METHOD AND DEVICE FOR DETECTING CORNERS

Description

[0001] The invention relates to a computer-implemented method for determining material interfaces of an object according to the preamble of claim 1, as well as a corresponding device according to claim 8 and a computer program product according to claim 9.

[0002] Determining the location of material interfaces in an object using imaging techniques is a ubiquitous problem in the state of the art. A material interface describes the precise boundary surface within an object, such as a workpiece, along which different materials adjoin one another. In addition to interfaces within an object, such as those forming a transition from a plastic to a metal, a material interface can also be understood as the surface that separates an object from its surroundings or the ambient air. Thus, the determination of interfaces can also be used, in particular, to determine the dimensions of objects under investigation.One technical area in which the precise determination of interfaces is becoming increasingly important is, for example, the computed tomographic examination of workpieces, which is used, among other things, in production for quality assurance.

[0003] Regardless of the imaging method used, the problem in the state of the art is that known algorithms for determining material interfaces are not capable of determining the exact position of material interfaces in areas where two or more interfaces meet at an angle. In particular, determining the exact position of the meeting point of the differently aligned material interfaces is not possible using state-of-the-art methods due to smearing effects when generating images of the geometry under investigation. Such geometries are frequently found on workpieces, for example, in the area of ​​cut edges or drill holes. The exact determination of the position of such angles is necessary for the exact determination of the dimensions of the geometries and is essential, for example, in the area of ​​quality assurance.Consequently, there is a great need for a technology that enables the precise determination of "corners," i.e., the areas where two or more material interfaces meet at an angle. Patents US 2006 / 262989 A1 and EP0930499 A1 disclose methods for image enhancement and more precise determination of image edges, respectively.

[0004] Main features of the invention are specified in claim 1, as well as in claims 8 and 9. Embodiments are the subject of claims 2 to 8. In a first aspect, the invention relates to a computer-implemented method for determining material interfaces of an object by means of at least one measurement on the object, wherein the measurement generates a rasterized representation of the object. The rasterized representation has a multiplicity of measurement points, wherein each measurement point has at least one piece of image information. The image information indicates a value of a measured variable for the object at the position of the measurement point. The method according to the invention first comprises determining a parameterization of the rasterized representation of the object, wherein the parameterization assigns at least one parameter to each of the measurement points of a subset of the measurement points of the representation.Subsequently, at least one parameter-dependent edge-finding operator is applied to the measurement points of the rasterized representation. An edge-finding operator is designed to determine the position of at least one material interface in the rasterized representation.

[0005] When determining the position of a material interface from the image information of a measurement point, the edge detection operator takes into account at least the image information of a subset of the measurement points adjacent to the measurement point in the rasterized representation. At least one of the parameters of a measurement point defines an analysis direction within the rasterized representation. When applied to a measurement point, the edge detection operators are designed to determine the position of at least one material interface along the analysis direction defined by the parameter of the measurement point. For a subset of the measurement points, an analysis direction is defined by at least two of the parameters of a measurement point, with at least one edge detection operator being applied to the measurement point for each analysis direction, which determines the position of at least one material interface along the respective analysis direction.

[0006] Any imaging technique can be used to perform the measurement. Examples include computed tomography, magnetic resonance imaging, positron emission tomography, and 3D sonography.

[0007] The analysis direction defined by a parameter can, for example, be derived from knowledge of the basic geometric shape of the object under investigation. Experiments have shown that a fixed definition of the analysis direction can improve the precision of edge detection compared to prior art methods that, for example, determine the analysis direction from a gradient of gray values. Furthermore, the definition of the analysis direction can take into account special geometries or circumstances of the object under investigation that could not be taken into account when determining the analysis direction in another way, for example by determining a gradient of gray values. The analysis direction used to determine a material interface is preferably oriented perpendicular to the material interface to be determined.

[0008] Specifying multiple analysis directions in which material interfaces are searched for starting from a single measurement point has the advantage that even complex geometries, such as right-angled corners, which are only imprecisely detectable using state-of-the-art methods, can be reliably and precisely detected. For example, determining the analysis direction from a gradient of gray values, as is known from the state of the art, does not allow for reliable and precise detection of corners and angles. Rather, using an analysis direction determined from a gradient results in a "blurring" or "rounding" of the interfaces near the corners, resulting in material interfaces near the corners appearing rounded rather than pointed.However, if the analysis of such a corner is split into one analysis per edge direction, the previously mentioned effects of improper edge detection in the area of ​​angles and corners can be avoided.

