METHOD AND DEVICE FOR MULTI-EDGE DETECTION

Description

[0001] The invention relates to a computer-implemented method for determining material interfaces of an object according to claim 1, as well as a corresponding device according to claim 9 and a computer program product according to claim 10.

[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 state of the art often faces the problem that closely spaced material interfaces cannot be distinguished precisely or, in the worst case, not at all. Such closely spaced interfaces occur, for example, in the coating of a body where the coating is only a few micrometers thick. Furthermore, thin structures or webs such as copper lines on a circuit board can often not be imaged, or only inaccurately, using the methods known from the state of the art. Another example of poorly detectable material interfaces are cracks and pores in workpieces. A crack or a pore is effectively also a sequence of closely spaced material interfaces at which a transition from the material of the workpiece under investigation to air and vice versa takes place.Since such cracks or pores can severely impair the functionality of an inspected workpiece, there is an urgent need in the state of the art for suitable methods that can detect such "multiple edges," i.e., closely spaced material interfaces, during the inspection of a workpiece. Likewise, there is a great need for a technology for detecting coatings and their thickness, since a continuous, undamaged, and sufficiently thick coating is often essential for the desired functionality of a workpiece. Reference is made to the patents EP0930499 A1, US 2006 / 262989 A1, and the publication by Ziou D et al.: "Edge Detection Techniques - An Overview," Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications, 1998, 8 (4), pp. 537-559, regarding edge detection.

[0004] Main features of the invention are set out in claim 1, as well as in claims 9 and 10. Embodiments are the subject of claims 2 to 8.

[0005] 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 plurality 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.

[0006] When determining the position of a material interface from the image information of a measurement point, the edge detection operator considers at least the image information of a subset of the measurement points adjacent to the measurement point in the rasterized representation. Furthermore, 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 arranged directly adjacent to one another within the vicinity of the measurement point.

[0007] Any imaging technique can be used to perform the measurement. Examples include computed tomography, magnetic resonance imaging, positron emission tomography, and 3D sonography.

[0008] The method according to the invention has the advantage that, through the targeted application of an edge-finding operator capable of resolving even directly adjacent material interfaces, 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.

[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 material in question. The measurand under consideration would therefore be the X-ray density of the irradiated material. 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] A "parameter," as described above, can be understood according to the invention not only as a simple number or value but also as an arbitrarily complex quantity. 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 quantity. 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 regarding the materials that abut one another at the material interface(s). For example, the parameter could already encode expected image information from a measurement point.Further, arbitrarily complex information relevant for the determination of a material interface can also be subsumed under the term "parameter".

[0013] As already explained above, methods known in the prior art for detecting material interfaces are often not able 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.

[0014] 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.

[0015] 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 examined. The application of such an operator to an image or a pixel is achieved by discretely convolving the image data of an image with the tensor of the operator.

[0016] 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.

[0017] 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 whether a sequence of directly adjacent material boundary layers needs to be detected. In this case, the parameter dependency consists in the fact that different operators are applied depending on the value of the parameter. However, the parameter dependency can also manifest itself in the fact that one or more of the operations performed when applying an operator depend on a 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.

[0018] For example, the parameter can include the impulse response of the imaging system, also known as the Point Spread Function (PSF), so that this can be taken into account when applying the operator.

[0019] 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.

[0020] 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 multiple edge detection operator is designed to determine the position of the individual material interfaces of a multiple edge, starting from a measurement point, by fitting a theoretical model of the gray values ​​for a multiple edge to the gray values ​​of measurement points and / or to values ​​derived from the gray values ​​in the vicinity of the measurement point. A "multiple edge" is understood to be a sequence of directly adjacent material interfaces. 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.To detect a multiple edge, the measurement point under consideration must be placed in the immediate vicinity of an edge, which may be a multiple edge. The "immediate vicinity of an edge" refers to all those pixels whose gray value is influenced by the gray values ​​of measurement points that represent the edge to be detected due to the impulse response of the system used.

[0021] The theoretical grayscale curve for a multiple edge 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. Furthermore, the theoretical grayscale curve can be determined depending on the expected number of material interfaces.Thus, 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.

[0022] By adapting the theoretical curve of the gray values ​​of a multiple edge to the available gray values, the position of the individual material boundary layers can be determined efficiently. Any method of fitting the theoretical curve to the measured values ​​can be used. For example, the least squares method can be applied here. By selecting the iterations performed for curve fitting, the accuracy of edge detection can be balanced against the resulting computational load.

