DE102021119462A1 - Procedure for calibrating an optical measurement setup - Google Patents

Abstract

The invention relates to a method for calibrating an optical measurement setup with a measurement volume (10) and a plurality of cameras (141, 142, 143), by means of which object points (12) in the measurement volume (10) are compared to image points (201, 202, 203) of corresponding camera images ( 161, 162, 163) can be imaged. Such a mapping can be described mathematically by a base mapping function known from a pre-calibration. The method includes: a) simultaneous imaging of the measurement volume (10) by means of the cameras (141, 142, 143), b) identifying those pixels (201, 202, 203) that are imaged on each camera image (161, 162, 163). Object point (12) are assigned,c) determining an approximated object point (24) which best corresponds to the imaged object point (12) at the time of imaging, andd) calculating an error in the basic imaging function in relation to the imaged object point (12) representative difference vector (28).e) providing an extended mapping function, comprising the basic mapping function and a correction vector field, the correction vector field consisting of a grid of support points (32) to which correction vectors (30) are assigned, by which the support points ( 32) Corresponding points to which the mapping function is to be applied as part of a measurement data evaluation, in addition to the application of the base mapping function locally are to be postponed.

Description

field of invention

1. a) zeitgleiches Abbilden des Messvolumens mittels der Kameras zur Erzeugung je eines Kamerabildes für jede Kamera,

sowie die mehrfach, nämlich jeweils für einen anderen Objektpunkt, durchgeführten Schritte:

• b) Identifizieren derjenigen Bildpunkte, die einem auf jedem Kamerabild abgebildeten Objektpunkt zugeordnet sind,
• c) Ermitteln, unter Verwendung der identifizierten Bildpunkte, desjenigen Raumpunktes als den approximierten Objektpunkt, der nach vorgegebenen Optimierungskriterien am besten demjenigen Raumpunkt entspricht, an dem sich der abgebildete Objektpunkt zum Abbildungszeitpunkt tatsächlich befand, und
• d) Berechnen eines für einen Fehler der Basis-Abbildungsfunktion in Bezug auf den abgebildeten Objektpunkt repräsentativen Differenzvektors.

The invention relates to a method for calibrating an optical measurement setup with a measurement volume and with at least two cameras, by means of which object points located at spatial points in the measurement volume can be imaged from different viewing angles onto pixels of corresponding camera images, such an image being mathematically based on a basis known from a precalibration mapping function (usually with errors) can be described, comprising the step:

1. a) simultaneous imaging of the measurement volume using the cameras to generate one camera image for each camera,

as well as the steps carried out several times, namely for a different object point:

• b) identifying those pixels that are assigned to an object point displayed on each camera image,
• c) determining, using the identified image points, that point in space as the approximated object point which, according to predetermined optimization criteria, best corresponds to that point in space at which the imaged object point was actually located at the time of imaging, and
• d) calculating a difference vector representative of an error of the basis mapping function with respect to the imaged object point.

State of the art

Such a calibration method is known from EP 1 926 049 B1 .

In many optical measurement tasks, it is necessary to infer three-dimensional positions within a measurement volume from two-dimensional image data. For example, for measuring currents, it is known to inoculate the flowing fluid with optically detectable particles and to observe them using cameras. A measurement volume through which the fluid flows is observed by several cameras from different observation angles. In order to be able to make precise statements about the details of the flow, it is necessary to be able to precisely determine the position of the particles, which are regarded as representative of the flow, in the measurement volume. A stereoscopic approach is often used for this, in which particle positions in the measurement volume can be calculated using camera images recorded simultaneously from different angles. Essential for this is the precise knowledge of the so-called imaging function of each camera, i.e. the function that relates a three-dimensional position in the measurement volume, referred to here as a “spatial point”, to the corresponding two-dimensional position in the camera image, referred to here as a “pixel”. Points in space at which there is actually an optically detectable object in the measurement volume at the time of imaging, e.g. a flowing particle, an area of a fixed structure or similar, are referred to here as "object points". Those skilled in the art will understand that the term “point”, particularly in the context of object and image points, is not to be interpreted in the narrow, mathematical sense. An extended element, represented by its center, for example, can also be understood as an object point; analogously, a "pixel" can be understood, for example, as an extended structure in the camera image, represented by its center, for example.

