position data of the image corner points and image outer edges can be carried out for all provided images, for example, before the step of determining the extrinsic detector parameters for each surface element using the determined intrinsic detector parameters is carried out.

[0053] In this way, the intrinsic detector parameters are optimized first before the extrinsic detector parameters are optimized.

[0054] The invention further relates to the use of a device according to the preceding description for calibrating a system for generating at least one image of an object.

[0055] Advantages and effects, as well as further developments of the use of the device, arise from the advantages and effects, as well as further developments of the device described above and, if applicable, the computer-implemented method described above. Therefore, reference is made to the preceding description in this regard.

[0056] In a further aspect, the invention relates to a computer program product with computer-executable instructions which, when executed on a computer, cause the computer to carry out the method according to the preceding description. Advantages and effects as well as further developments of the computer program product arise from the advantages and effects as well as further developments of the method described above. Reference is therefore made in this regard to the preceding description. A computer program product can be understood, for example, as a data carrier on which a computer program element is stored which has computer-executable instructions. Alternatively or additionally, a computer program product can also be understood, for example, as a permanent or volatile data storage device, such as flash memory or RAM, which has the computer program element.However, this does not exclude other types of data storage that contain the computer program element.

[0057] Further features, details, and advantages of the invention will become apparent from the wording of the claims and from the following description of exemplary embodiments with reference to the drawings. They show:

[0058] Fig. 1 is a schematic representation of a basic body of the device;

[0059] Fig. 2 is a schematic representation of a surface element with calibration objects;

[0060] Fig. 3 is a schematic representation of a system for generating at least one

[0061] image of an object;

[0062] Fig. 4a-c is a schematic representation of an image of the device; and

[0063] Fig. 5 is a diagrammatic representation of the computer-implemented method.

[0064] In the following, the device for calibrating a system for generating at least one image of an object is designated in its entirety by the reference symbol 10, as shown in Figure 1.

[0065] The device 10 comprises a base body 12, which in this example is designed as a regular icosahedron. The base body 12 has vertices 14 that form end pieces of straight outer edges 16. The outer edges 16 surround surface elements 18, which in this example are designed as equilateral triangles. An example of a surface element 18 designed as an equilateral triangle is shown in Figure 2. The device further comprises a plurality of calibration objects 20, 22, 24. The calibration objects 20, 22, 24 can be designed as spheres.

[0066] A first subset of the calibration objects is arranged at the corner points 14. These calibration objects are designated by the reference symbol 20.

[0067] A second subset of the calibration objects is arranged on the outer edges 16. These calibration objects are designated by the reference symbol 22. The calibration objects 22 of the second subset can be arranged centrally between the corner points 14 on the outer edges 16.

[0068] A third subset of the calibration objects is arranged on the surface elements 18.

[0069] These calibration objects are designated by the reference symbol 24. In this example, the calibration objects 24 of the third subset can be arranged on the surface element 18 at one of four predefined positions 26-32 within the surface. The remaining predefined positions 26-32 can be free of calibration objects 20, 22, 24. The predefined position 26 can be arranged at the center of the surface element 18. The predefined positions 28-32 can be arranged outside the center of the surface element 18, each offset from a corner point 14 of the surface element 18.

[0070] The device 10 has at least two surface elements 18, each of which has a different arrangement of the respective calibration object 24 of the third subset. This means that the calibration objects 24 of the third subset of the two surface elements 18 are arranged at different predefined positions.

[0071] Furthermore, a subset of the predefined positions 26-32 can be invariant under all symmetry transformations of the surface element 18. For example, if the vertices 14 are permuted, the predefined positions 26-32 of the subset are transformed into each other.

[0072] In this example, in which the base body 12 is formed as a regular icosahedron, all surface elements 18 have the same shape, which is shown in Figure 2. The relative positions of the calibration objects 20 of the first subset and the calibration objects 22 of the second subset are then the same for all surface elements 18 of the base body 12. Only the relative positions of the calibration objects 24 of different surface elements 18 with respect to the calibration objects 20, 22 of the first and second subsets can differ between the surface elements 18. Under Euclidean spatial transformations, the calibration objects 24 of the third subset exhibit no symmetries. Thus, the calibration objects 24 of the third subset break the symmetry of the calibration objects or of the base body 12.

[0073] In this example, in which the base body 12 is formed as a regular icosahedron, four non-adjacent surface elements 18 can be selected, in which the calibration objects 24 of the third subset are arranged at position 26 in the center of the respective surface element 18. Each vertex 14 then borders exactly one surface element 18 in which a calibration object 24 of the third subset is arranged at position 26.

