Computer-implemented method for segmenting measurement data from a measurement of an object

Abstract

Described is method for segmenting measurement data from a measurement of an object having at least one material transition region, the measurement data generating a digital object representation having the at least one material transition region and comprising pieces of spatially-resolved image information of the object. The method comprises: determining the measurement data comprising at least one artefact; determining at least two homogeneous regions in the measurement data and/or in the digital object representation; analysing a local similarity of pieces of spatially resolved image information; adjusting an extent of each homogeneous region until at least one boundary region of each homogeneous region is located at an expected position of a material transition region; segmenting the digital object representation based on the adjusted homogeneous regions. The method improves segmenting measurement data from a measurement of an object having poor data quality, while correctly detecting material transitions from the measurement data.

Claims

1. A computer-implemented method for segmenting measurement data from a measurement of an object, the object having at least one material transition region, a digital object representation with the at least one material transition region being generated by way of the measurement data, the digital object representation having a multiplicity of spatially resolved image information items of the object, the method including the following steps: determining the measurement data, the measurement data containing at least one artifact; determining at least two homogeneous regions in the measurement data and/or in the digital object representation; analyzing a local similarity of the multiplicity of spatially resolved image information items; adapting an extent of each homogeneous region until at least one boundary region of each homogeneous region is arranged at an expected position of a material transition region; segmenting the digital object representation on the basis of the adapted homogeneous regions.

2. The method as claimed in claim 1, wherein the at least one material transition region is a multi-material transition region.

3. The method as claimed in claim 1, wherein the analysis of the local similarity is based on a change sequence of the multiplicity of spatially resolved image information items and/or a local variance of the multiplicity of spatially resolved image information items.

4. The method as claimed in claim 1, wherein the method further includes the following step that precedes the determination of at least two homogeneous regions of the digital object representation: aligning a digital representation of a target geometry with the digital object representation; with the determination of at least two homogeneous regions being carried out on the basis of the digital representation of a target geometry.

5. The method as claimed in claim 1, wherein the method further includes the following step after the step of segmenting the digital object representation: determining the position of the at least one material transition region in the at least one boundary region by means of the at least two homogeneous regions.

6. The method as claimed in claim 1, wherein the method further includes the following step after the segmentation of the digital object representation: changing an extent of at least one of the homogeneous regions on the basis of a visualization of the homogeneous regions in the digital object representation.

7. The method as claimed in claim 1, wherein the method further includes the following steps after the segmentation of the digital object representation: changing a local similarity of the multiplicity of spatially resolved image information items in the segmented digital object representation for the purposes of correcting the analyzed local similarity; and repeating the step of segmenting the digital object representation on the basis of the corrected analyzed local similarity.

8. The method as claimed in claim 1, wherein the step of adapting an extent of each homogeneous region until at least one boundary region of each homogeneous region is arranged at an expected position of a material transition region includes the following sub-step: determining at least one artifact region containing at least one artifact in the digital object representation on the basis of the at least two homogenous regions and/or a digital representation of a target geometry; determining at least one boundary region on the basis of the analyzed local similarity, with a boundary region being determined in the artifact region if the local similarity between the image information items is lower than outside of the at least one artifact region.

9. The method as claimed in claim 1, wherein the step of adapting an extent of each homogeneous region until at least one boundary region of each homogeneous region is arranged at an expected position of a material transition region includes the following sub-steps: determining at least one geometry type of a volume region of the digital object representation; comparing the determined geometry type with geometry types from a target geometry of the object; determining at least one boundary region on the basis of the analyzed local similarity, with a boundary region being determined in the volume region if the local similarity between the image information items is lower than outside of the volume region and if the determined geometry type is not similar to any of the geometry types from the target geometry of the object.

10. The method as claimed in claim 1, wherein the step of adapting an extent of each homogeneous region until at least one boundary region of each homogeneous region is arranged at an expected position of a material transition region includes the following sub-steps: determining a quality value of at least one volume region of the digital object representation; determining at least one boundary region on the basis of the analyzed local similarity in the volume region if the local similarity between the image information items is lower than outside of the volume region and if the determined quality value for the at least one volume region is smaller than a predefined threshold for the quality value.

11. The method as claimed in claim 1, wherein the method further includes the following steps after the segmentation of the digital object representation: adapting the multiplicity of image information items in the segmented digital object representation by means of an artifact correction method based on the determined homogeneous regions; and segmenting the digital object representation on the basis of the multiplicity of adapted image information items.

