RELATED APPLICATION INFORMATION

This patent claims priority from International PCT Patent Application No. PCT/EP2018/061939, filed May 8, 2018 entitled, “METHOD FOR DETERMINING UNCERTAINTIES IN MEASUREMENT DATA FROM THE MEASUREMENT OF AN OBJECT”, which claims priority to German Patent Application No. 10 2017 114 811.6, filed Jul. 3, 2017 entitled, “METHOD FOR DETERMINING UNCERTAINTIES IN MEASUREMENT DATA FROM THE MEASUREMENT OF AN OBJECT”, all of which are incorporated herein by reference in their entirety.

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BACKGROUND

The invention relates to a computer-implemented method for determining uncertainties in measurement data from a measurement of an object.

A multiplicity of methods for measuring and subsequently imaging objects, for example workpieces, are known in the prior art. In the industrial environment in particular, these measurement methods have become established in the meantime as a selection resource for workpiece testing. Both methods which image only the surface of an object and methods which make it possible to completely represent the internal structure of an object are found in this case. For testing workpieces, a surface or surface geometry of a workpiece is usually checked with regard to its dimensions and is compared with a reference value. It is therefore possible to test, for example in a random manner, whether a production process for a workpiece is able to comply with the desired specifications for a workpiece.

In addition to the dimensions of the workpiece, an important criterion for testing workpieces is an uncertainty of the dimensions derived from measurement data of a measurement. In this case, depending on the imaging method used, a multiplicity of error sources can result in an uncertainty in the dimensions of an image of an object. Whereas systematic imaging errors can be determined, for example, by using a material measure, few methods which can also take into account statistical imaging errors to a sufficient extent and can quantify them, in particular, are known in the prior art.

Against this background, the present invention is based on the objective technical object of providing an improved method for determining uncertainties in measurement data from a measurement of an object which overcomes the above-mentioned disadvantages of the prior art.

Main features of the invention are stated in this document.

In a first aspect, the invention relates to a computer-implemented method for determining uncertainties in measurement data from a measurement of an object, wherein a digital representation of the object is generated by the measurement. The object representation has a multiplicity of items of image information relating to the object, wherein an item of image information indicates a value of a measurement variable for the object at a defined position of the object. Statistical noise is superimposed on the image information, wherein the method has the following steps.

In a first method step, the measurement data are first of all determined. A distance field is then determined from the image information relating to the object representation, wherein the distance field has a multiplicity of distance values. In this case, a distance value indicates, for a particular point in the distance field, the shortest distance between the point and a closest material boundary surface of the object. A strength of the statistical noise in the image information relating to the measurement points of the measurement data is then determined and an uncertainty of the distance values of the distance field is determined on the basis of the strength of the statistical noise. An uncertainty of the position of at least one point on at least one material boundary surface is then determined from the uncertainty of the distance values of the distance field.

In order to determine the uncertainty of the position of a point on at least one material boundary surface, the position of a point of a material boundary surface can first of all be determined, for example, from a subset of distance values of the distance field. The mean uncertainty of all of those distance values which were taken into account when determining the position of the point of the material boundary surface is then assumed as the uncertainty of the determined position of the point. In addition to forming a simple mean value, weighting of the uncertainties of the distance values which were taken into account when determining the position of the point of the material boundary surface can also be provided. In this case, a lower weight can be assigned to the uncertainties of comparatively high distance values, for example, than to the uncertainties of comparatively low distance values.

The invention is based on the knowledge that a significant part of the uncertainty of imaging of an object by means of an imaging method is caused by statistical noise to which the recorded measurement data are subject. In this case, statistical noise may arise as a result of a multiplicity of factors. For example, noise may already be inherent in a measurement method used to determine the measurement data. For example, an electronic detector used to determine the measurement data may have a defined noise behavior. Furthermore, further noise may also be introduced as a result of the processing of measurement data or raw data on which the measurement data are based. In this case, statistical noise is understood as meaning noise whose effect on the noisy measurement data follows a statistical, that is to say substantially random, distribution, for example a normal distribution. The type of statistical distribution on which the noise is based can be locally different here over the image of the object, in which case, in addition to symmetrical distributions which include the above-mentioned normal distribution, the noise may also be based on asymmetrical distributions.