[0009] The rasterized representation of the object under investigation, which is generated as a result of the measurement, can be either two-dimensional or three-dimensional. In the case of a three-dimensional representation, the measurement points are volume pixels or voxels, whereas in a two-dimensional representation, the image points are simple pixels. The image information of a voxel represents the average value of a measured quantity for the object, which is obtained by convolving the neighborhood around the observed voxel with the point spread function (PSF) of the system used. It is also possible to decompose a three-dimensional representation of an object into a series of two-dimensional cross-sectional images of the three-dimensional representation.

[0010] A "value of a measurand" is generally a numerical value that quantifies a specific property of a material in the object under investigation in such a way that the corresponding material can be distinguished from other materials in the rasterized representation. The value of the measurand should not be confused with the parameter(s) of a measurement point, which are assigned to the measurement points as a result of the parameterization of the rasterized representation. While the value of the measurand describes the material or a material property of the object under investigation, the parameterization parameters serve as additional information that can be used in the determination of material interfaces.For example, if the imaging technique used for the measurement is computed tomography, the value of the measurand can describe the degree of attenuation experienced by X-rays when passing through the corresponding material. The measurand under consideration would therefore be the X-ray density of the irradiated medium. However, if the imaging technique is magnetic resonance imaging, the value of the measurand can be the resonance frequency or the relaxation time of the material.

[0011] The grid used for the rasterized display can, in principle, have any shape. In the simplest case, the grid has orthogonal axes that are divided into segments at regular intervals in all three spatial directions. The volume circumscribed by each segment in all spatial directions then defines exactly one voxel. However, the grid used is not limited to such a uniform and orthogonal grid. Rather, the axes of the grid can also follow other arrangements, resulting in a different, for example non-cubic, shape for the voxels. For example, a grid can also be hexagonal. In this case, not all voxels or pixels in the rasterized display have to be the same size. Rather, it is also possible, for example, to combine a large number of measurement points with identical image information into a single common voxel or pixel.

[0012] According to the invention, a "parameter," as described above, can be understood as any quantity of any complexity. To define an analysis direction, the parameter can, for example, specify a direction in the grid of the rasterized representation in the form of a vector. Furthermore, a parameter could also contain information regarding the materials that collide at a material interface. For example, the parameter could already encode expected image information from a measurement point. Other, arbitrarily complex information relevant for determining a material interface can also be subsumed under the term "parameter" below.

[0013] In the field of digital image processing, operators for analyzing and processing image data are known in many different forms. A prominent example of an operator frequently used in digital image processing for edge detection is the Sobel operator. The Sobel operator is essentially a tensor of rank n with defined entries. The rank of the tensor depends on the number of dimensions of the image being analyzed. The application of such an operator to an image or pixel is achieved by discretely convolving the image data of an image with the tensor of the operator.

[0014] In the context of this application, however, the term "operator" does not necessarily refer to a mere tensor. Rather, a single operator within the context of the present invention can be any complex combination of convolution tensors, arithmetic operations, curve fits, or the like, which are executed sequentially in a specific sequence and each further process the results of previous operations of the operator. In the context of this application, an operator does not necessarily have to include a convolution tensor in the sense of the Sobel operator described above. Rather, it is also possible for an operator to operate entirely without performing a convolution of the image data, using a convolution tensor. The only relevant factor in defining an operator is that the application of the operator to the image data achieves the desired result, namely the detection of material interfaces.

[0015] The meaning of the term "applying a parameter-dependent operator" can vary depending on the application and the type of operator. For example, as previously discussed, a parameter can indicate the direction in which a material interface should be searched for. In this case, the parameter dependency consists in the fact that, depending on the value of the parameter, one or more of the operations performed when applying an operator are adapted to the analysis direction specified by the parameter or take this into account. However, the parameter dependency can also manifest itself in the fact that different operators are applied depending on the value of the parameter. A parameter can influence the execution of an operator in a variety of ways. For example, a parameter can encode an offset that should be taken into account when performing a calculation operation.Furthermore, a parameter can also specify a specific set of measurement points to be considered when applying the operator. It is also possible for the parameter to encode additional information that influences the application of the operator. For example, the parameter can contain the impulse response of the imaging system, also known as the point spread function (PSF), so that this can be considered when applying the operator.

[0016] According to the invention, the position of a material interface is not determined by the grid or the arrangement of the grid points. Rather, the position of a material interface determined during the method can also be located between the grid points. Thus, the method according to the invention also enables sub-pixel or sub-voxel-precise determination of material interfaces, whereby interfaces can be determined with an accuracy of 1 / 100 of a voxel or less, depending on the quality of the measurement data used.