12. The method as claimed in claim 11, wherein the method further includes the following step: repeating the steps of: adapting the multiplicity of image information items in the segmented digital object representation by means of an artifact correction method based on the determined homogeneous regions and segmenting the digital object representation on the basis of the multiplicity of adapted image information items for as long as a predefined repetition condition is satisfied.

13. The method as claimed in claim 1, wherein a material is assigned to each homogeneous region following the segmentation of the digital object representation.

14. The method as claimed in claim 1, wherein the method further includes the following step after the segmentation of the digital object representation: performing a dimensional measurement in the segmented digital object representation on the basis of the boundary regions.

15. A computer program product with instructions which are executable on a computer and which when executed on a computer prompt the computer to carry out the method as claimed in claim 1.

Description

[0047] Further features, details and advantages of the invention emerge from the wording of the claims and from the following description of exemplary embodiments on the basis of the drawings, in which:

[0048] FIG. 1 shows a flowchart of the computer-implemented method;

[0049] FIG. 2 shows a flowchart with sub-steps of an exemplary embodiment of the adapting step;

[0050] FIG. 3 shows a schematic representation of a multi-material transition region; and

[0051] FIGS. 4a-e show a schematic illustration of a sequence of steps of an exemplary embodiment of the method.

[0052] The computer-implemented method for segmenting measurement data from a measurement of an object is denoted in its entirety below using the reference sign 100. The computer-implemented method 100 is first of all explained by means of FIG. 1.

[0053] FIG. 1 shows a flowchart of an embodiment of the computer-implemented method 100 for segmenting measurement data from a measurement of an object. In this case, the object has at least one material transition region.

[0054] In a first step 102, the measurement data relating to the object are determined. In this case, the measurement data can be determined, for example, by means of a computed tomography (CT) measurement. However, other methods for determining the measurement data, for example magnetic resonance imaging etc., are not excluded thereby. The measurement data are used to generate a digital object representation having the at least one material transition region. The digital object representation comprises a multiplicity of spatially resolved image information items relating to the object.

[0055] If the measurement data are CT data, they need not necessarily consist of only a single grayscale value per voxel. They may be multimodal data, that is to say data from a plurality of sensors, or data from a multi-energy CT scan, with the result that a plurality of grayscale values are present for each voxel. Furthermore, results from analyses on the original measurement data can also be used as a further spatially resolved grayscale value in the method 100, for example the result of an analysis of the fiber orientation or of the local porosity. The additional information items, which can be referred to as color channels for example, can therefore be interpreted like colored voxel data even though no colors of the visible spectrum are represented. These additional information items can be advantageously used in the method 100.

[0056] Further, the measurement data comprise at least one artifact. In this case, the measurement data include at least one artifact, that is to say they have a low data quality. The at least one artifact can be, e.g., a streak artifact, noise or other image defects.

[0057] In an optional step 112, a digital representation of a target geometry of the object is aligned with the digital object representation from the determined measurement data according to step 102. The digital representation of a target geometry of the object may be, for example, a CAD representation of the object which was created before producing the object. The geometry in the CAD model need not necessarily be described as a surface or material transition region. Instead or in addition, it may also be implicitly represented as a stack of images, a voxel volume or a distance field. This can be used during additive manufacturing, in particular. Furthermore, this information can be converted into a label field directly and without complicated conversion. However, further forms of representation of the target geometry are not excluded thereby.

[0058] During the alignment, that is to say when adapting the geometric regions of the target geometry to the measurement data, it is possible to take into account which materials are involved in the grayscale value transition and how they are arranged. The orientation of the material transition can emerge from the arrangement of the materials. This information is usually known in the target geometry and can be locally easily determined from the measurement data in each case. This makes it possible to prevent material transition regions which do not match one another from being assigned to one another, which would result in incorrect alignment.

[0059] The alignment can also be carried out by means of a non-rigid mapping between the measurement data and the target geometry.

[0060] At least two homogeneous regions are determined in the measurement data and/or in the digital object representation in a step 104 on the basis of the digital representation of the target geometry. To this end, the image information items are analyzed to the effect of whether homogeneous regions are present, for example regions within a grayscale value interval or with a similar texture. Since the material transition regions and the components of the object or the regions in the object with homogeneous materials are known in the digital representation of the target geometry, homogeneous regions in the measurement data or in the digital object representation generated from the measurement data can be deduced from the digital representation of the target geometry following the alignment in step 112.