[0023] According to a further embodiment, the parameterization for a subset of the measuring points assigns at least two parameters to each measuring point of the subset. For the measuring points of the subset, a parameter-dependent edge detection operator is applied to the measuring point for each assigned parameter. For example, it may happen that when creating the parameterization, it is known where potentially multiple edges could occur, but not how many individual material boundary layers are contained in the multiple edges. In this case, the parameterization can define different numbers of individual material interfaces in the multiple edges to be detected, so that the corresponding multiple edge detection operators are applied to the measuring point. For example, a suitable parameterization can define a defined spectrum of potential multiple edges.

[0024] In addition to displaying information about whether a multiple edge is present in the vicinity of a measurement point, the parameterization parameters can also contain further information that can be useful in detecting material boundary layers. Thus, according to a further embodiment, 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-finding operators are then configured to determine the position of at least one material boundary surface along the analysis direction defined by the parameter of the measurement point. 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.

[0025] The analysis direction defined by a parameter can be derived, for example, 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 characteristics of the object under investigation that could not be considered when determining the analysis direction in other ways, for example, by determining a gradient of gray values.

[0026] According to a further embodiment, the previously described definition of analysis directions can be combined with the idea that at least two parameters are assigned to at least one subset of the measuring points. Thus, according to one embodiment, an analysis direction is defined for a subset of the measuring points by at least two of the parameters of a measuring point, with at least one edge-finding operator being applied to the measuring point for each analysis direction, which determines the position of at least one material interface along the respective analysis direction. By specifying several analysis directions in which material interfaces are searched for starting from a measuring point, there is the advantage that even complex geometries that can only be detected imprecisely using methods known in the prior art, such as right-angled corners, can be reliably and precisely detected.For example, when determining the analysis direction from a gradient of gray values, as is known from the prior art, reliable and accurate detection of corners and angles is not possible. Rather, when using an analysis direction determined from a gradient, a "blurring" or "rounding" of the interfaces can be observed in the corner area, resulting in material interfaces in the corner area appearing rounded rather than sharp. However, by splitting the analysis of such a corner into one analysis per edge direction, the aforementioned effects of inaccurate edge detection in the area of ​​angles and corners can be avoided.

[0027] 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 where coatings are provided, where experience has shown that cracks can occur in the material during the production of an object, or where special geometries such as corners and angles are present in the object that must be separately considered when determining the material interfaces. 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.

[0028] 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.

[0029] In addition to using a CAD model, a further 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 where multiple edges are expected using an appropriate input device. Furthermore, the user can also define the analysis directions for the subsequent edge detection using an appropriate interface in the displayed rasterized representation.

[0030] Furthermore, a parameterization, at least with regard to the application of a multiple edge detection operator, can also be derived directly from the rasterized representation obtained from the measurement of the object. For this purpose, the invention provides that determining the parameterization first involves applying a single edge detection operator to the measurement points of the rasterized representation, wherein the single edge detection operator is designed to determine the position of a single material interface in the rasterized representation. Subsequently, an uncertainty measure is determined for the position of the previously determined material interfaces.If the uncertainty measure for a material interface determined in this way exceeds a defined limit value, the determination of the parameterization further includes assigning a parameter to the measuring points in the vicinity of the material interface, whereby the parameter indicates that several material interfaces are arranged directly adjacent to one another within the vicinity of the measuring point and consequently a multiple edge operator should be used.

[0031] An uncertainty measure for the location of a detected material interface can be determined, for example, by determining the gradient of the gray values ​​across the detected material interface. If the material interface is actually an isolated, single material interface, it would be expected that the gradient across the material interface is essentially determined by the impulse response of the system used and the operator used to determine the gradient. Assuming a Gaussian impulse response and Gaussian smoothing to determine the gradient, it would be expected that the gradient across a material interface would have a Gaussian shape.However, if the determined gradient deviates significantly from the expected Gaussian shape, the detected material interface is likely not an isolated edge, but at least a sequence of two or more directly adjacent edges. The threshold value used can be determined, for example, through repeated measurements or parameterization determinations and a comparison of the parameterization with the actual conditions of the object under investigation. In this way, even if information regarding the geometry of the object under investigation is initially missing, a suitable parameterization of the object under investigation can be determined, which can then be used for reliable edge detection.

[0032] To determine an uncertainty measure, it is also possible to directly check how well the gray values ​​in the area of ​​an examined material interface fit to a single edge. When determining the edge position by fitting a model of a single edge to the gray values ​​in the area of ​​the material interface, the results can be χ 2< tests are used to check how well the model of the single edge fits the available gray values. Above a certain threshold for χ 2<, it can then be assumed that the basic assumption that the material interface is a single edge cannot be correct. Consequently, a parameter can be assigned to the corresponding pixels, indicating that a multiple edge is likely present.

