Patent Publication Number: US-2021190941-A1

Title: More reliable classification of radar data from dynamic settings

Description:
CROSS REFERENCE 
     The present application claims the benefit under 35 U.S.C. § 119 of German Patent Application No. DE 102019220069.9 filed on Dec. 18, 2019, which is expressly incorporated herein by reference in its entirety. 
     FIELD 
     The present invention relates to the classification of radar data, which have been obtained by querying, in particular, dynamic settings. 
     BACKGROUND INFORMATION 
     In order for a vehicle to be able to move in road traffic in an at least semi-automated manner, it is necessary to detect the surroundings of the vehicle and to initiate countermeasures if a collision with an object in the surroundings of the vehicle is imminent. The creation of a surroundings representation and localization are also necessary for safe automated driving. 
     The detection of objects with the aid of radar is not dependent on the lighting conditions and, for example, is possible at greater distances even at night, without the oncoming traffic being blinded by high beam light. The distance and velocity of objects also result directly from the radar data. These pieces of information are important for assessing whether a collision with the objects may result. However, the type of objects involved is not directly identifiable from the radar signals. 
     This identification is resolved instantaneously by the calculation of attributes from the digital signal processing. 
     German Patent No. DE 10 2018 204 494 B3 describes classifying radar signals with the aid of neural networks with respect to the objects indicated by the radar signals. A generator with which synthetic training data may be provided in order to remedy a shortage of training data during the training of the networks is also described in this document. 
     SUMMARY 
     Within the scope of the present invention, a method is provided for classifying radar data. The radar data have been obtained by registering radar radiation using at least one detector. The radar radiation has been emitted by a transmitter and reflected by at least one object. In this way, the radar radiation has arrived at the detector. 
     In accordance with an example embodiment of the present invention, radar data are provided, which include observations of a setting (i.e., a scene) recorded at different points in time. The term “observations of a setting” in this case is not to be understood as restrictive in the sense that the observations must be fully congruent with respect to one another. If, for example, the traffic situation directly ahead of a driving vehicle is observed with a radar sensor, then the observable detail of the setting is a different one for each observation, because one part of the setting departs the detection area of the sensor and another part of the setting newly enters into the detection area. It is still the same setting, however. 
     At least one portion of the radar data is ascertained, which is rotated and/or scaled in at least one of the observations as compared to at least one other of the observations. A fixed point of the rotation and/or of the scaling is ascertained. 
     With this ascertained fixed point as the origin, at least one two-dimensional representation of at least one portion of the observations is transformed into logarithmic polar coordinates. This at least one transformed two-dimensional representation is mapped by at least one classifier onto at least one class of a predefined classification. This classifier encompasses a neural network including at least one convolution layer. 
     It has been found that it is possible in this way to improve the reliability of the classification, for example, of the objects contained in the setting and to also simplify the training of the classifier. The cause of this lies in the fact that as a result of the transformation into the logarithmic polar coordinates, changes of the radar data due solely to a change of the relative spatial perspective between the radar sensor and objects may be separated from changes that are due to the presence of different types of objects. 
     Thus, for example, the larger an object appears in the radar data, the closer it is to the radar sensor. The object is rotated as a function of the angle at which it is observed. During the conventional training of classifiers, the training data include many instances of each object to be identified scaled and/or rotated in this manner and are each annotated (“labeled”) as involving precisely this object. Thus, the classifier learns, based on many examples, in which forms the object (for example, a vehicle or a particular traffic sign) may come into the radar data. Due to its ability to generalize, this places the classifier in the position of correctly classifying the object even in further observation situations not covered in the training. 
     If, however, two-dimensional representations of observations are then transformed into logarithmic polar coordinates, a scaling of the input observation is manifested in the result of the transformation in a shift in one dimension. A rotation of the input observation is manifested in the result of the transformation in a shift in another dimension. The convolution operations that are utilized by classifiers in convolution layers are, however, invariant toward such shifts. 
     This means that one and the same object at the output of the convolution layer always produces the same result, regardless of by which factor it is scaled or at which angle it is rotated, which is ultimately further processed to form the result of the classification. The ability of the classifier to correctly identify the object in all observation situations is thus no longer tied to the fact that the training data show the object in a multitude of different combinations based on angle and distance of the observation. 