[0074] For the remaining surface elements 18, the calibration objects 24 are each arranged at one of the positions 28, 30, 32. The distribution to the positions 28, 30, 32 is carried out in such a way that when circulating around a corner point 14 over the surface elements 18 adjacent to it, starting from the surface element 18 in which a calibration object 24 of the third subset is arranged at position 26, a unique distribution over the positions 28, 30, 32 is created with respect to the other corner points, regardless of the orientation in which the respective distribution is traversed.

[0075] It is particularly advantageous if the different distributions differ as clearly as possible.

[0076] Between the three subsets, the calibration objects 20, 22, and 24 can differ from each other. Calibration objects 20, 22, and 24 can differ from each other, for example, in their size or shape.

[0077] If the device 10 is designed to calibrate a system that creates images by means of radiographic measurements, the absorption properties of the calibration objects 20, 22, 24 differ from the absorption properties of the base body 12.

[0078] Figure 3 shows a system 34 for generating at least one image of an object. In this example, the system 34 has a radiation source 36 and a detector 38. The radiation source 36 is only present in systems that perform a transmissive measurement. If the system 34 generates the image using optical radiation, the radiation source 36 can be omitted. For the calibration of the system 34, the device 10 is arranged such that the detector 38 can detect radiation that is reflected by the device 10 in the case of optical radiation and transmitted in the case of a transmissive measurement.

[0079] If a radiation source 36 is present, the radiation source 36 emits radiation in the direction of the device 10. Then the device 10 is arranged between the radiation source 36 and the detector 38.

[0080] In the following, it is assumed that system 34 performs a radiative measurement and can generate corresponding images of objects. However, the following explanations also apply to systems that generate images using radiation reflected from the surface.

[0081] For calibrating system 34, the computer-implemented method 100 for calibrating a system configured to generate at least one image of an object can be used. Device 10 is used to perform method 100. A flowchart of method 100 is shown in Figure 5.

[0082] According to step 102, the system 34 can generate at least one image 40 of the device 10 and provide it to the method 100, e.g., directly or by reading it from a file previously stored on a storage medium. Examples of images 40 are shown in Figures 4a to 4c.

[0083] According to Figure 4a, an image 40 shows the result of a transmission measurement of the device 10. Figure 40 includes representations of the calibration objects 20, 22, 24 of the device, these representations being referred to below as image calibration objects 42, 44, 46. Since the calibration objects 20, 22, 24 are spherical, they were depicted as elliptical dark areas in Figure 40. Initially, it is unknown at which positions in Figure 40 the image calibration objects 42, 44, 46 of the calibration objects 20, 22, 24 are arranged.

[0084] Therefore, in step 104, the image position data of the image calibration objects 42, 44, 46 visible in the image are determined. This can be done, for example, using known edge detection methods or the like.

[0085] The center points of the imaged elliptical surfaces of the image calibration objects 42, 44, 46 are preferably used as image position data. In step 106, the image surface elements 48, as shown in Figure 4b, are identified in the image 40 shown there. This image 40 can be the same image shown in Figure 4a. In this example, several images were used, and step 104 was performed in all of them.

[0086] The image position data is used for step 106. Since the relative positional relationships of the calibration objects 20, 22, 24 in the device 10 are known, these relative positional relationships can also be used in the identification of the image surface elements 48.

[0087] The identification of the image surface elements 48 can be further simplified and performed with greater reliability if the calibration objects 20, 22, 24 of the three subsets have different shapes and / or sizes. Then, in principle, the image calibration objects 42 that have the correct shape and / or size can be directly assigned as images to the first subset of the calibration objects 20, although a direct assignment of the image calibration objects 42 corresponding to the calibration objects 20 is not yet possible at this point. The same applies to the calibration objects 22, 24.In order to group three image calibration objects 42 together with three image calibration objects 44 and one image calibration object 46 into one surface element 48 each and thus to identify the corresponding surface element in the image, the following procedure can be used: For all possible combinations of three (assumed) image calibration objects 42 and three (assumed) image calibration objects 44, it must first necessarily apply that, within a tolerance range, the three (assumed) image calibration objects 44 are arranged relative to the three (assumed) image calibration objects 42 such that exactly one of the (assumed) image calibration objects 44 lies on the connecting line of two of the (assumed) image calibration objects 42. If this is the case, then with the knowledge of the exact geometric shape of the surface element, ieWith the knowledge of the exact (known) relative positions of the calibration objects 20, 22 within the equilateral triangle, which are identical for each surface element, a so-called plane homography can be constructed, which reverses the perspective distortions that arise during the perspective imaging of the plane defined by the triangle.