geschrieben, wo der Index i eine spezielle Kamera identifiziert, x, y die zweidimensionalen Koordinaten im zugeordneten Kamerabild bezeichnen und X, Y, Z die (auch „Welt“-Koordinaten genannten) Raumkoordinaten im Messvolumen bezeichnen. Typische Formen für Abbildungsfunktionen sind sog. Pinhole-Funktionen oder Polynome.The mapping function M is usually given in the general form $$\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)=M_i\left(X,Y,Z\right)=\left(\begin{array}{c}{M}_{ix}\left(X,Y,Z\right)\\ M_{iy}\left(X,Y,Z\right)\end{array}\right),$$

written, where the index i identifies a specific camera, x, y denote the two-dimensional coordinates in the associated camera image and X, Y, Z denote the spatial coordinates (also called "world" coordinates) in the measurement volume. Typical forms for mapping functions are so-called pinhole functions or polynomials.

The determination of these mapping functions is referred to as calibration.

A two-stage calibration method is known from the generic publication mentioned above. First, a pre-calibration is carried out, which is typically done using so-called calibration plates. For this purpose, a structure provided with known markings is introduced into the measurement volume and imaged using the cameras. By comparing the camera images with the known structure, the corresponding parameters of the basic mapping functions can be calculated. The term "basic mapping function" is intended to express the fact that it is a mapping function of the above form that can be used, but which is still open to refinement in order to achieve greater accuracy, ie a better correspondence between "world" and "map". is. The pre-calibration is in fact comparatively rough and, in order to be suitable for certain precision measurements, still needs such a refinement, which is shown in a refined image tion function M' results. The case also occurs that in the time between pre-calibration and the actual measurement, the optical structure changes, for example due to mechanical instabilities, or there are changes in the basic imaging function during the measurement, for example due to vibrations. The mapping functions are often in the form of polynomials, pinhole functions or ray tracing fields, but can also be designed differently, in particular more complexly. The notion of basis mapping function is not intended to imply limitation to any particular mathematical form.

The publication mentioned proposes a correction of the pre-calibrated basic mapping functions using known triangulation methods. First, a common object point that is visible to all cameras must be imaged on all camera images. The corresponding pixels are identified. By inverting the basic imaging functions, the triangulation lines of sight are then determined on which the object point in the measurement volume could lie in order to be imaged at the respectively identified image point in the camera images (because of the dimensional difference between the two-dimensional camera image and the three-dimensional measurement volume, there is a clear point assignment not possible by applying the inverted base mapping function to a single camera image). This back projection is done under the (preliminary) assumption that the basis mapping functions are correct. If the basic imaging functions are actually correct, the triangulation lines of sight of all cameras meet at a common spatial point in the measurement volume, namely at the actual position of the object point at the time of imaging. However, this is not always the case after the only rough pre-calibration. Rather, the triangulation lines of sight calculated from the individual camera images are usually skewed to one another, i.e. without a common point of intersection. The publication mentioned therefore proposes that the spatial point in the measurement volume that has the smallest distance to all calculated triangulation lines of sight is to be assumed to be the "true" object point, i.e. to be determined as an approximated object point. The publication also proposes determining a difference vector in the camera image between the pixel onto which the object point was actually mapped and the pixel onto which the approximated object point would be mathematically mapped when using the basic mapping function.

These steps are repeated several times for different object points, in particular for a large number of particles recorded at the same time in the measurement volume (which in the context of this description also includes the parallel calculation for different object points). A virtual grid results in the measurement volume, whose grid points are each assigned such a difference vector. From this, a global correction of the basic mapping function, which is present in polynomial form in the cited document, is then derived by means of suitable adaptation algorithms (fits), in particular by modifying its polynomial parameters.

This approach has performed very well in cases where the accuracy of the mapping functions remains essentially the same over the area of the measurement volume observed by the cameras.

However, local areas of the measurement volume that are subject to strong optical distortions when they are imaged on the cameras prove to be problematic. This can be caused, for example, by distortions occurring mainly in the image edge areas caused by the camera lens, refractions on curved boundary walls of the measurement volume, etc. The above approach then often leads to a "correction" that overcorrects errors in the basis mapping function in some areas and undercorrects them in others. For this reason, typical measurement setups are often adapted in such a way that only a central, optically uncritical area of the measurement volume is observed. However, optically critical areas of the measurement volume remain inaccessible to precise measurement.

task

It is the object of the present invention to specify an improved calibration method that is also capable of correcting strong, local errors in the basic mapping function.