In this case, the statistical noise is usually characterized by a defined strength with which it influences the image information relating to the object representations. If the strength of the statistical noise is known, it is possible to estimate how great the uncertainty of an item of distance information relating to the distance field is, which distance information is derived from the noisy image information. If the uncertainties of the distance values of a distance field are known, it is again possible to directly derive an uncertainty of a position of a material boundary surface, which is derived from the distance field, and, in particular, the position of individual points on the material boundary surface of a represented object therefrom. Consequently, when determining material boundary surfaces of an object from the image information relating to a measured object representation, the method according to the invention allows errors to be estimated for positions of material boundary surfaces of the object or of points on such material boundary surfaces which are derived from the object representation. It is therefore possible to assess geometrical properties of an imaged object with an error by means of the method according to the invention.

In this case, the distance field can code the position of a material boundary surface in substantially two ways. In a first approach, a distance value of the distance field represents only the absolute value of the distance between a corresponding point in the distance field and the closest material boundary surface. However, in this case, as a result of the pure distance information at a point in the distance field, the side of a material boundary surface on which the point is arranged is not yet clear. However, this information can be additionally coded in the distance field by virtue of the distance values additionally being provided with a sign. In this case, a positive sign is assigned to distance values of data points on a first side of the material boundary surface, whereas a distance value having a negative sign is assigned to data points on the second side of the material boundary surface. The sign of a distance value of a data point can then be used to derive, for example, whether a data point is inside a geometry or a body or outside. This additional information can be used to determine dimensions of the imaged object.

In this case, such a distance field with signed distance values is known as a “signed distance field” (SDF). According to one embodiment, an unsigned distance field can be converted in this case into a signed distance field by adapting the distance values in such a manner that, although their absolute value remains unchanged, the gradient of the entire distance field is equal to 1 at each point.

A measurement from which the image information is obtained should be understood in this case as meaning any desired form of imaging of the object or properties of the object. For example, the measurement can be carried out within the scope of a magnetic resonance tomographic examination. The image information obtained in this process quantifies properties of the object, for example material composition, position of surfaces or similar parameters, which can be derived from measurement variables, for example a spin relaxation time or the like. In order to determine the measurement data, both the performance of a measurement and the reading of a storage medium can be provided in this case. For example, it is possible to resort to measurements which have already been carried out and archived data which are intended to be subsequently assessed with respect to an uncertainty of the image.

The above-described strength of the statistical noise in the image information is a measure which describes how greatly the image information is influenced by the statistical noise. The effect of the noise superimposed on the measurement data or image information is substantially the fact that the determined numerical value for a measurement variable differs by a particular amount from the numerical value actually determined without noise. In this case, a numerical value may be both too small and too large on account of the noise. There are different approaches for determining the strength of the noise which will be discussed in yet more detail below. In this case, the strength of the statistical noise, like an item of image information as well, can be represented as a numerical value which describes how greatly the image information differs from the actually expected value on account of the noise.

In order to determine an uncertainty of a distance value from the strength of the statistical noise, the following procedure can be used according to one embodiment: an error in the image information relating to a defined point of the object is first of all determined from the strength of the statistical noise. A computing rule which is used to determine distance values from the image information relating to the object representation is then determined. The uncertainty of the distance value is then determined from the effect of the error on the result of the computing rule. In order to determine the error in an item of image information, the numerical value of the determined strength of the statistical noise, for example, can be assumed as an error interval for the numerical value of an item of image information.