[0088] Such a plane homography can be constructed as soon as at least four points are known that lie on a common plane. In this case, the six points defined by the selected image calibration objects 42, 44 are used. For all other image calibration objects that can be assumed in principle to potentially form a surface element 48 together with the three (presumed) image calibration objects 42 and the three (presumed) image calibration objects 44 as image calibration object 46, the plane homography is used to determine at which point in the (presumed) equilateral triangle this (presumed) image calibration object 46 would be positioned.If the position now determined in this way lies within the (assumed) equilateral triangle within a tolerance range at one of the positions 26, 28, 30, 32, it is (initially) assumed in the further course of action that the seven image calibration objects 42, 44, 46 grouped in this way are assigned to an image surface element 48. With the identification of the image surface element 48 through the assignment of seven image calibration objects 42, 44, 46 to known geometric positions (corners, edges and surface) described here, it has now also been determined in each case which of the seven image calibration objects are assigned to the calibration objects 20, 22, 24 of the first, second or third subset, if this could not already be determined beforehand, e.g. via the different sizes and / or shapes of the calibration objects 20, 22, 24. With this knowledge, perspective distortions of the detector or camera on this common plane can be reversed.

[0089] With the optional step 120, the intrinsic detector parameters can now be determined. For this purpose, the image position data of the image corner points and image outer edges of the image surface elements 48 on which the image calibration objects 42, 44 are arranged are used. This determination can also be referred to as an estimation of the intrinsic detector parameters.

[0090] Knowledge of the plane homographies can be used for step 120. With a known metric plane homography, as determined here for each image surface element, two linear conditions for the components of the image of the absolute conic (IAC) result for each of these planes. This allows an overdetermined linear system of equations to be set up. This system of equations can be solved, for example, using a possibly linear least squares method. The intrinsic detector parameters can then be obtained, for example, using a Cholesky factorization of the IAC. This can thus be done before it is known which calibration object 20, 22, 24 is imaged onto which image calibration object 42, 44, 46.

[0091] In step 108 of method 100, a test calibration is selected. To select the test calibration, corresponding calibration objects 20, 22, 24 are assumed for some image calibration objects 42, 44, 46, which are mapped onto these image calibration objects 42, 44, 46. Using this test calibration, corresponding calibration objects 20, 22, 24 are then determined for further determined image calibration objects 42, 44, 46, preferably all determined image calibration objects, and this assignment is recorded or stored. If step 120 has not been performed, in step 108 a plurality of surface elements 18, at least two, preferably three, are selected for which correspondences between the calibration objects 20, 22, 24 and the image calibration objects 42, 44, 46 are determined, wherein the correspondences for the remaining surface elements 18 are then determined by means of the selected test calibration.In this case, the extrinsic and intrinsic detector parameters are only implicitly defined by determining the test image. At least one condition for determining the correspondences is that the calibration objects 20 of the first subset are mapped to the image calibration objects 42, and the calibration objects 22 of the second subset are mapped to the image calibration objects 44.

[0092] If, in an alternative example, optional step 120 has been performed, the test calibration can be selected using a single surface element 18, for which correspondences between the calibration objects and the image calibration objects are determined. The optional sub-step 122 can then be performed, in which case only the extrinsic detector parameters for the test calibration need to be selected in step 108, since the intrinsic detector parameters are already known by performing step 120.

[0093] In an example not shown, the optional step 120 may also be an optional sub-step of step 108.

[0094] In sub-step 122, the extrinsic detector parameters of a test calibration can be determined, e.g., using a perspective-n-point method. For each image surface element identified in the image, one can guess which of the surface elements was imaged here. In addition, the permutation of the calibration objects of the first subset must be guessed. Using an equilateral triangle as an example surface element, there are a maximum of six possible permutations depending on the positioning of the calibration object of the third subset. There is only a small number of possible mappings for a specific surface element.Then, for each of these possibilities, the extrinsic detector parameters can be determined using the perspective-n-point method, using the intrinsic detector parameters and the resulting correspondences between the image position data and the object position data, even though all three-dimensional object position data lie in a common plane. A set of extrinsic detector parameters determined in this way, in combination with the intrinsic detector parameters, can define a test calibration. In the test calibrations determined in this way, the calibration objects of the first and second subsets are generally mapped onto the image position data on which the image calibration objects, which are images of the first and second subsets, are arranged.A test calibration is then selected, which is then used to generate a test image of the device 10 in step 110. This test image can be simulated or calculated without performing an actual image. The test image position data of the images of the calibration objects 24 of the third subset are determined in the test image.