[0061] In a step 106, the local similarity of the multiplicity of spatially resolved image information items is analyzed. In this case, a change sequence of the multiplicity of spatially resolved image information items can be analyzed, for example. Alternatively or in addition, a local variance of the multiplicity of spatially resolved image information items can be analyzed. The local variance can be calculated more quickly and more robustly at multi-material transition regions than the use of change sequences. Expected positions of the material transition regions between different components of the object can be determined from the local similarity. These expected positions of the material transition regions are the positions of expected boundaries of the homogeneous regions determined in step 104.

[0062] In a further step 108, the homogeneous regions are then adapted. For this purpose, the extent of each homogeneous region is changed, with the result that a boundary region of each homogeneous region is arranged at the expected position of a material transition region. The expected positions of the material transition regions therefore delimit the homogeneous regions in the object representation.

[0063] In a further step 110, at least two homogeneous regions from the digital object representation are segmented. Step 110, together with steps 106 and 108, can be referred to as main segmentation. In this case, determined homogeneous regions in the digital object representation are adapted and delimited from one another.

[0064] In step 110, information items from further sensors, for example in addition to the measurement data of a computed tomography measurement, can be used. When adapting the position of the material transition regions, the surface information items obtained with these sensors are used to extend the material transition regions in this direction or to prevent material transition regions from being extended beyond the surfaces determined in this manner.

[0065] In the optional step 118, a local similarity of the multiplicity of spatially resolved image information items in the segmented digital object representation can be changed for the purposes of correcting the analyzed local similarity. In the process, it is possible to highlight regions in which material transition regions are present in a user's opinion. In this case, anchor points are set, with the processing being able to be carried out as a material transition region and, as it were, as meta-information, instead of the image information items being changed directly in the representation of the local similarity.

[0066] Further, a local similarity changed by a user can be automatically adapted by way of suitable algorithms such that the changed local similarity collides with other regions that have an equivalent local similarity. This makes handling easier for the user since the accuracy with which the user must change the local similarity is reduced as a result of the assistance by the algorithm.

[0067] Subsequently, step 110 is repeated according to the further optional step 120 in order to obtain an improved segmentation.

[0068] In a further optional step 114, the position of the at least one material transition region in the at least one boundary region can be determined by means of the at least two homogeneous regions.

[0069] In this case, the position of the at least one material transition region can be determined on the basis of a label field, which for example was created in step 104 and for example adapted in step 108. A local material transition region is then calculated with increased accuracy. The position can be defined by coordinates.

[0070] The material transition regions which can represent a local surface, for example, are calculated with greater accuracy on the basis of the adapted label field. A further algorithm specialized for this can be used for this purpose. In this case, the exact position of the material transition region is searched for in a small surrounding area, for example a few voxels. This is usually the prerequisite for exact dimensional measurements which are intended to be carried out on CT data.

[0071] Different algorithms may, in principle, be used for this purpose, for example algorithms which work directly on the measurement data. They can determine the local position of the surface, for example by means of a local or global threshold or by searching for the maximum gradient or for a point of inflection of the grayscale value profile.

[0072] Furthermore, the exact local position of the material transition regions can be determined, for example, in the representation of the local similarity or the gradient or variance representation by adapting a second-degree polynomial to the grayscale value profile, for example. The position of the extremum of this polynomial can be used as the position of the surface.

[0073] However, further algorithms are not excluded by the explanations stated above.

[0074] The knowledge of the, possibly approximate, direction of a surface normal, of a surface arranged in the material transition region or of the materials arranged in the material transition region can be derived from the label field and the representation implicitly stored therein. This knowledge can be used by some algorithms to achieve more exact results. This knowledge, if available, can also be alternatively gathered from the desired geometry, for example a CAD model.

[0075] This is then carried out in combination with an algorithm which requires or can use the information relating to a starting surface to calculate the exact position of the surface on the basis thereof.

[0076] In a further optional step 116, an extent of at least one of the homogeneous regions can be changed on the basis of a visualization of the homogeneous regions in the digital object representation.

[0077] To this end, it is possible to mark individual regions of which it is known that they belong to a material. An algorithm is used to enlarge the relatively small marking up to the next material transition region so that a user can easily mark these regions.

[0078] In this case, in particular, algorithms for region growing or operations such as opening, closing, erosion and dilatation, the inversion, Boolean operators or smoothing tools such as filters can be used to process the regions in the label field.