Presentation of the invention

This object is achieved in connection with the features of the preamble of claim 1 by providing, for each camera image, an extended mapping function, comprising the basic mapping function and a correction vector field, the correction vector field consisting of a grid of support points which are derived from the calculated difference vectors Correction vectors are assigned, by which points corresponding to the support points, to which the extended mapping function as part of a measurement data evaluation (directly or inversely) is to be applied, are to be shifted locally in addition to the application of the basic mapping function.

Preferred embodiments are subject of the dependent claims.

The basic idea of the present invention is not to carry out the necessary "refinement" of the basic mapping function, as is known from the prior art, in the form of a single, global correction of said basic mapping function, but rather an extended mapping function with a preferably purely globally effective correction To provide component and a purely locally active component. This does not stand in the way of the fact that the basic mapping functions are already formulated in a complex manner and, in addition to globally effective components, also contain purely locally effective ones.

In the preferred embodiment, the base mapping function is adopted unchanged for the global component. “Unchanged” refers to that form of the basic mapping function that is used in the context of the method according to the invention, in particular in the context of steps c) and d). This by no means excludes cases in which an even more roughly pre-calibrated basic mapping function is used first and is pre-refined by preceding refinement steps, as known from the prior art, for example, before the method according to the invention is applied. Such a pre-refinement can easily be based on the same recorded camera images as the final refinement according to the invention.

The local component of the refined mapping function, on the other hand, is a correction vector field that can be defined in the measurement volume or in the respective camera image and carries a correction vector at each of its support points, which represents a displacement which - depending on the specific application - can be applied to a spatial, object or Image point is to be used if the corresponding point is subjected to the (refined) mapping function or its inverse as part of a measurement data evaluation. The specific choice of which type of point is subjected to which form of the mapping function depends, as those skilled in the art will recognize, on the specific definition of the correction vector field and the specific measurement data evaluation task. However, the various conceivable constellations, which are explained in more detail below, are mathematically equivalent and follow the same basic inventive idea.

The particular advantage of this approach is that an appropriate mapping function can also be assigned to areas of the measurement volume that are imaged with strong, local distortion, without this having a negative impact on the (regularly significantly larger) areas of the measurement volume that have significantly less distortion be mapped. This is because the basic imaging function then applies to all areas, which can be optimized for the (predominant) areas of low distortion. The additional correction by the correction vector field turns out to be rather small in these areas, i.e. the corresponding correction vectors only have a short length. The remaining areas, in which the basic imaging function does not lead to a satisfactory description of the actual image due to the strong optical distortion, receive an individual, local correction by means of a correspondingly longer correction vector. As a result, this approach also makes it possible, for example, to include edge areas of the measurement volume in a measurement that can only be imaged in a highly distorted manner, for example due to curved boundary walls. The previous restriction of the measurement to the optically uncritical, i.e. low-distortion measurement volume areas is abolished.

Those skilled in the art will understand that the specific mathematical formulation of the refined mapping function is not important for realizing the idea according to the invention. It is thus within the scope of the invention to formulate a “mapping field” whose individual elements each include both the value of the (global) basic mapping function and a (local) correction vector individual to the element. It is also possible to "put the global part in front of the brackets" as a term and to reserve the correction vector field according to its name solely for the element-specific correction vectors.

Several options are conceivable for defining the correction vector field according to the invention. In a first variant, it is provided that the support points are defined on a three-dimensional grid in the measurement volume. Selected spatial points in the measurement volume are thus determined and the correction vector appropriate there is calculated for them. It should be noted that the interpolation points do not have to match the (approximate) object points to which the previously calculated difference vectors relate. Rather, the interpolation points in the measurement volume can be distributed independently and even unevenly, with the respective correction vectors being able to be calculated using suitable statistical and/or interpolation or extrapolation methods. In the case of an irregular lattice of support points, the lattice can be denser in areas of strong, local optical distortion than in areas of largely constant optical conditions. It is also conceivable to make the density of the grid locally dependent on the amount of measurement data available for the respective areas. For spatial points located between the support points, a corresponding correction vector can be obtained by suitable interpolation or extrapolation. Methods known to those skilled in the art, such as linear or spline interpolations or extrapolations, can be used.