[0017] An "analysis direction" can be understood as a direction within the grid of the selected representation of the object. The analysis direction can be specified, for example, by a vector defined in the coordinate system spanned by the grid.

[0018] According to one embodiment, the image information of a measurement point includes at least one gray value that indicates the value of the measured variable for the object at the location of the measurement point. The at least one edge-finding operator is designed to determine the position of the material interface starting from a measurement point by fitting a theoretical model of the gray values ​​for a material interface to the gray values ​​of measurement points and / or values ​​derived from the gray values ​​in the vicinity of the measurement point. The term "at the location of the measurement point" describes precisely that point or spatial region of the object being examined which corresponds to the pixel or voxel under consideration in the rasterized representation. In order to detect a material interface, the measurement point under consideration must be placed in the immediate vicinity of the material interface.The "near environment of a material interface" is understood to mean the set of all those pixels whose gray value is influenced by the gray values ​​of measuring points that represent the material interface to be detected due to the impulse response of the system used.

[0019] The theoretical grayscale curve for a material interface can be determined by considering a variety of influencing factors. For example, this makes it possible to consider the effect of the PSF of the imaging system used to acquire the measurement points when creating the theoretical model. The PSF of an imaging system generally leads to a "smearing" of the measured values, so that sharp edges of an object under investigation, as they actually exist at material interfaces, appear as a blurred, gradual transition in the image. When determining the theoretical curve, other factors can also be considered, if known, which lead to a non-ideal image of the object when measuring the object. Any suitable method of fitting the theoretical curve to the measured values ​​can be used.For example, the least squares method can be applied here. By choosing the number of iterations performed for curve fitting, the accuracy of edge detection can be balanced against the resulting computational load.

[0020] If an analysis direction is specified by the parameter of a measurement point, this is taken into account when determining a material interface by a fit according to one embodiment in that at least one edge-finding operator is configured to determine the position of a material interface by the fit along the analysis direction indicated by the at least one parameter. For example, the course of the gray values ​​can be determined starting from the considered measurement point along a vector in the direction of the analysis direction. The position of a material interface can then be determined by fitting a theoretical course of the gray values ​​for a material interface to the course of the gray values ​​determined in this way.

[0021] The parameterization used according to the invention to determine material interfaces is determined, according to one embodiment, from a model of the object under investigation. For example, it is possible to directly derive from a model the locations of corners and angles and how the interfaces that meet at the corner are aligned. The parameter model determined in this way can then be transferred to the data from a measurement on the object, so that the subsequent determination of the material interfaces can be carried out using suitable edge-finding operators, which in turn depend on the parameters of the parameterization. Such a model can be derived through a further measuring process, for example through an optical measurement. For example, the surface of the object to be examined can first be scanned using a laser so that a surface model can be created.

[0022] Alternatively, according to one embodiment, the model of the object under investigation is a CAD model. The use of a CAD model has the advantage that the model of the object under investigation is already available in full digital form with the planned dimensions, so it can be transferred to measurement data from a measurement on the object with little effort.

[0023] In addition to using a CAD model, another embodiment can also provide for the parameterization to be generated by at least one user input. For example, a user monitoring the examination of the object can inspect the rasterized representation of the object being examined generated during the measurement and, based on visual inspection or empirical values, mark areas containing corners and angles using an appropriate input device. Furthermore, the user can also define the analysis directions for the subsequent edge detection using a corresponding interface in the displayed rasterized representation.

[0024] In addition to the previously described embodiments for determining the parameterization, the parameterization is determined according to the invention from the image information of at least a subset of the measurement points. The subset of pixels used here is preferably selected such that it maps at least the material interfaces present in the object representation. Preferably, the subset of pixels also maps an area around the material interfaces so that a sufficient amount of image information is available for determining the parameterization. The direct determination of the parameterization from the image information itself has the advantage that automating edge detection is easier, since apart from the actual measurement data, no additional information is required for determining the parameterization and the subsequent edge detection.

[0025] According to a further embodiment, at least one of the edge detection operators is a multiple edge detection operator, which, when applied to a measurement point, is designed to determine the position of at least two directly adjacent material interfaces in the object. The multiple edge operator is applied to a measurement point precisely when at least one of the parameters of the measurement point indicates that several material interfaces are directly adjacent to one another within the vicinity of the measurement point.