[0095] The test image position data are compared in step 112 with the image position data of the calibration objects 46 of the third subset. This comparison is clearly illustrated in Figure 4c. If the test calibration is assumed correctly and sufficiently accurate, the test image position data do not deviate from the image position data within a predefined tolerance range. However, if the test calibration is assumed incorrectly, deviations 50 arise between the test image position data and the image position data. The deviations 50 resulting from an inaccurate test calibration are graphically represented in Figure 4c as lines emanating from the corresponding image position data in Figure 4c.

[0096] If the comparison from step 112 does not result in a sufficiently accurate test calibration, i.e., if the test image position data and the image position data of the third subset of calibration objects do not map to one another within a predefined tolerance range, steps 116, 110, and 112 are repeated in step 114. The originally used test calibration is then discarded, as are any recorded correspondences between the image calibration objects 42, 44, 46 and the calibration objects 20, 22, 24. In step 116, a modified test calibration is selected which, in a test image, maps the object position data of the first subset and second subset of calibration objects to the image corner points and the object position data of the second subset of calibration objects to the image outer edges in the image. Step 116 is identical to step 108 except for the use of a modified test calibration.Therefore, steps 110 and 112 are repeated with the modified test calibration.

[0097] If the optional sub-step 122 has been performed, the test calibration determined to be inaccurate is discarded during the repetition and a previously untested set of extrinsic detector parameters is linked to the intrinsic detector parameters to form a modified test calibration.

[0098] If the comparison from step 112 results in a sufficiently accurate test calibration, i.e., if the test image position data and the image position data of the third subset of calibration objects are mapped to each other within a predefined tolerance range, the method can continue with the optional step 118. Furthermore, correspondences between the object position data and the image position data are then known.

[0099] In an alternative example of the procedure, all possible test calibrations are examined and then compared to decide which test calibration is the most accurate.

[0100] In optional step 118, the accuracy of the determined sufficiently accurate test calibration can be increased using a nonlinear optimization method. Furthermore, with the sufficiently accurate test calibration, an estimate, a so-called initial guess, of the intrinsic and extrinsic detector parameters is now known, which also takes into account special imaging properties of the detector, in particular square and non-affinely distorted pixels, at least approximately. With such an initial guess and the correspondences thus determined, the intrinsic and extrinsic detector parameters can be adjusted with the aid of the nonlinear optimization method in such a way that the so-called geometric error of the determined correspondences between the image position data and the object position data is minimized.

[0101] If the optional step 120 was not performed, an imaging matrix is ​​optimized in optional step 118 to improve the implicitly defined detector parameters. If the optional step 120 was performed, the detector parameters are optimized in step 118. The special imaging properties of the detector, in particular square and non-affinely distorted pixels, are precisely taken into account, since the intrinsic detector parameters are then immediately further optimized. The nonlinear optimization from step 118 then takes into account the special imaging properties of the detector, i.e. the intrinsic detector parameters determined from step 120, which already precisely take these special imaging properties of the detector into account. After the optimization in step 118, the special imaging properties listed above continue to apply exactly to the optimized test calibration.

[0102] The above-described steps of method 100 can advantageously be performed using only a single image of the device. Alternatively, the above-described steps of method 100 can be performed with multiple images of the device, wherein the device is preferably imaged in each of the images used under a different orientation relative to the detector or camera of the system. In a further optional step 124, a bundle adjustment method can be performed across all images generated by the device with the system. The bundle adjustment method can, for example, compensate for slight shifts in the object position data of the calibration objects compared to the target position data of the calibration objects in the device.

[0103] A nonlinear optimization method can be used to optimize the detector parameters of all images and the object position data of the calibration objects together to minimize the reprojection error of the correspondences found between the image position data and the object position data across all images. The previously determined detector parameters and the known target positions of the calibration objects serve as the initial guess for the nonlinear optimization.

[0104] The invention is not limited to one of the above-described embodiments, but can be modified in a variety of ways. All features and advantages apparent from the claims, the description, and the drawings, including structural details, spatial arrangements, and method steps, may be essential to the invention both individually and in a wide variety of combinations.