[0079] The method further includes optional step 136, in which the multiplicity of image information items in the segmented digital object representation are changed by means of an artifact correction method based on the determined homogenous regions.

[0080] Hence, prior knowledge about the homogeneous regions can be used to carry out an artifact correction.

[0081] A further optional step 138 comprises the segmentation of the digital object representation on the basis of the multiplicity of adapted image information items obtained from step 136.

[0082] Hence, a high-quality segmentation then is available, in particular for objects with various homogeneous regions, that is to say regions with different homogeneity in this example. Hence knowledge about the geometry of the object is exploited for the correction in order to obtain, e.g., improved measurement data, optionally, if the measurement data are volume data, via the detour by way of corrected projection data. A segmentation of the various homogeneous regions accordingly allows the corrections to be carried out in optimized fashion. A new, more accurate segmentation is possible on the basis of the corrected data.

[0083] In a further optional step 140, steps 136 and 138 can be repeated until a predefined repetition condition is no longer satisfied. Hence, a new segmentation is carried out iteratively on the basis of the data corrected in steps 136 and 138.

[0084] In a further optional step 142, a material is assigned to each homogeneous region after step 110.

[0085] Further, a dimensional measurement in the segmented digital object representation can be carried out on the basis of the boundary regions in a further optional step 144. The dimensional measurement, which is based on the segmented measurement data or on the segmented digital object representation, can be carried out with very high accuracy as a result of the very accurate determination of the position of the material transition regions.

[0086] FIG. 2 illustrates optional sub-steps of step 108.

[0087] Step 108 may include the two optional sub-steps 122 and 124 in this case. In sub-step 122, at least one artifact region including at least one artifact is determined in the digital object representation on the basis of the at least two homogeneous regions and/or a digital representation of a target geometry. Hence, the digital representation of the target geometry or a preliminary segmentation of the digital object representation can be used to predict the regions of low data quality. On account of previous knowledge about the determination for the measurement data, this for example allows predictions to be made as to where artifacts such as streak artifacts or noise on account of a significant transillumination length of the object will occur in the measurement data or in the digital object representation. Hence, at least one boundary region can be determined in sub-step 124 on the basis of the analyzed local similarity, with a boundary region being determined in the artifact region if the local similarity between the image information items is lower than outside of the at least one artifact region.

[0088] Further, step 108 may include optional sub-steps 126, 128 and 130. Sub-step 126 relates to determining at least one geometry type of a volume region of the digital object representation. In sub-step 128, the determined geometry type is compared with geometry types from the target geometry of the object. Then, at least one boundary region is determined in sub-step 130 on the basis of the analyzed local similarity, with a boundary region being determined in the volume region if the local similarity between the image information items is lower than outside of the volume region and if the determined geometry type is not similar to any of the geometry types from the target geometry of the object. Hence, the homogeneous regions are analyzed in respect of their geometry types arranged there and are compared with the geometry types that should be present in the object. In this case, prior knowledge that geometries of a certain type cannot be present in the object, for example plane surfaces in foam structures, is used. Corresponding regions of reduced homogeneity which reproduce such geometry types are accordingly identified less frequently as a material transition region in the main segmentation.

[0089] Step 108 may further include the optional sub-steps 132 and 134. A quality value of at least one volume region of the digital object representation is determined in sub-step 132. In this case, the quality value specifies a quality or uncertainty of an image information item. Here, the quality value can be calculated for each image information item, for example a voxel or volume region, a type of quality or uncertainty of a grayscale value. In the process, real projection data can be compared to a forward projection, that is to say a calculated projection on the basis of the reconstruction, for example. This can be used for an estimate for where in the volume the data quality is expected to be low since inconsistent measurement data are available for these positions.

[0090] Then, at least one boundary region is determined in sub-step 134 on the basis of the analyzed local similarity in the volume region if the local similarity between the image information items is lower than outside of the volume region and if the determined quality value for the at least one volume region is smaller than a predefined threshold for the quality value. Here, the predefined threshold can be specified by a user or an evaluation rule.

[0091] FIG. 3 shows an example of a multi-material transition region having multiple edges. In this case, the materials 48, 54 and 56 are illustrated in FIG. 3. In this case, the material 48 is arranged between the materials 54 and 56 and has a very short extent in comparison with the other two materials. The material transition region 52 is arranged between the material 48 and the material 54. The material transition region 50 is arranged between the material 48 and the material 56. Overall, the two material transition regions 50 and 52 form a multi-material transition region which can be resolved only with difficulty using conventional methods. Conventional segmentation methods generally detect such regions as merely one material transition region. However, a plurality of material transition regions which are very close together can be detected using the computer-implemented method 100 of the invention described above.