[0026] The parameter-dependent application of an edge-finding operator, which is capable of resolving even directly adjacent material interfaces, has the advantage that even very thin structures such as cracks and coatings in an examined object can be detected. Experiments have shown that algorithms for the targeted search for a sequence of directly adjacent material interfaces entail increased computational effort compared to algorithms for determining a single, isolated material interface. However, this increased computational effort is reduced to a manageable level according to the invention by applying a multiple edge-finding operator based on a parameterization of the measurement points only when the application is indicated by a corresponding parameter of the measurement points. Thus, the computational effort for detecting multiple edges is reduced to a minimum.However, if the parameterization of a measuring point does not indicate that a multiple edge detection operator should be applied, the method provides for an edge detection operator to be applied to the measuring point which is only designed to detect a single material interface.

[0027] For example, a single parameter of a measurement point can indicate whether or not there is a direct sequence of adjacent material interfaces in the vicinity of the measurement point. In this case, the parameter could be defined as a binary value. The parameter could also provide information about how many material interfaces are present in the immediate vicinity of the measurement point. Finally, a parameter could also contain information about the materials that collide at the material interface(s).

[0028] Methods known in the prior art for detecting material interfaces are often unable to distinguish a dense sequence of material interfaces arranged directly next to one another from a single material interface, or to precisely determine the respective positions of the individual material interfaces in a dense sequence of material interfaces arranged next to one another.

[0029] This is usually due to blurring effects in the generated images of the object under investigation. The term "directly adjacent material interfaces" therefore refers to all those sequences of material interfaces that can no longer be resolved as individual material interfaces by an edge-finding operator designed solely to detect a simple material interface. The term "directly adjacent" can refer to different length units depending on the imaging technique used and the measurement situation. For a highly magnified image of an object with a very small focus of the measuring equipment, the term "directly adjacent" can refer to a distance between two interfaces of a few micrometers, whereas at lower magnifications, a sequence of "directly adjacent material interfaces" can also exist with a distance of a few millimeters between the material interfaces.

[0030] According to one embodiment, a parameter of a measurement point can indicate not only whether a multiple edge is present in the immediate vicinity of the measurement point, but also how many individual material boundary layers the multiple edge contains. Accordingly, when applying the multiple edge detection operator, the exact expected theoretical gray value distribution can be used to determine the positions of the material boundary layers, which was determined assuming the correct number of individual material boundary layers.

[0031] If the position of the individual material interfaces is determined by adjusting the theoretical gray value curve to the actually measured gray values, the theoretical gray value curve can be determined depending on the expected number of material interfaces. By adjusting the theoretical gray value curve of a multiple edge to the available gray values, the position of the individual material interfaces can be determined efficiently.

[0032] In a further aspect, the invention relates to a device for carrying out measurements on an object and for determining material interfaces of an object by means of at least one measurement on the object, wherein the measurement generates a rasterized representation of the object. The rasterized representation has a plurality of measuring points, wherein each measuring point has at least one piece of image information which indicates a value of a measured variable for the object at the position of the measuring point. The device is designed to carry out at least one measurement on the object and to determine a parameterization of the rasterized representation of the object obtained from the measurement, wherein the parameterization assigns at least one parameter to each of the measuring points of a subset of the measuring points of the representation.Furthermore, the device is designed to apply at least one parameter-dependent edge-finding operator to the measurement points of the rasterized representation, wherein an edge-finding operator is designed to determine the position of at least one material interface in the rasterized representation.

[0033] When determining the position of a material interface from the image information of a measurement point, the edge-finding operator considers at least the image information of a subset of the measurement points adjacent to the measurement point in the rasterized representation. At least one of the parameters of a measurement point defines an analysis direction within the rasterized representation, wherein the edge-finding operators, when applied to a measurement point, are designed to determine at least one material interface along the analysis direction defined by the parameter of the measurement point.For a subset of the measurement points, an analysis direction is defined by at least two of the parameters of a measurement point of the subset, wherein for each analysis direction at least one edge finding operator is applied to the measurement point, which determines the position of at least one material interface along the respective analysis direction, wherein the parameterization is determined from the image information of at least one subset of the measurement points.

[0034] In yet another aspect, the invention relates to a computer program product having computer-executable instructions which, when executed on a computer, cause the computer to carry out the method according to one of claims 1 to 7 8-.

[0035] 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: Fig. 1 schematic representations of a corner with different analysis directions, Fig. 2 schematic representations of a simple material interface and a multiple edge, and Fig. 3 a flow chart for carrying out the method according to the invention,

[0036] In the following, similar or identical features are identified by the same reference symbols.