[0033] The described determination of the parameterization can be implemented as an iterative process. First, the material interfaces are determined across the entire rasterized representation using an operator for detecting isolated material interfaces. Subsequently, as described above, a check is performed to determine whether the material interfaces thus determined are not isolated interfaces but must be treated as multiple edges. In cases where it is determined that the determined material interface may be a multiple edge, a parameter is set at the corresponding measurement points, indicating the application of an edge detection operator to detect double edges, i.e., two directly consecutive material interfaces.

[0034] Subsequently, a new determination of material interfaces is carried out for all those areas in which such a parameter was set. During the second pass, an edge detection operator for double edges is applied to the measurement points in the areas indicated by the corresponding parameters. Subsequently, the determined double edges are again checked to determine whether they are not a sequence of two material interfaces, but rather a larger number of material interfaces. For all those areas where this is the case, a corresponding parameter is then again set at the relevant measurement points, so that in a subsequent edge detection process, an edge detection operator is applied which is designed to detect a sequence of three directly adjacent material interfaces.

[0035] By iteratively increasing the number of material interfaces to be searched, the rasterized representation can be successively executed according to multiple edges of any order, i.e. with any number of consecutive material interfaces.

[0036] In a further aspect, the invention relates to a 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, wherein the measurement generates a rasterized representation of the object, and wherein the rasterized representation has a plurality of measurement points. A measurement point has at least one piece of image information which indicates a material-specific parameter of the object at the position of the measurement point. The device is designed 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 measurement point 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 from the image information of a measurement point. When determining the position of a material interface from the image information of a measurement point, the edge-finding 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 edge-finding operators is a multiple edge-finding 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 detection operator is applied to a measurement point if and only if at least one of the measurement point's parameters indicates that several material interfaces are located directly adjacent to each other within the vicinity of the measurement point. Determining the parameterization involves the following steps: Applying at least one single edge finding operator to the measurement points of the rasterized representation, wherein the single edge finding operator is designed to determine the position of an individual material interface in the rasterized representation, determining an uncertainty measure for the position of the determined material interfaces if the determined uncertainty measure for a material interface exceeds a defined limit value, assigning a parameter to the measurement points in the vicinity of the material interface, wherein the parameter indicates that several material interfaces are arranged directly adjacent to one another within the vicinity of the measurement point.

[0037] In yet another aspect, the invention relates to a computer program product with computer-executable instructions which, when executed on a computer, cause the computer to perform the method as described above. Further features, details, and advantages of the invention emerge 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 simple material interface and a multiple edge, Fig. 2 schematic representations of a corner with different analysis directions, and Fig. 3 a flow chart for carrying out the method according to the invention.

[0038] In the following, similar or identical features are identified by the same reference symbols.

[0039] In the Fig. 1 a) , which is idealized but technically not feasible, is shown schematically. This image represents the transition between a first region 102 with a first material and a second region 104 with a second material in an object. A two-dimensional representation of the transition is shown on the right. Such a representation can theoretically be obtained, for example, by examining an object using a computer tomography scanner. An object is x-rayed, and after passing through the object being examined, the x-rays illuminate a detector located behind the object. Due to the different x-ray densities of the materials present in an object, the x-rays penetrating the object are attenuated to different degrees, so that the x-ray intensity absorbed by the detector is used to determine the respective density orX-ray absorption of the irradiated media of the object being examined can be determined. In a computed tomography (CT), X-ray images are taken from different angles, and a three-dimensional image of the object is then reconstructed from the total of the X-ray images. The data in . 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.

[0040] At the Fig. 1 a) The material interface 100 shown may, for example, be the transition from air to a metal. Due to the lower X-ray absorption of air, region 102 appears darker than region 104.

[0041] In Fig. 1 a) Also shown on the left is a representation of the X-ray density along arrow 106. Arrow 106 is oriented perpendicular to the material interface 100. The position along arrow 106 is plotted on the horizontal axis, while the corresponding X-ray density at each position is plotted on the vertical axis. The transition between regions 102 and 104 is represented as a sharp interface, which can be mathematically described by a step function.

[0042] As already stated, in Fig. 1 a) only an idealized image of a material interface 100 is shown. However, such an image is technically not feasible due to various circumstances. For example, 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.