[0092] An example of steps 104, 106 and 108, optional step 142 and some more steps of the method 100 are explained in more detail below by means of FIGS. 4a to 4e, which represent a use of a label field in the context of the method 100. In this case, FIG. 4a schematically shows a digital representation 10 of image information items from measurement data relating to a section of an object. This schematic digital object representation may be, for example, a sectional representation of a computed tomography measurement. In this case, the image information items may be grayscale values which, for reasons of clarity, are not illustrated as grayscale values in FIG. 4a.

[0093] Only transition regions in which the grayscale values change greatly are illustrated as lines.

[0094] The object has the subregions 12, 14, 16 and 18, the image information items of which respectively form homogeneous regions. The subregion 12 is delimited from the subregion 14 by means of the material transition region 20. The subregion 12 is delimited from the subregions 16 and 18 by means of the material transition region 22. The material transition region 24 is arranged between the subregion 16 and the subregion 18. However, in the digital representation 10 of the image information items, the transition regions 26, 28 and 30 can also be seen, but result from shadowing or other artifacts and are not material transition regions.

[0095] In this case, conventional algorithms have problems with distinguishing the transition regions 26, 28 and 30 from material transition regions 20, 22 and 24. Therefore, it is possible to initially carry out an optional pre-segmentation in which the image information items are analyzed.

[0096] In this case, FIG. 4b illustrates the representation 10 of the image information items from FIG. 4a with a grid as a label field 32. The label field 32 may have any desired resolution and may be, for example, coarser than the resolution of the voxels or pixels, may have voxel/pixel accuracy or subvoxel/subpixel accuracy. The label field 32 and/or the distance field will in most cases have the same structure and resolution as the measurement data. However, a lower resolution and therefore larger cells, or an anisotropic resolution and therefore cuboids instead of cubes, can be selected, for example. Further, the structure can also be adapted, for example tetrahedrons instead of cubes. In addition, it is not absolutely necessary to make it possible to represent the material transition regions with subvoxel accuracy with the aid of one or more distance fields. This may become necessary only when or after determining the position of the material transition regions. Therefore, computing time and storage space can be saved if work is carried out only on the label field during segmentation and distance fields are used only when determining the positions of the material transition regions.

[0097] If the image information items are grayscale values, for example, grayscale values below a certain threshold can be assigned to a first material, for example air, which is indicated with the label “o” in FIG. 4b. Grayscale values above a further threshold are assigned to a second material which is illustrated with the label “+” in FIG. 4b. Grayscale values which are between the two thresholds can be assigned to a third material which is indicated with the “x” in FIG. 4b.

[0098] The label field can be combined with a distance field.

[0099] Further, the information items from the target geometry relating to the individual parts of the object, for example in the case of connectors having numbered pins 1-9, can be used to obtain information items relating to the respective materials. Therefore, regions of the same material can also be divided among different parts of the object. In this manner, the practice of evaluating the measurement data becomes clearer. Ideally, the regions are listed or indicated in a hierarchical structure already defined in the target geometry.

[0100] In a similar manner, the regions of the same material which are separated or are not connected in the label field can also be automatically divided into different parts.

[0101] In a next step according to FIG. 4c, a representation 34 which is obtained from analyzing the local similarity of the image information items is determined. This may be a gradient representation, for example. Here, the material transition regions 20 and 22 and 24 are clearly discernible. The transition regions 26 to 30 cannot be seen in this representation. However, in contrast to the representation 10 of the image information items, the individual subregions of the object cannot be qualitatively distinguished from one another. That is to say, the material of a subregion cannot be inferred from the representation according to FIG. 4c.

[0102] The representation 34 is linked to the label field 32, as is illustrated by way of example in FIG. 4d. In this case, it becomes discernible that the homogeneous regions are not delimited by the material transition regions 20, 22 and 24 in all sections. The boundaries of the homogeneous regions are therefore shifted during a main segmentation by relabeling homogeneous regions, for example from “o” to “x” at the arrows 36 and 40 and from “+” to “x” at the arrow 38. The region which had the label “o” at the arrows 36 and 40 has disappeared in FIG. 4e and now belongs to the region with the label “x”. The region with the label “+” was reduced at the arrow 38 and the region with the label “o” was increased. A similar process takes place at the arrows 42, 44 and 46. At the arrows 46 and 44, two previously separate homogeneous regions with the label “+” grow together, with a region with the label “x” disappearing.