[0037] The Fig. 1 a) shows a schematic representation of a corner, i.e., a geometry where two material interfaces 102 and 104 meet at a right angle. A material interface characterizes precisely the interface where a first material and a second material meet. If such a geometry is imaged using an imaging technique, such as computer tomography, one obtains, for example, the Fig. 1 a) Figure shown on the right.

[0038] When examining an object using computed tomography, the object is examined using X-rays. After passing through the object, the X-rays illuminate a detector located behind the object. Due to the varying X-ray densities of the materials present in an object, the X-rays penetrating the object are attenuated to varying degrees, so that the respective density or X-ray absorption of the media through which the object is being examined can be deduced from the X-ray intensity absorbed by the detector. In computed tomography, X-ray images are taken from different directions, and a three-dimensional image of the object is then reconstructed from the sum of the X-ray images. Fig. 1 a) The depicted representation is a two-dimensional sectional view, which can be derived from the three-dimensional image. However, the invention is not limited to such a two-dimensional image, but can also be applied to a three-dimensional image. The two-dimensional representation was chosen solely for reasons of ease of representation.

[0039] In the Fig. 1 a) The material interfaces 102 and 104 shown can, for example, each represent the transition from air to a metal. Due to the lower X-ray absorption of air, the area 106 on the left appears darker than the area 108 on the right.

[0040] If you compare the ideal corner, which is in Fig. 1 a) shown on the left, with the corner imaged by an imaging technique in Fig. 1 a) right, the actually sharply defined material interfaces 102 and 104 appear washed out and blurred. In particular, the tip 110 of the corner shown, i.e. the point where the material interfaces 102 and 104 meet, appears rounded. The reason for such blurred imagery has various technical reasons. It is known from the theory of electrical signal processing that a signal can only ever be processed with a limited bandwidth. Consequently, a sharp edge, which mathematically corresponds to the superposition of an infinite number of periodic signals, is not feasible in signal and image processing. Rather, the point spread function (PSF) of the imaging system always flows into the image of an object. Mathematically, the effect of the band-limited imaging system corresponds to a convolution of the signal to be imaged with the PSF of the system.The PSF of an imaging system often has the approximate shape of a Gaussian bell.

[0041] From the folding of the sharp edges or material interfaces 102 and 104, as shown in Fig. 1 a ) with a Gaussian PSF of the imaging system, blurred edges result where the exact position of the material interfaces 102 and 104 is no longer clearly recognizable. In the area of ​​the corner, the convolution of the actual object with the PSF of the imaging system also leads to a rounding of the interface profile. There are various approaches in the prior art for determining an edge position from such an edge profile despite the blurred interface. A prominent example of this is the Canny algorithm, which determines the edge position using the gradient and the second derivative of the gray value profile. Another approach to determining the edge position is to determine the difference between the maximum and minimum gray values ​​in areas 106 and 108 and then to assume that the edge must be at the point where the gray value corresponds to half of this difference.

[0042] However, algorithms that use the gradient of a gray value to determine the position of a blurred material interface inevitably produce an error in determining the position of the material interfaces in the area of ​​the tip 110 in the case of a blurred corner. For this purpose, examples are provided in the Fig. 1 b) The local gradients along the material interfaces are represented by arrows 112. In the areas where the material interfaces 102 and 104 have a straight course and the gray values ​​of the material interfaces 102 and 104 are not influenced by the transition in the area of ​​the tip 110, the gradient is actually perpendicular to the material interfaces 102 and 104. Thus, good results in determining the position of the material interfaces can be expected here when applying the Canny operator.

[0043] However, this approach no longer works in the area of ​​peak 110. As in Fig. 1. b ), the gradient in the area of ​​the tip 110 only gradually pivots from the orientation in the area of ​​the first material interface 102 to the orientation in the area of ​​the second material interface 104. However, if the corner were perfectly imaged, the gradient at the tip 110 would have to "flip" instantly from its first orientation to the second orientation. However, this is not the case due to the blurred corner. Consequently, the Canny operator would not detect a sharp corner, but merely a rounded corner. The exact position of the tip 110 and the exact course of the material interfaces 102 and 104 up to the tip cannot be determined by the Canny operator.