Alternatively, the numerical value of the determined strength of the statistical noise can also be converted, with the result that the error in the image information can be quantified by the value obtained in this manner. This may be necessary, for example, if the strength of the statistical noise is derived from an item of information which initially differs from the actual image information, but can be converted into the latter. In this case, an error interval for the numerical value of an item of image information need not necessarily be arranged symmetrically around the numerical value. Rather, an error interval may also be distributed asymmetrically around the numerical value of an item of image information, in particular if the statistical noise is based on an asymmetrical statistical distribution. For example, it is possible for an error interval which extends from 147 to 156 to be assigned to an item of image information having a numerical value of 150 from the estimation of the statistical noise. Both a symmetrical and an asymmetrical error interval can likewise also be determined for stating the uncertainty of a distance value or of a position of a point on a material boundary surface.

The computing rule for determining the distance values may assume various forms in this case. However, it will in any case include, as an input value, the image information relating to the object representation, which information is converted into a distance value on the basis of a mathematical formula. The effect of an error in the input values on the result of the calculation can be determined from the knowledge of such a formula, for example by means of the Gaussian error propagation.

For example, according to one embodiment, the uncertainty of a distance value can be determined from the quotient of the strength of the statistical noise in the image information on which distance value is based and the gradient of the image information in the region of that point in the distance field which is assigned to the distance value.

It has already been stated above that the strength of the statistical noise in the image information relating to the measurement data is determined as part of the method according to the invention. In this case, the strength of the noise can be determined globally for the entire measurement image or the entire object representation, for example. This is useful, for example, when the statistical noise which is superimposed on the measurement data is reflected to the same extent over the entire imaged region.

In most cases, however, the effect of the statistical noise in the image information is different in different regions of an object representation. This is due to different characteristics of the imaging apparatus for different regions of the image and to a relationship of the effect of the noise of the image information itself, which relationship can often be observed. For this reason, another embodiment provides for the method to comprise the subdivision of the measurement points into spatial regions of the object, wherein the strength of the statistical noise is respectively determined separately for the different spatial regions of the measurement data. In this case, the regions are preferably selected in such manner that the effect of the statistical noise on the image information is constant to the greatest possible extent within a region. In this case, a single value for the strength of the statistical noise can be assigned to a complete region.

In order to determine the strength of the statistical noise for a region, one embodiment can then provide for this strength to be determined from the image information relating to a subset of the measurement points of the region. This makes it possible to reduce the computing complexity for determining the noise information without the fear of a significant loss of information. On account of the homogeneity of the effect of the noise within a region owing to the corresponding choice of the region, no relevant gain in information relating to the strength of the noise can be expected any more after a particular number of input values for determining the strength of the noise by a further addition of further points or measurement data relating to the points. However, the accuracy with which the strength of the noise is estimated from the variance is improved with an increasing number of values taken into account in the process. The desired accuracy with which the variance is estimated in comparison with the computing load produced as a result can therefore be effectively estimated, and the number of processed measured values can accordingly be adapted.

The strength of the statistical noise in the image information for one of the regions can be determined as follows according to one embodiment:

An average value of the image information relating to the region is first of all determined. The mean deviation of the image information relating to the region from this average value is then determined and the mean deviation is defined as the strength of the statistical noise in the image information. This approach can be used, in particular, in regions with a homogeneous distribution of the effect of the statistical noise and a homogeneous distribution of the image information. A homogeneous distribution of the image information is present, for example, if only a single, defined material of an imaged object is represented by means of corresponding image information over a particular image section.

The information determined in this manner relating to the strength of the statistical noise can also be extrapolated, for example, to regions with an inhomogeneous distribution of the image information. For this purpose, provision may be made, for example, for different regions to be defined in which the above-mentioned determination of the strength of the statistical noise is possible on account of the homogeneity of the image information and/or the effect of the statistical noise. Regions which extend between such homogeneous regions can then be assessed with regard to the effect of the statistical noise by means of an interpolation method.