[0103] Alternatively or in addition, individual regions which belong to a material can be marked in the digital object representation in order to create the label field. The marking is intelligently automatically extended to the next material transition region. It is also possible to allow a material transition region to be indicated by a user and to automatically increase it until the material transition region collides with other material transition regions, for example, with the result that the user is not forced to indicate a complete material transition region. Accurate marking is therefore not necessary. Furthermore, operations such as opening, closing, erosion and dilatation, an inversion, Boolean operators or smoothing tools such as filters can be used to process the regions in the label field.

[0104] Furthermore, it is possible to highlight regions in which material transition regions are present in a user's opinion. In this case, anchor points are set, with the processing being able to be carried out as a material transition region and, as it were, as meta-information, instead of the image information items being changed directly in the representation of the local similarity.

[0105] Alternatively, erroneous material transition regions can also be removed or weakened. After processing, the label field is recalculated on this basis. In this case, it is also possible to output a warning if no meaningful material transition region can be found at the location defined by the user.

[0106] A surface-based determination of a local data quality can also be used. In this case, a quality value representing the accuracy of the material transition region can be assigned to each material transition region.

[0107] The representation of the local similarity can be calculated from the measurement data, in particular from volume data, using different methods. For example, a Sobel operator, a Laplace filter or a Canny algorithm can be used. The choice of which algorithm is used and how it is parameterized can be manually made by the user. For example, that algorithm which produces the best results when creating the label field can be selected on the basis of a preview image. In addition, the representation of the local similarity can be processed by means of filtering before adapting the label field in order to achieve the best possible results. An example would be the use of a Gaussian filter in order to minimize the negative influence of noise on the result when adapting the label field.

[0108] Depending on the algorithm, it is possible for even smaller regions to be incorrectly segmented after the label field has been adapted. In order to rectify this, sub-steps can optionally also be carried out.

[0109] In this case, morphological operators such as opening and/or closing can be applied to the individual material regions, thus removing small regions.

[0110] Furthermore, contiguous regions below a defined maximum size can be deleted and can be assigned to the surrounding material(s). Regions which are surrounded by two or more other materials can optionally be provided with a differing or larger maximum size or cannot be deleted at all, whereas regions which are surrounded only by one other material are still treated with the above-mentioned maximum size. In this manner, thin layers of a material between two further materials can be retained, for example.

[0111] FIG. 4e shows the result of the main segmentation. Here, the boundaries of the label fields correspond approximately to the material transition regions 20, 22 and 24. The components or materials 12, 14 and 16 are therefore segmented.

[0112] The material transition regions which can represent a local surface, for example, are calculated with greater accuracy on the basis of the adapted label field. A further algorithm specialized for this can be used for this purpose. In this case, the exact position of the material transition region is searched for in a small surrounding area, for example a few voxels. This is usually the prerequisite for exact dimensional measurements which are intended to be carried out on CT data.

[0113] Different algorithms may, in principle, be used for this purpose, for example algorithms which work directly on the measurement data. They can determine the local position of the surface, for example by means of a local or global threshold or by searching for the maximum gradient or for a point of inflection of the grayscale value profile.

[0114] Furthermore, the exact local position of the material transition regions can be determined, for example, in the representation of the local similarity or the gradient or variance representation by adapting a second-degree polynomial to the grayscale value profile, for example. The position of the extremum of this polynomial can be used as the position of the surface.

[0115] However, further algorithms are not excluded by the explanations stated above.

[0116] The knowledge of the, possibly approximate, direction of a surface normal, of a surface arranged in the material transition region or of the materials arranged in the material transition region can be derived from the label field and the representation implicitly stored therein. This knowledge can be used by some algorithms to achieve more exact results. This knowledge, if available, can also be alternatively gathered from the desired geometry, for example a CAD model.

[0117] This is then carried out in combination with an algorithm which requires or can use the information relating to a starting surface to calculate the exact position of the surface on the basis thereof.

[0118] Furthermore, cone beam artifacts, sampling artifacts and noise can be reduced before or after creating the label field.

[0119] The invention is not restricted to one of the embodiments described above, but rather can be modified in various ways.

[0120] All of the features and advantages emerging from the claims, the description and the drawing, including design details, spatial arrangements and method steps, can be essential to the invention both alone and in the wide variety of combinations.