[0044] The inventive solution to this problem is exemplified in the Fig. 1 c) shown. According to the invention, when determining the material interfaces 102 and 104, the direction along which a material interface is to be searched for is determined in advance. A first analysis direction 114 (left) is defined for a first material interface 102 and a second analysis direction 116 (right) is defined for a second material interface 104. The analysis directions are maintained across the entire width of the material interfaces 102 and 104. This leads, among other things, to a search for a material interface from individual measuring points in several directions in the area of ​​the tip 110. Thus, according to the invention, several parameters are assigned to these measuring points, each of which specifies an analysis direction. This is shown in the Fig. 1 c) However, for the sake of clarity, this is not explicitly shown. By specifying the analysis direction, an exact determination of the position of the material interfaces 102 and 104 is possible, particularly in the area of ​​the tip 110.

[0045] Although in the Fig. 1 While only the two-dimensional case is shown, the invention can also be applied analogously to a three-dimensional image of an object. In this scenario, individual measurement points can be assigned more than two parameters to define an analysis direction.

[0046] In the Fig. 2 a) An idealized, but technically impractical, image of a material interface 200 is shown schematically. This image represents the transition between a first region 202 containing a first material (e.g., air) and a second region 204 containing a second material (e.g., a metal) in an object. A two-dimensional, idealized representation of the transition is shown on the right. The different material-specific parameters of the first and second materials are represented by different gray values. For example, the material-specific parameter can be its X-ray density.

[0047] In Fig. 2 a) On the left, a representation of the material-specific parameter or X-ray density is shown along the arrow 206. The arrow 206 is oriented perpendicular to the material interface 200. The position along the arrow 206 is plotted on the horizontal axis, while the corresponding X-ray density at each position is plotted on the vertical axis. The transition between the regions 202 and 204 is shown as a sharp interface, which can be mathematically described by a step function. As already explained, in Fig. 2 a) only an ideal image of a material interface 100 is shown. However, such an image is not technically feasible due to various circumstances, as already explained above.

[0048] In Fig. 2 b) A real representation of the same material transition 200 is shown. Here, too, a two-dimensional top view of the material transition 200 is shown on the right, while the X-ray density curve along arrow 206 is shown on the left. For the reasons already explained, the sharp transition 200 from the first region 202 to the second region 204 is blurred due to the impulse response of the system used to image the structure, so that the exact position of the interface 200 is initially no longer directly recognizable.

[0049] The Canny algorithm described above, as well as other edge detection algorithms, are basically able to use different approaches to Fig. 2 b) The position of the material interface 200 can be deduced from the blurred course of the material interface 200 shown in Figure 1. However, these approaches are problematic when there is not an isolated interface, but a sequence of closely adjacent material interfaces. Such a case is shown in an idealized, non-blurred representation, exemplified in Figure 1. Fig. 2 c) Here, too, air is present in the first region 202, for example, while a metal is present in the second region 204. The Fig. 2 c) The image shown can arise, for example, if the metal in region 204 is coated on its surface with a specific X-ray absorption that differs from the absorption of metal. The coating is then visible as an additional region 208 with a different gray level than that of air and metal. Region 208 is very narrow. A coating can, for example, be a layer with a thickness of a few micrometers.

[0050] The previously described "smearing" of the edge profile due to the PSF of the system now leads to the smeared profile of the simple material interface being barely distinguishable from a sequence of closely adjacent material interfaces. In fact, the result of a folding of the Fig. 2 c) The edge profile shown is very similar to the edge profile shown in Fig. 2 b) As shown in Figure 1. Consequently, the methods known in the prior art initially do not allow distinguishing a simple edge from a sequence of closely adjacent edges, i.e., a "multiple edge," because these algorithms are not capable of detecting the individual interfaces.

[0051] According to one embodiment, however, the position of the individual material interfaces can also be determined from the smeared profile of a multiple edge if it is already known from the examination of the gray value profile that it is not an isolated interface but a multiple edge. Knowing that a multiple edge is present, it can be deduced what such a multiple edge would look like after convolution with the system's PSF. By comparing the resulting model with the existing gray value profile and / or with a profile of values ​​derived from the gray values, the positions of the individual material interfaces of the multiple edge can be determined.According to the invention, parameters assigned to the pixels indicate whether an isolated interface should be assumed when examining a gray value gradient in the area of ​​a material interface, or whether a multiple edge is present, so that a corresponding model should be used as a basis.

[0052] Within the scope of the present invention, it is also quite possible to examine geometries that represent a combination of the circumstances shown in Figures 1 and 2. For example, it is also quite possible that one or both of the Fig. 1 material interfaces 102 and 104 shown are coated again, so that the Fig. 2 c) The situation illustrated arises. In this case, particularly when examining tip 110, it can be provided that several closely spaced material interfaces are searched for from a single measuring point in several specified directions. In this way, the exact positions of the material interfaces can be reliably determined even in very complex geometries.