In an alternative approach, the strength of the statistical noise may be the standard deviation of the statistical noise according to one embodiment. The use of the standard deviation of the statistical noise as a measure of the strength of the noise has the advantage here that the standard deviation indicates a generally easily determinable measure of uncertainty of a variable which is subject to a statistical fluctuation, as is the case in statistical noise.

In regions with an inhomogeneous distribution of the grayscale values, for example in the region of material boundary surfaces, the strength of the statistical noise can be determined, for example, by first of all creating a theoretical model for the progression of the grayscale values in the corresponding region. For this purpose, a theoretical model of the grayscale values can be fitted to the actual grayscale values by means of a fit method, for example. The deviations of the individual grayscale values from the progression of the grayscale values which is provided by the fitted model can then be interpreted as being caused by the statistical noise and can be used as a basis for determining the strength of the statistical noise.

In this case, one embodiment provides for the standard deviation of the statistical noise for a point in the object representation to be determined from the image information within a defined environment around the point. For example, in a two-dimensional representation of an object, a circle of a particular radius can be drawn around a point in the object representation, wherein all image information within this circle is used to determine the standard deviation. The computing complexity for determining the standard deviation can thus be reduced, while the determination of the standard deviation can be simultaneously restricted to a region within which the effect of the statistical noise is constant to the greatest possible extent. In this case, the size of the defined environment can be dimensioned, in terms of its extent, in such a manner that there are sufficient statistics from which a reliable item of information relating to the strength of the statistical noise can be derived. When selecting the size of the environment, the resulting computing complexity for determining the strength of the noise can be taken into account at the same time, with the result that the scope of the statistics can be weighed up against the resulting computing complexity.

In addition to the above-described determination of uncertainties with regard to the position of material boundary surfaces of an object or of individual points on such material boundary surfaces, one embodiment provides for the information relating to the uncertainty of distance values to be used to estimate an error for further properties of the represented object. For this purpose, provision is made for the method to also comprise the determination of at least one dimension of the object from the distance values of the distance field and the determination of an uncertainty of the dimension on the basis of the uncertainty of the distance values. In this case, a dimension can be understood as meaning, for example, the diameter of a drilled hole or the length of an edge. Dimensions of the represented object can be directly determined here, for example, from the positions of material boundary surfaces coded by the distance values of the distance field.

In this case, a dimension and the uncertainty of a dimension can be determined both directly from the distance values and the corresponding uncertainties themselves and from the determined positions of the material boundary surfaces and the determined uncertainty of the positions of points on the material boundary surfaces.

In addition to the above-described determination of dimensions of a represented object directly from the material boundary surfaces coded by the distance field, the actually expected geometrical shape of an object can also be taken into account when determining dimensions according to another embodiment. For this purpose, one embodiment provides for the determination of a dimension of the object from the distance values of the distance field to comprise determining and fitting a target geometry of the object into the distance field by using a fit method. The dimension of the object is then determined according to the embodiment on the basis of the target geometry which has been fitted in in this manner.

This makes it possible to directly compare an envisaged target geometry of the represented object and the true actual geometry, wherein corresponding dimensions of the target geometry can be directly compared with the corresponding dimensions of the object determined from the actual geometry taking into account the corresponding uncertainties of the dimensions. For example, it is possible to check whether predefined manufacturing tolerances have been complied with in the case of an examined object or whether an examined object can be used for further assembly steps on account of the determined dimensions taking into account the uncertainties.

In this case, a fit method which is used to fit the determined target geometry of the object into the distance field can be understood as meaning any mathematical method which is suitable for fitting a specific geometry into digital data in such a manner that the geometry has the best possible congruence with the digital data from the representation of the object. In this case, the uncertainty of the distance values can be taken into account when determining the error propagation when using a fit method.

According to one embodiment of the invention, for example for fitting in the determined target geometry, it is possible to use the least squares method which is also known as a Gaussian fit in the prior art. In this case, a target geometry is fitted into the material boundary surfaces represented by the measurement data in such a manner that the mean square distance of the target geometry from the material boundary surfaces from the digital representation is as short as possible. This method can generally be carried out with little computing complexity and is particularly suitable when there are no boundary conditions in terms of the position of the target geometry relative to the material boundary surfaces represented by the measurement points in the digital representation.