[0043] In Fig. 1b a real representation of the same material transition 100 is shown. Here, too, a two-dimensional top view of the material transition 100 is shown on the right, while the course of the X-ray density along the arrow 106 is shown on the left. From the folding of the sharp edge, as shown in Fig. 1 a) shown, with a Gaussian PSF of the imaging system, this results in a blurred edge in which the exact position of the material interface 100 is no longer clearly recognizable. However, 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 from 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 the areas 102 and 104 and then to assume that the edge must be located at the point where the gray value corresponds to half of this difference.

[0044] However, these approaches are problematic when there is not an isolated interface, but a sequence of closely spaced material interfaces. Such a case is illustrated in an idealized, non-blurred representation, for example in Fig. 1 c) Here, too, air is present in the first region 102, for example, while a metal is present in the second region 104. The Fig. 1 c) The image shown can arise, for example, if the metal in region 104 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 108 with a different gray level than that of air and metal. Region 108 is very narrow. A coating can, for example, be a layer with a thickness of a few micrometers.

[0045] 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. 1 c) The edge profile shown is very similar to the edge profile shown in Fig. 1 b) As a result, the methods known in the prior art do not initially allow distinguishing a simple edge from a sequence of closely adjacent edges, i.e., a "multiple edge."

[0046] According to the invention, 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.

[0047] 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.

[0048] The Fig. 2 a) shows a schematic representation of a corner, i.e. a geometry in which two material interfaces 202 and 204 meet at a right angle. If such a geometry is imaged by an imaging technique, such as computer tomography, one obtains, for example, the Fig. 2 a) The figure shown on the right. Fig. 2 a) The material interfaces 202 and 204 shown can, for example, again be the transition from air to a metal.

[0049] The previously described mechanisms, which lead to a "blurring" of inherently sharp edges, cause a rounding of the inherently sharp corner 210 in the area of ​​the corner 210, i.e. the point at which the material interfaces 202 and 204 meet, as shown in Fig. 2 a) shown on the right. Algorithms such as the aforementioned Canny algorithm, which utilize the gradient of a grayscale 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 210 in the case of a blurred corner. Examples of this are shown in the Fig. 2 b) The local gradients along the material interfaces are represented by arrows 212. In the areas where the material interfaces 202 and 204 have a straight course and the gray values ​​of the material interfaces 202 and 204 are not influenced by the transition in the area of ​​the tip 210, the gradient is actually perpendicular to the material interfaces 202 and 204. Thus, good results in determining the position of the material interfaces can be expected here when applying the Canny operator.

[0050] However, this approach no longer works in the area of ​​peak 210. As in Fig. 2 b) As can be clearly seen, the gradient in the area of ​​the tip 210 only gradually pivots from the orientation in the area of ​​the first material interface 202 to the orientation in the area of ​​the second material interface 204. However, if the corner were perfectly imaged, the gradient at the tip 210 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 only a rounded corner. The exact position of the tip 210 and the exact course of the material interfaces 202 and 204 up to the tip cannot be determined by the Canny operator.

[0051] The inventive solution to this problem is exemplified in the Fig. 2 c) shown. According to the invention, when determining the material interfaces 202 and 204, the direction along which a material interface is to be searched for is determined in advance. In this case, a first analysis direction 214 (left) is determined for a first material interface 202 and a second analysis direction 216 (right) is determined for a second material interface 204. The analysis directions are maintained across the entire width of the material interfaces 202 and 204. 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 210. 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. 2 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 202 and 204 is possible, particularly in the area of ​​the tip 210.

[0052] Although in the Fig. 2 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.

[0053] 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.

[0054] 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, for example, be 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. However, the method can also be applied to the measurement results of other imaging methods, such as magnetic resonance imaging or 3D ultrasound.

[0055] 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 204, 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 predetermined by the arrangement of the individual sensors in the sensor array used.However, it is also possible to define a different grid.

[0056] After the object under investigation has been reconstructed and rasterized, a parameterization of the rasterized object is determined in step 306. For this purpose, a user interface can be provided, for example, through which a user can mark areas of the reconstructed, examined object where multiple edges are present. Furthermore, the parameterization can also specify a direction in which, starting from a voxel, material interfaces should be searched for.

[0057] 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 being examined, which indicates that a multiple edge or a curved edge should be searched for here.

[0058] After the parameterization of the reconstructed object has been completed, parameter-dependent edge detection operators are applied to the reconstructed object in step 308. Edge detection 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 detection operator applied is determined by the parameter assigned to the voxel. For example, if the 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 detection operator is applied to the examined voxel, which searches for just such a multiple edge. It is quite possible that several parameters are assigned to a voxel.For example, the parameterization of a voxel can indicate that a sequence of multiple material interfaces exists in a specific direction. The multiple edge operator is then configured to create a theoretical model of the grayscale gradient corresponding to the parameterization values ​​and compare the model with the grayscale values ​​of the surrounding voxels. The exact position of the material interfaces can then be determined by comparing the actual grayscale values ​​with the theoretical model.