Alternatively, the correction vector field can also be determined in the planes of the camera images. In this case, it is provided that the support points are defined on a two-dimensional grid in the respective camera image and each support point is assigned a group of correction vectors lying in the camera plane, each element of the group of correction vectors having a different position on the triangulation table assigned to the corresponding support point. line of sight is assigned. As mentioned above, the assignment of a pixel in the two-dimensional camera image to a spatial point in the three-dimensional measurement volume is not unambiguous. All spatial points lying on a common layer line would be imaged on the same image point, provided there was an imageable object point at their position. However, since the locally differentiating refinement of the imaging function according to the invention is based on local differences in the measurement volume, it would not be sufficient to assign each pixel just one correction vector, which would then be representative of all spatial points on the line of sight assigned to the pixel in question. Therefore, in the mentioned embodiment of the invention, it is provided that each reference point defined in the camera image (i.e. an image point) is assigned several correction vectors, each of which is representative of only one point in space on said line of sight. Those skilled in the art will understand that such a two-dimensional grid, each with a family of correction vectors at its support points, can also be understood as a three-dimensional grid with “mixed” coordinates, namely the x, y coordinates of the camera image and, for example, along the z coordinate the line of sight. A corresponding correction vector can be determined by suitable interpolation for pixels located between the support points.

Analogously to what was said above, it should be noted here that the support points do not have to match the image points of imaged object points to which the previously calculated difference vectors relate. Rather, the supporting points of the image plane can be distributed independently and even unevenly, with the respective correction vectors being able to be calculated using suitable statistical and/or interpolation or extrapolation methods. In the case of an irregular grid of support points, the grid of support points in image areas onto which measurement volume areas of strong, local optical distortion are mapped can be denser than in other areas. It is also conceivable to make the density of the grid locally dependent on the amount of measurement data available for the respective areas. It should also be noted that the support points - as well as the pixels in general - do not have to coincide with pixels of a detector, but much finer, i. H. in the sub-pixel range, can be defined. A corresponding correction vector can be determined by suitable interpolation or extrapolation for pixels located between the support points. Methods known to those skilled in the art, such as linear or spline interpolations or extrapolations, can be used.

These are the main variants where the correction vectors can be defined. However, there are also different variants for the how of the correction vector definition. A correction vector can thus prescribe a shift of a pixel to be carried out as part of the measurement data evaluation, i.e. a shift in the camera image. Alternatively, a correction vector can also prescribe a displacement of an object point or point in space in the measurement volume. It is irrelevant where said correction vector is defined. It can be provided, for example, that the points to which the extended mapping function is to be applied as part of the measurement data evaluation are pixels in the camera image and the shifts to be made according to the assigned correction vectors are shifts in the camera image plane. Alternatively, it can be provided that the points to which the extended imaging function is to be applied as part of the measurement data evaluation are object points in the measurement volume and the displacements to be undertaken according to the assigned correction vectors are displacements in the measurement volume.

Taking into account the different variants of the where of a definition of the correction vectors as well as the different variants of the how of such a definition, four mainly relevant constellations result. However, those skilled in the art will understand that these different definition constellations are mathematically equivalent to one another and can be converted into one another using suitable transformations. They only represent differences in the technical implementation of the inventive idea. Depending on the specific measurement task and the experimental setup of the measurement arrangement, one or the other of these definition constellations can be advantageous.

As already stated above, the correction vectors from which the correction vector field according to the invention is constructed are derived from the difference vectors calculated in step d). Possible embodiments of steps a) to d) that are suitable for calculating these difference vectors are known from the prior art cited at the outset. However, alternative calculation methods are conceivable.

First of all, it is possible to prepare the measurement volume to be imaged in step a) differently. It is conceivable that during the imaging according to step a), a fluid inoculated with a large number of optically detectable particles flows through the measurement volume. In the case of a high particle density, a difficulty can arise in the identification according to step b) of the image points in the camera images assigned to a specific object point, and therefore to a specific particle. However, the person skilled in the art is familiar with suitable methods for this, for example based on correlation analyses.

Alternatively, it can be provided that a speckle plate with a random or pseudo-random point pattern is positioned in the measurement volume during imaging according to step a). Such a plate can be used at different points of the measurement volume, so that the method according to the invention can be carried out for different positions of the speckle plate and the individual results can be combined with one another if necessary.

A similar approach can be implemented by positioning a calibration plate with a regular calibration pattern in the measurement volume during imaging according to step a). In particular, this latter variant opens up the possibility of using the additional information about the absolute position of the calibration marks on the calibration plate that is typical for a calibration plate when used as intended. In particular, the precalibration and the calibration according to the invention can be carried out as part of a joint measurement and calculation run.