[0053] The method according to the invention is not limited to a direct sequence of two material interfaces. Rather, it is also possible to specify any number of closely adjacent interfaces, so that, for example, a sequence of five adjacent material interfaces is assumed when analyzing the gray values. Such a sequence can arise, for example, in a painted surface where a primer, a color coat, and a clear coat are applied one above the other, each with a thickness of only a few micrometers.

[0054] In Fig. 3 A flowchart of an embodiment of the method according to the invention is shown. The method can be implemented, for example, with a device comprising at least one computed tomography scanner and a data processing device connected to the computed tomography scanner. The data processing device does not necessarily have to be a coherent, physical entity, but can also be implemented in a decentralized manner, for example, in the sense of cloud computing.

[0055] In a first method step 302 of the Fig. 3 In the method 300 shown, a measurement is performed on an object to be examined. The object can be, for example, a component that has been removed from a production line and is to be tested for quality assurance purposes. The measurement is preferably a computed tomography measurement, as already described above.

[0056] However, the method can also be applied to the measurement results of other imaging techniques, such as magnetic resonance imaging or 3D ultrasound.

[0057] The measurement initially generates raw data which, in the case of computed tomography, for example, corresponds to a large number of x-ray images of the object under examination from a large number of directions. From the raw data thus obtained, a three-dimensional image of the object under examination is generated in step 304, wherein the image is rasterized. To reconstruct the object, for example, a filtered backprojection can be applied to the previously determined raw data. The rasterization of the reconstructed object can then be achieved, for example, by overlaying the reconstructed object with a three-dimensional grid, wherein each volume element of the grid is assigned the corresponding local gray value of the object in the area of ​​the volume element (voxel). Typically, in computed tomography, for example, the grid is specified by the arrangement of the individual sensors in the sensor array used.However, it is also possible to define a different grid.

[0058] Following reconstruction and rasterization of the examined object, a parameterization of the rasterized object is determined in step 306. For this purpose, a user interface can be provided, for example, via which a user marks areas of the reconstructed, examined object where special geometries, such as corners and angles, or multiple edges are present. Furthermore, during the parameterization, one or more directions can be specified in which, starting from a voxel, material interfaces are to be searched for. In addition to input via a user interface, such parameterization for specifying directions for determining an edge profile in the area of ​​corners and angles can also be determined directly from the measurement data itself.

[0059] In addition to user input, parameterization can also be determined by initially scanning the reconstructed object for material interfaces. For example, assuming that the entire object has only straight, simple material interfaces, the entire object can be scanned to determine a large number of edge positions. The edge positions thus determined can then be checked to determine how well the grayscale curve present at the edge position matches the theoretically expected grayscale curve for an isolated, straight material interface.If it is determined, for example using a chi-square test, that the gray value curve found does not match the expected gray value curve sufficiently well, a parameter is assigned to the voxels in the vicinity of the material interface under investigation, which indicates that a multiple edge or a curved edge should be searched for here.

[0060] After the reconstructed object has been parameterized, parameter-dependent edge-finding operators are applied to the reconstructed object in step 308. Edge-finding operators are applied to each voxel or at least a subset of the voxels, which determine the position of material interfaces from the gray value of the voxel and the gray values ​​of the neighboring voxels. The type of edge-finding operator applied is determined by the parameter assigned to the voxel. If, for example, one or more analysis directions are defined by the parameter, corresponding edge-finding operators are applied to the voxel, which search for a material interface in the analysis directions indicated by the parameter.Furthermore, if a parameter of the examined voxel indicates that there is a multiple edge in the vicinity of the voxel, which is made up of three individual material interfaces, a corresponding edge-finding operator is applied to the examined voxel, which searches for such a multiple edge in the specified analysis direction. It is quite possible that several parameters are assigned to a voxel. For example, the parameterization of a voxel can indicate a plurality of analysis directions, whereby only for some of the analysis directions is the indication that a multiple edge is expected in the analysis direction. To determine the material interfaces, the edge-finding operators are designed to create a theoretical model of the gray value curve that corresponds to the parameterization values ​​and to compare the model with the gray values ​​of the surrounding voxels.By comparing the actual gray values ​​with the theoretical model, the exact positions of the material interfaces can then be determined.

[0061] The invention is not limited to one of the embodiments described above, but can be modified in many ways within the scope of the claims.