In some cases, however, the situation may occur in which a determined target geometry is intended to be fitted into the digital representation of the object with a number of boundary conditions. In this respect, embodiments provide for the determined target geometry to be fitted into the distance field as an inscribed or circumscribing figure. In this case, an inscribed figure should be understood as meaning a figure which lies completely within the material boundary surfaces of the object which are coded by the distance field. Conversely, a circumscribing figure is a figure which lies completely outside the material boundary surface coded by the distance field. For example, the use of an inscribed figure is useful, in particular, when the internal diameter of a drilled hole is intended to be determined by fitting in a corresponding target geometry, namely a cylinder. In this case, it is usually only relevant for practical applications whether the drilled hole has a certain minimum diameter. Fitting in the target geometry as an inscribed figure ensures in this case that the dimensions of the target geometry which has been fitted in represent the minimum diameter of a drilled hole.

In the opposite case in which a pin projecting from an object, for example, is intended to be represented by a target geometry, it is advantageous if the target geometry, again a cylinder, is fitted into the distance field as a circumscribing figure. This is because the maximum diameter of the projecting pin is represented in this case by the geometry which has been fitted in. In this case, it is entirely possible to have to respectively separately decide, in different regions of the imaged object, whether a target geometry to be fitted in is intended to be fitted into the distance field as an inscribed or circumscribing figure.

According to another embodiment, it is also possible to use a minimum zone fit to fit in the determined target geometry. The individual selection of which fit method is used depends on the respective application situation, as described above.

According to one embodiment, the distance field used during the method according to the invention can be determined in this case by first of all determining the position of material boundary surfaces from the image information relating to the object representation. A closest material boundary surface to a data point and the respective distance between the data points and the respective closest material boundary surface are then respectively determined for the data points of the data field. The respectively determined distance is then assigned to the respective data points as a distance value. Edge detection methods which are generally known in the prior art can be used to determine the position of material boundary surfaces from the image information relating to the object representation. Examples of such methods are the Canny algorithm or the ISO50 algorithm.

According to one embodiment, the object representation is a rastered representation of the object, wherein the rastered representation has a multiplicity of measurement points of a measurement of the object which are arranged in a raster, wherein a measurement point has at least one item of image information.

Another embodiment also provides for the measurement to be a computer tomographic measurement, wherein the image information relating to a measurement point describes the local x-ray absorption of the object at the location of the measurement point. Computer tomography has the advantage here that inner regions of an object can also be determined and imaged, with the result that a non-destructive integrated representation of an object is possible.

Particularly when using a computer tomographic measurement to generate the object representation, the statistical distribution on which the noise in the image information is based can differ from a symmetrical distribution, which can also include the above-mentioned normal distribution, and can vary locally over the object representation. This circumstance is due to the fact that, in the case of a computer tomographic measurement, projection data are first of all measured and have to be converted into an image of the object by means of corresponding reconstruction mathematics. However, the mathematics used here are generally non-linear. A direct consequence of this is that the actually substantially symmetrical Gaussian noise behavior of a detector of a computer tomograph, does not necessarily result in a symmetrical noise behavior of the image information relating to the object representation. Rather, the statistical distributions on which the noise in the image information is based can also become asymmetrical and/or locally vary greatly in the object representation. It can often be observed, for example, that bright regions of a computer tomographic image, which indicate strong x-ray absorption by the examined object, have stronger noise than dark regions of the image.

For this reason, it may be useful to derive the noise behavior or the strength of the statistical noise in the image information from the projection data on which the object representation is based, rather than from the image information relating to the object representation.

In another aspect, the invention relates to a computer program product having instructions which can be executed on a computer and, when executed on a computer, cause the computer to carry out the method as described above.