In particular, but not exclusively in connection with such fixed calibration objects, such as a calibration plate or a speckle plate, the term "simultaneous" imaging is to be understood in a broad sense. It describes the general case that in the period between the "simultaneous" recordings there is no significant change in or in the depicted measurement volume in the context of the objective of the invention, in particular that the positions of object points do not change to an extent relevant to the specific measurement.

There are also different options for the subsequent step c) of determining the approximated object point. The triangulation method known from the prior art is generally preferred. In this case, the image points identified as being associated with a common object point are subjected to the inverse of the basic imaging function in order to mathematically generate their triangulation lines of sight to the common object point. However, due to the defectiveness of the basic imaging function, these lines of sight do not intersect at a common point in space, but are skewed to one another. The "true" object point can therefore not be determined exactly. However, an approximated object point can be determined, for which there are again different procedures. In the case of crooked triangulation lines of sight, for example, provision can be made for that point in space to be determined as the approximated object point which overall has the smallest distance from the triangulation lines of sight. This means that the optimization criteria used for the approximation relate to the measurement volume and here, for example, select that point whose sum over its squared distances to the triangulation lines of sight is minimal.

Alternatively, it can be provided that in the case of skewed triangulation lines of sight, that point in space is determined as the approximated object point whose calculated projection using the base mapping function on the camera images has the smallest overall deviation from the identified image points. In this case, the respective pixel in each camera image is calculated for various candidate spatial points using the basic imaging function and its distance from the pixel on which the assigned object point was actually imaged is measured. For example, a minimum of the sum of the squares of the respective distance vectors in the camera images can serve as the optimization criterion for selecting a point in space as an approximate object point.

• - dem im jeweiligen Kamerabild identifizierten Bildpunkt einerseits und
• - der rechnerischen Projektion des approximierten Objektpunktes unter Verwendung der zugeordneten Basis-Abbildungsfunktion andererseits.

Dies entspricht einer Definition des Differenzvektors im Kamerabild.If the approximated object point is fixed and the associated identified image points are known, there are different possibilities for the subsequent calculation of the difference vector in step d). It is conceivable to calculate the difference vector in each camera image as the difference between

• - the pixel identified in the respective camera image on the one hand and
• - the computational projection of the approximated object point using the assigned basis mapping function on the other hand.

This corresponds to a definition of the difference vector in the camera image.

• - dem approximierten Objektpunkt einerseits und
• - der rechnerischen Rückprojektion des im jeweiligen Kamerabild identifizierten Bildpunktes unter Verwendung der zugeordneten invertierten Basis-Abbildungsfunktion.

Dies entspricht einer Definition des Differenzvektors im Messvolumen. Wie zuvor bereits erläutert, liefert die Rück-Projektion eines Bildpunktes durch reine Anwendung der invertierten Basis-Abbildungsfunktion zunächst keinen Raumpunkt sondern lediglich eine Sichtlinie aller Raumpunkte, von denen ausgehend ein Objektpunkt auf den fraglichen Bildpunkt abgebildet würde. Die genannte Variante zur Berechnung des Differenzvektors ist also so zu verstehen, dass sie auch eine Bestimmung des Ortes entlang dieser Sichtlinie umfasst. Dies kann bspw. durch Übernahme der Z-Koordinate des approximierten Objektpunktes oder durch Ermittlung des geringsten Abstandes zwischen approximiertem Objektpunkt und rückprojizierter Sichtlinie erfolgen.Alternatively it can be provided that the difference vector is calculated in step d) for each camera image as the difference between

• - the approximated object point on the one hand and
• - The computational back projection of the identified in the respective camera image pixel using the assigned inverted base mapping function.

This corresponds to a definition of the difference vector in the measurement volume. As already explained above, the back-projection of a pixel by simply using the inverted basis mapping function initially does not provide a point in space but only a line of sight of all points in space from which an object point would be mapped onto the pixel in question. The variant mentioned for calculating the difference vector is therefore to be understood in such a way that it also includes a determination of the location along this line of sight. This can be done, for example, by taking over the Z coordinate of the approximated object point or by determining the smallest distance between the approximated object point and the back-projected line of sight.