Claims

Patent claims Device for calibrating a system (34) for generating at least one image of an object, wherein the device (10) has a plurality of calibration objects (20, 22, 24) and a base body (12) with corner points (14) and outer edges (16) which extend between the corner points (14) and delimit surface elements (18), wherein a first subset of the calibration objects (20) is arranged on the corner points (14) of the base body (12), characterized in that a second subset of the calibration objects (22) is arranged on the outer edges (16) between the corner points (14) and a third subset of the calibration objects (24) is arranged between the outer edges (16) on the surface elements (18).Device according to claim 1, characterized in that the arrangement of the calibration objects (24) of the third subset relative to the calibration objects (20, 22) of the first subset and the second subset differs between at least two surface elements (18). Device according to claim 1 or 2, characterized in that each outer edge (16) is assigned at most one calibration object (22) of the second subset of calibration objects and / or the second subset of calibration objects (20) is arranged centrally between the corner points (14) on each outer edge (16).Device according to one of claims 1 to 3, characterized in that each surface element (18) has at least two, preferably at least three, more preferably at least four, predefined positions (26, 28, 30, 32) within its surface, wherein each surface element (18) is assigned a calibration object (24) of the third subset of the calibration objects, which is arranged at one of the predefined positions (26, 28, 30, 32) and the other predefined positions (26, 28, 30, 32) are free of calibration objects (24), wherein more preferably a subset of the predefined positions (26, 28, 30, 32) is invariant under all symmetry transformations of the surface element (18). Device according to one of claims 1 to 4, characterized in that the relative arrangement of the calibration objects (20, 22) of the first subset and the second subset to each other is the same on each surface element (18).

6. Device according to one of claims 1 to 5, characterized in that the surface elements (18) are triangular surfaces, preferably equilateral triangular surfaces, and / or the base body (12) is a polyhedron, preferably a regular polyhedron, more preferably a regular icosahedron.

7. Device according to one of claims 1 to 6, characterized in that the third subset of the calibration objects (24) with respect to the base body (12) is not a symmetry under Euclidean space transformations.

8. Device according to one of claims 1 to 7, characterized in that the subsets of the calibration objects (20, 22, 24) differ from one another in shape and / or size and are preferably designed as spheres.

9. A computer-implemented method for calibrating a system for generating at least one image of an object by means of a device according to one of the preceding claims, wherein each surface element has a shape, wherein object position data of the calibration objects in the device are known relative to one another, and wherein the object position data of the calibration objects of the third subset differs relative to the object position data of the calibration objects of the first subset and the second subset between at least two surface elements, wherein the method (100) comprises the following steps: Providing (102) at least one image of the device by means of the system, wherein the calibration objects in the at least one image are mapped onto image calibration objects; Determining (104) image position data of all visible image calibration objects in the at least one image; Identifying (106) image surface elements of the device depicted in the at least one image by means of the determined image position data, the shapes of the surface elements and the object position data of at least the first subset and the second subset of the calibration objects, wherein image corner points and image outer edges are determined by means of the identified image surface elements; Selecting (108) a test calibration in which, in a test image, the object position data of the first subset of the calibration objects are mapped to the image corner points and the object position data of the second subset of the calibration objects are mapped to the image outer edges; Determining (110) test image position data of the third subset of the calibration objects by means of the test calibration; Comparing (112) the test image position data with the image position data of the third subset of the calibration objects; Until the test image position data and the image position data of the third subset of calibration objects are mapped to each other within a predefined tolerance range: Repeat (114) the steps: Selecting (116) a modified test calibration, in which, in a test image, the object position data of the first subset and second subset of the calibration objects are mapped to the image corner points and the object position data of the second subset of the calibration objects are mapped to the image outer edges in the image, and Determining (110) test image position data of the third subset of the calibration objects and comparing (112) the test image position data with the image position data of the third subset of the calibration objects with the modified test calibration. The method according to claim 9, characterized in that, if the test image position data and the image position data of the third subset of the calibration objects are mapped to one another within a predefined tolerance range, the method (100) further comprises the following step: Optimizing (118) the test calibration using a nonlinear optimization method. Method according to claim 9 or 10, characterized in that the method (100) further comprises the step (108) of selecting a test calibration: Determining (120) the intrinsic detector parameters using at least the image position data of the image corner points and image outer edges; wherein the step (108): selecting a test calibration comprises the following sub-step: Determining (122) extrinsic sample detector parameters using the determined intrinsic detector parameters and the image position data of an image surface element. The method according to claim 11, characterized in that the method (100) further comprises the following step; Performing (124) a bundle adjustment procedure over all images for which intrinsic and extrinsic detector parameters were determined. Method according to claim 11 or 12, characterized in that the step (120): determining the intrinsic detector parameters using at least the image position data of the image corner points and image outer edges is carried out for all provided images before the step (122): determining the extrinsic detector parameters for each surface element using the determined intrinsic detector parameters is carried out. Use of a device (10) according to one of claims 1 to 8 for calibrating a system (34) for generating at least one image of an object or for solving a sphere correspondence problem. Computer program product with computer-executable instructions which, when executed on a computer, cause the computer to carry out the method according to one of the preceding claims.

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