[0059] 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.

[0060] All features and advantages arising from the claims, the description and the drawings, including design details, spatial arrangements and process 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

[0061] 100Material interface 102First area 104Second area 106Direction 108Third area 202Material interface 204Material interface 206Area 208Area 210Tip 212Arrow 214First analysis direction 216Second analysis direction

Claims

1. Computer-implemented method for determining material interfaces of an object by means of at least one measurement on the object, wherein a rasterized representation of the object is generated by the measurement, wherein the rasterized representation has a multiplicity of measurement points, wherein a measurement point has at least one item of image information which indicates a value of a measurement variable for the object at the position of the measurement point, wherein the method has the following steps: • 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, • applying at least one parameter-dependent edge-detection operator to the measurement points of the rasterized representation, wherein an edge-detection operator is designed to determine the location of at least one material interface in the rasterized representation, wherein, in the determination of the location 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, wherein 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, and wherein the multiple edge-detection operator is applied to a measurement point if and only if at least one of the parameters of the measurement point indicates that a plurality of material interfaces are arranged directly adjacent to one another within the surroundings of the measurement point, and wherein determining the parameterization comprises the following steps: • applying at least one single edge-detection operator to the measurement points of the rasterized representation, wherein the single edge-detection operator is designed to determine the location of an individual material interface in the rasterized representation, • determining a measure of uncertainty for the location of the material interfaces determined, if the measure of uncertainty determined for a material interface exceeds a defined threshold value, assigning a parameter to the measurement points in the surroundings of the material interface, wherein the parameter indicates that a plurality of material interfaces are arranged directly adjacent to one another within the surroundings of the measurement point.

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 location of the measurement point, and wherein the multiple edge-detection operator is designed to determine the location of the individual material interfaces of a multiple edge proceeding from a measurement point by fitting a theoretical model of the grey-scale values for a multiple edge to the profile of the grey-scale values of measurement points in the surroundings of the measurement point.

3. Method according to Claim 1 or 2, characterized in that the parameterization for a subset of the measurement points assigns in each case at least two parameters to each measurement point of the subset, wherein for the measurement points of the subset, a parameter-dependent edge-detection operator is applied to the measurement point for each assigned parameter.

4. Method according to any one of the preceding claims, characterized in that at least one of the parameters of a measurement point defines an analysis direction within the rasterized representation, wherein the edge-detection operators are designed, when applied to a measurement point, to determine the location of at least one material interface along the analysis direction defined by the parameter of the measurement point.

5. Method according to Claim 4, characterized in that an analysis direction is defined for each subset of the measurement points by at least two of the parameters of a measurement point of the subset, wherein, for each analysis direction, at least one edge-detection operator is applied to the measurement point which determines the location of at least one material interface along the analysis direction in question.

6. Method according to any one of the preceding claims, characterized in that the parameterization is determined from a model of the object under examination.

7. Method according to Claim 6, characterized in that the model is a CAD model.

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

9. 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 a rasterized representation of the object is generated by the measurement, wherein the rasterized representation has a multiplicity of measurement points, wherein a measurement point has at least one item of image information which indicates a value of a measurement variable for the object at the position of the measurement point, wherein the device is designed 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 measurement points of a subset of the measurement points of the representation, • apply at least one parameter-dependent edge-detection operator to the measurement points of the rasterized representation, wherein an edge-detection operator is designed to determine the location of at least one material interface in the rasterized representation from the image information of a measurement point, wherein, in the determination of the location 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, wherein 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, and wherein the multiple edge-detection operator is applied to a measurement point if and only if at least one of the parameters of the measurement point indicates that a plurality of material interfaces are arranged directly adjacent to one another within the surroundings of the measurement point, and wherein the device is furthermore designed to the effect that determining the parameterization comprises the following steps: • applying at least one single edge-detection operator to the measurement points of the rasterized representation, wherein the single edge-detection operator is designed to determine the location of an individual material interface in the rasterized representation, • determining a measure of uncertainty for the location of the material interfaces determined, if the measure of uncertainty determined for a material interface exceeds a defined threshold value, assigning a parameter to the measurement points in the surroundings of the material interface, wherein the parameter indicates that a plurality of material interfaces are arranged directly adjacent to one another within the surroundings of the measurement point.

10. Computer program product having instructions which are executable by a computer and, when executed on a computer, cause the computer to carry out the method according to any one of Claims 1 to 8.