Further details and advantages of the invention result from the following specific description and the drawings.

character list

• 1: einen ersten Schritt im Rahmen einer bevorzugten Ausführungsform des erfindungsgemäßen Verfahrens,
• 2: einen zweiten Schritt im Rahmen einer bevorzugten Ausführungsform des erfindungsgemäßen Verfahrens,
• 3: einen dritten Schritt im Rahmen einer bevorzugten Ausführungsform des erfindungsgemäßen Verfahrens,
• 4: einen vierten Schritt im Rahmen einer bevorzugten Ausführungsform des erfindungsgemäßen Verfahrens,
• 5: einen fünften Schritt im Rahmen einer bevorzugten Ausführungsform des erfindungsgemäßen Verfahrens sowie
• 6: den Kern der Erfindung in Form einer symbolischen Formeldarstellung

Show it:

• 1 : a first step in a preferred embodiment of the method according to the invention,
• 2 : a second step in a preferred embodiment of the method according to the invention,
• 3 : a third step in a preferred embodiment of the method according to the invention,
• 4 : a fourth step in a preferred embodiment of the method according to the invention,
• 5 : a fifth step in a preferred embodiment of the method according to the invention and
• 6 : the core of the invention in the form of a symbolic formula representation

Description of Preferred Embodiments

The same reference symbols in the figures indicate the same or analogous elements.

1 shows a highly schematic representation of an exemplary measurement setup and the first step carried out thereon of a particularly simple embodiment of the calibration method according to the invention. A measurement volume 10 is shown, which has curved boundary walls on which strong local optical distortions can occur when imaging the measurement volume. An object point 12 is arranged in the measurement volume. The representation of only one object point 12 is used solely for simplification for the purpose of better comprehension. Those skilled in the art will understand that there are typically a large number of differently positioned object points 12 in the measurement volume 10 . For example, it can be particles flowing through the measurement volume or components or sections of solid calibration bodies, for example calibration or speckle plates. The person skilled in the art will also understand that the term "point" is a simplification introduced for the sake of easier understanding and that the term is to be interpreted correspondingly broadly, as already explained in the general part of the description.

A plurality of cameras 141 , 142 , 143 , three in the embodiment shown, are arranged around the measurement volume 10 . The measurement volume 10 can be recorded with the cameras 141 , 142 , 143 and imaged on camera images 161 , 162 , 163 . In particular, the object point 12 is imaged, symbolized by the imaging arrows 181, 182, 183, onto a respective image point 201, 202, 203 assigned to it in the camera images 161, 162, 163.

Mathematically, this mapping can be approximately described for each camera 141, 142, 143 with an assigned base mapping function M ₁ , M ₂ , M ₃ . This is a function of the space or world coordinates X, Y, Z in the measurement volume 10. The wording "roughly" is intended to indicate that the description of the mapping is by the base mapping function, which typically has the form of a pinhole function or a polynomial , usually contains errors. In particular in areas of the measurement volume 10 between which and the associated camera 141, 142, 143 optical distortion sources are arranged, this mathematical description can differ significantly from the actual mapping of the object point 12 onto the or one of the image points 201, 202, 203. Achieving an improvement here is the task of the calibration according to the invention.

It must therefore first be estimated how large the error is between the mathematical description using the basic mapping functions M ₁ , M ₂ , M ₃ and the actual mappings. For this purpose, in the embodiment shown, as in 2 Illustrated, the pixels 201, 202, 203 of the actual image of the object point 12 using the inverse M ₁ ^-1 , M ₂ ^-1 , M ₃ ^-1 of Basic imaging functions M ₁ , M ₂ , M ₃ are mathematically back-projected into the measurement volume 10 . The inverses M ₁ -1 ^, M ₂ ^-1 , M ₃ ^-1 are functions of the image coordinates x, y. Due to the dimensional difference between the image coordinates x, y and the world coordinates X, Y, Z, an unambiguous back-projection on the individual image level is not possible. Instead, only so-called triangulation lines of sight 221, 222, 223 can initially be calculated from the individual pixels 201, 202, 203, which in the ideal case intersect at a common spatial point in the measurement volume, namely at the object point 12. However, due to the imperfection of the basis mapping functions M ₁ , M ₂ , M ₃ this is not the case. Rather, the triangulation lines of sight 221, 222, 223 are skewed to one another.