[0062] All features and advantages arising from the claims, the description and the drawings, including design details, spatial arrangements and method steps, may be essential to the invention both individually and in a wide variety of combinations within the scope of protection of the claims. Bezugszeichenliste

[0063] 102 material interface 104 material interface 106 area 108 area 110 tip 112 arrow 114 first analysis direction 116 second analysis direction 200 material interface 202 first area 204 second area 206 arrow 208 additional area

Claims

1. Computer-implemented method for determining material interfaces of an object from at least one measurement on the object, a rasterized representation of the object being produced by means of the measurement, the rasterized representation having a plurality of measurement points, a measurement point having at least one piece of image information which indicates a value of a measurement variable for the object at the position of the measurement point, the method comprising the following steps: • determining a parameterization of the rasterized representation of the object, the parameterization assigning at least one parameter to each of the measurement points of a subset of the measurement points of the representation, • applying at least one parameter-dependent edge-detection operator to the measurement points of the rasterized representation, an edge-detection operator being designed to determine the location of at least one material interface in the rasterized representation, and in the determination of the location of a material interface from the image information of a measurement point, the edge-detection operator taking into consideration at least the image information of a subset of the measurement points adjacent to the measurement point in the rasterized representation, at least one of the parameters of a measurement point defining an analysis direction within the rasterized representation, wherein, when applied to a measurement point, the edge-detection operators are designed to determine at least one material interface along the analysis direction defined by means of the parameter of the measurement point, an analysis direction being defined in each case for a subset of the measurement points by means of at least two of the parameters of a measurement point of the subset, at least one edge-detection operator being applied to the measurement point for each analysis direction, which edge-detection operator determines the location of at least one material interface along the particular analysis direction, the parameterization being determined from the image information of at least a subset of the measurement points.

2. Method according to Claim 1, characterized in that the image information of a measurement point comprises at least one grey-scale value which indicates the value of the measurement variable for the object at the position of the measurement point, the at least one edge-detection operator being designed, on the basis of a measurement point, to determine the location of the material interface by means of a fit of a theoretical model of the grey-scale values for a material interface to the curve of the grey-scale values of measurement points in the vicinity of the measurement point.

3. Method according to Claim 2, characterized in that at least one edge-detection operator is designed to determine the location of a material interface by means of the fit along the analysis direction indicated by the at least one parameter.

4. Method according to any of the preceding claims, characterized in that the parameterization is determined from a model of the object being investigated.

5. Method according to Claim 4, characterized in that the model is a CAD model.

6. Method according to any of the preceding claims, characterized in that the parameterization is generated by at least one user input.

7. Method according to any of the preceding claims, characterized in that at least one of the edge-detection operators is a multiple edge-detection operator, which is designed, when applied to a measurement point, to determine the location of at least two directly adjacent material interfaces in the object, wherein the multiple edge-detection operator is applied to a measurement point exactly when at least one of the parameters of the measurement point indicates that a plurality of material interfaces are arranged directly adjacent to each other within the vicinity of the measurement point.

8. Device for performing measurements on an object and for determining material interfaces of an object by means of at least one measurement on the object, a rasterized representation of the object being produced by means of the measurement, the rasterized representation having a plurality of measurement points, a measurement point having at least one piece of image information which indicates a value of a measurement variable for the object at the position of the measurement point, the device being designed to: • carry out at least one measurement on the object, • determine a parameterization of the rasterized representation of the object obtained from the measurement, the parameterization assigning in each case at least one parameter to the measurement points of a subset of the measurement points of the representation, and • apply at least one parameter-dependent edge-detection operator to the measurement points of the rasterized representation, an edge-detection operator being designed to determine the location of at least one material interface in the rasterized representation, in the determination of the location of a material interface from the image information of a measurement point, the edge-detection operator taking into consideration at least the image information of a subset of the measurement points adjacent to the measurement point in the rasterized representation, at least one of the parameters of a measurement point defining an analysis direction within the rasterized representation, wherein, when applied to a measurement point, the edge-detection operators are designed to determine at least one material interface along the analysis direction defined by means of the parameter of the measurement point, an analysis direction being defined in each case for a subset of the measurement points by means of at least two of the parameters of a measurement point of the subset, at least one edge-detection operator being applied to the measurement point for each analysis direction, which edge-detection operator determines the location of at least one material interface along the particular analysis direction, the parameterization being determined from the image information of at least a subset of the measurement points.

9. Computer program product having instructions executable by a computer, which when executed on a computer cause the computer to carry out the method according to any of Claims 1 to 7.