An approximated object point 24 is therefore determined, ie a spatial point in the measurement volume 10 which is assumed to be the actual object point 12, or a spatial point which comes as close as possible to the “true” object point 12 within the framework of predetermined optimization criteria. At the in 2 In the illustrated embodiment, the point in space in the measurement volume 10 that has the shortest overall distance from the triangulation lines of sight 221, 222, 223 is determined as the approximated object point 24. This can be determined, for example, by least squares minimization algorithms. Alternative methods for determining the approximated object point 24 have already been referred to in the general part of the description.

In the following, in 3 only for the first camera image 161, a mathematical projection of the approximated object point 24 onto the camera image 161 takes place, as symbolized by the projection arrow 251. The basis of this calculation is again the basic mapping function M ₁ . In other words, that pixel 261 is determined on which the approximated object point 24 would be imaged on the camera image 161 using the basis imaging function M ₁ . The same applies to the other camera images 162, 163, which, however, in 3 are not shown for reasons of clarity.

In the ideal case, ie with error-free basic mapping functions M, the actual pixel 201 and the calculated pixel 261 coincide. However, due to the defectiveness of the basis mapping function M ₁ , this is generally not the case, particularly not in areas that are subject to strong optical distortion.

4 shows this discrepancy again in the first camera image 161. A difference vector 28 can be defined between the actual pixel 201 and the calculated pixel 261. In other embodiments of the invention, it is also possible to define the difference vector 28 in the measurement volume 10, for example as the difference between the approximated object point 24 and that point in space on the associated triangulation line of sight 221 with the same Z coordinate as the approximated object point 24.

In the next method step, the difference vectors 28 are converted into correction vectors 30. In the illustrated embodiment, as in FIG 5 shown, a grid of support points 32 is spanned in the camera image. A correction vector 30 is then assigned to each of the support points 32 . In the simplest case, the correction vector 30 corresponds to a displacement vector interpolated from neighboring difference vectors 28 . The person skilled in the art will understand that the steps described above must be carried out for a large number of object points 12 in order to be able to construct a sufficiently precisely interpolated grid of correction vectors 30 over the entire image plane or the entire observed measurement volume 10 .

In 5 only one correction vector 30 per interpolation point 32 is shown to simplify the illustration. In practice, however, each interpolation point 32 is assigned a whole family of correction vectors 30, the specific application of which depends on the Z plane of the measurement volume 10 in which the pixel corresponding to the interpolation point 32 is located. If the correction vector grid is set up in the measurement volume, which, as already explained in the general part of the description, is possible in other embodiments of the invention, such an assignment of correction vector groups to individual support points 32 is not necessary, since in the measurement volume 10 a three-dimensional Grid can be built, the support points must be assigned only a single correction vector.

As also already explained in the general part of the description, it is not absolutely necessary for the correction vectors to encode displacements to be carried out in the image plane; Variants are also conceivable in which the correction vectors in the measurement volume 10 encode displacements to be carried out.

These shifts are to be understood in the context of the application of the mapping function (direct or inverted) required in the context of a measurement data evaluation. The resultant correction vector field V ₁ is used to create a refined mapping function, which is composed of the base mapping function adopted unchanged and said correction vector field V ₁ . Must therefore be part of a measurement data If a point - be it a spatial or object point or an image point - is subjected to the extended mapping function, the same, ie global base mapping function for all points is applied separately and a locally differentiating shift according to the specification of the correction vector field V ₁ . It depends on the definition of the specific correction vector, the order in which the operations mentioned are to be applied to the point in question. In the (usual) cases where a point to which the mapping function is to be applied does not exactly coincide with one of the support points 32, the correction vector to be used can be determined by suitable interpolation between the support points.

This provision is symbolic in 6 as a formula, with the "+" sign deliberately placed in quotation marks to make it clear that it is usually not an addition in the mathematical sense but a separate application of two function components, as described immediately above.

Of course, the embodiments discussed in the specific description and shown in the figures only represent illustrative exemplary embodiments of the present invention.

Reference List

10

measurement volume

12

object point

141,142,143

camera

161, 162, 163

camera image

181, 182, 183

illustration arrow

201, 202, 203

(actual) pixel

221, 222, 223

Triangulation line of sight

24

approximate object point

251

projection arrow

261

(calculated) pixel

28

difference vector

30

correction vector

32

base

QUOTES INCLUDED IN DESCRIPTION

This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• EP 1926049 B1 [0002]

Claims (16)

Method for calibrating an optical measurement setup with a measurement volume (10) and with at least two cameras (141, 142, 143), by means of which object points (12) located at spatial points in the measurement volume (10) are viewed from different viewing angles onto image points (201, 202, 203 ) corresponding camera images (161, 162, 163) can be imaged, with such an image being able to be described mathematically by a basic imaging function known from a precalibration, comprising the step: a) simultaneous imaging of the measurement volume (10) by means of the cameras (141, 142 , 143) for generating a camera image (161, 162, 163) for each camera (141, 142, 143), as well as the steps performed multiple times, namely for a different object point (12): b) identifying those image points (201 , 202, 203), which are assigned to an object point (12) imaged on each camera image (161, 162, 163), c) determining, using the identified image points (201, 202, 203), of that igen point in space as the approximated object point (24), which, according to predetermined optimization criteria, best corresponds to that point in space at which the imaged object point (12) was actually located at the time of imaging, and d) calculating a for an error in the basic imaging function in relation to the difference vector (28) representative of the imaged object point (12), characterized by providing, for each camera image (161, 162, 163), an extended mapping function, comprising the basic mapping function and a correction vector field, the correction vector field consisting of a grid of support points (32) consists, to which correction vectors (30) derived from the calculated difference vectors (28) are assigned, around which points corresponding to the support points (32) to which the extended mapping function is to be applied as part of a measurement data evaluation, in addition to the application of the base mapping function locally move. procedure after claim 1 , characterized in that for points to which the extended mapping function is to be applied as part of a measurement data evaluation, but which do not correspond to one of the support points (32), the corresponding correction vector (30) by interpolation between or extrapolation from the support points (32) can be determined. Method according to one of the preceding claims, characterized in that a triangulation is carried out to determine the approximated object point (24) in step c. procedure after claim 3 , characterized in that in the case of crooked triangulation lines of sight (221, 222, 223) that spatial point is determined as the approximated object point (24) which overall has the smallest distance from the triangulation lines of sight (221, 222, 223). procedure after claim 3 , characterized in that in the case of skewed triangulation lines of sight (221, 222, 223), the point in space is determined as the approximated object point (24) whose calculated projections using the base mapping function on the camera images (161, 162, 163) overall has the smallest deviation from the identified pixels (201, 202, 203). Method according to one of the preceding claims, characterized in that the difference vector (28) is calculated in step d in each camera image (161, 162, 163) as the difference between - the pixel (201 , 202, 203) on the one hand and - the computational projection of the approximated object point (24) using the assigned basis mapping function on the other hand. Method according to one of the preceding claims, characterized in that the difference vector (28) is calculated in step d for each camera image (161, 162, 163) as the difference between - the approximated object point (24) on the one hand and - the calculated back-projection of the respective Camera image (161, 162, 163) of the identified pixel (201, 202, 203) using the associated inverse basis mapping function. Method according to one of the preceding claims, characterized in that the grid of support points (32) is a regular or irregular grid. Method according to one of the preceding claims, characterized in that the support points (32) are defined on a two-dimensional grid in the respective camera image (161, 162, 163) and each support point (32) is assigned a group of correction vectors (30) lying in the camera image plane where each element of the family of correction vectors (30) is associated with a different position on the triangulation line of sight associated with the corresponding support point (32). Procedure according to one of Claims 1 until 8th , characterized in that the support points (32) are defined on a three-dimensional grid in the measurement volume (10). Procedure according to one of claims 9 until 10 , characterized in that the points to which the extended mapping function is to be applied as part of the measurement data evaluation are pixels in the camera image (161, 162, 163) and the displacements to be undertaken according to the assigned correction vectors (30) are displacements in the camera image plane. Procedure according to one of claims 9 until 10 , characterized in that the points to which the extended mapping function is to be applied as part of the measurement data evaluation are object points (12) in the measurement volume (10) and the displacements to be undertaken according to the assigned correction vectors (30) are displacements in the measurement volume (10). Method according to one of the preceding claims, characterized in that the calculation of a correction vector is based on a plurality of difference vectors. Method according to one of the preceding claims, characterized in that during the imaging according to step a, a fluid inoculated with a large number of optically detectable particles flows through the measurement volume (10). Procedure according to one of Claims 1 until 13 , characterized in that a calibration plate with a regular calibration pattern is positioned in the measurement volume (10) during imaging according to step a. Procedure according to one of Claims 1 until 13 , characterized in that during the imaging according to step a, a speckle plate with a random or pseudo-random point pattern is positioned in the measurement volume (10).

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