     Accordingly, fewer training data and less computing time are required for training the classifier in order to achieve a classification of, for example, traffic-relevant objects in traffic situations with a predefined accuracy. 
     This is advantageous, in particular, with respect to a classification of objects, for example, which, though they occur relatively infrequently in traffic situations, must be strictly noted when they do occur. Training data for classifiers, for example, of traffic signs and of other traffic-relevant objects are typically acquired by a test vehicle driving particular routes or areas and collecting radar data. The number of different combinations based on angle and distance, with which a particular object is represented in the training data is a function of how frequently the object even occurs on the routes traveled or in the areas traveled. Thus, for example, signs that order “stop,” “yield right of way” or speed limits occur so frequently in the public traffic area that the training data practically inevitably contain numerous instances of these signs in numerous sizes and at numerous rotation angles. By comparison, unguarded railroad crossings and roads leading to unsecured shorelines occur comparatively infrequently. Thus, the training data inherently contain far fewer instances of the hazard signs that refer to these situations in different combinations and based on size and perspective distortion. Should the safe identification of these hazard signs suffer as a result, the vehicle could at worst crash into the water or be crushed by an oncoming train. With the transformation of the observations into logarithmic polar coordinates neutralizing the influence of rotations and scalings of the objects virtually before the classifier, the minimum number of instances with which each object to be classified must occur in the training data of the classifier for a safe identification, is significantly reduced. 
     In one particularly advantageous embodiment of the present invention, two-dimensional or three-dimensional spatial distributions of at least two measured variables resulting from the reflected radar radiation are combined in a multi-dimensional tensor. In this case, two or three dimensions of the tensor represent the spatial dimensions of the distributions. A further dimension of the tensor represents the number of available measured variables. In radar measurements, in particular, one and the same coordinate in the three-dimensional space may, for example, be associated with values of a plurality of measured variables. Examples of such measured variables are the intensity of the reflected radar radiation, the radar cross section of objects in the setting as well as a velocity component of objects in the propagation direction of the radar radiation. 
     The organization of the measured variables in the tensor ensures that the spatial distributions of the measured variables may be transformed into logarithmic polar coordinates independently of one another in the manner described. The influence of the distance and of the spatial orientation between the radar sensor used for the measurements and the observed objects is then neutralized in each individual one of these distributions, as explained above. Accordingly, the classifier has complete freedom in terms of ascertaining the one or multiple correct classes of the predefined classification on the basis of a transformed meaningful measured variable, or also on the basis of a combination of such measured variables. Thus, for example, objects that are similar in shape are distinguished from one another based possibly on their characteristic movement patterns. A public-transit bus has a shape similar to a motorhome, for example, but must be accelerated and decelerated significantly more carefully so that standing passengers do not fall and become injured. 
     As explained above, the transformation into the logarithmic polar coordinates presupposes the prior ascertainment of a fixed point. There is a freedom of choice in terms of how this ascertainment proceeds in particular. In one particularly advantageous embodiment, the ascertainment of the fixed point encompasses assessing multiple candidate fixed points using a quality function in terms of how well they conform to the observations. The fixed point is selected based on these assessments. In the simplest case, for example, all candidate fixed points of one discrete coordinate grid may be assessed, and one candidate fixed point having the best assessment may then be selected as the fixed point. 
     A parameterized approach including free parameters may also be established for the candidate fixed points, for example. The free parameters may then be optimized with the aim of the quality function assuming an extremum. A parameterized approach is not tied to one particular discrete coordinate grid, so that the fixed point may be determined with a better accuracy than that it corresponds to the smallest unit of such a coordinate grid. In addition, previous knowledge, for example, may also be introduced into the parameterized approach to the extent in which sub-area of all possible candidate fixed points the fixed point should be reasonably sought. 
     It is also possible, for example, to feed multiple observations to a trained classifier and/or regressor, which maps these observations onto the fixed point sought. A classifier and/or regressor may therefore be trained to the effect that a particular set of observations relating to a particular setting, may only be consistent with particular fixed points. 
     In one particularly advantageous embodiment of the present invention, radar data are selected, which have been detected using a detector mounted at or in a vehicle. Classes of the predefined classification then represent traffic signs, other road users, traffic lane boundaries, obstacles and/or other traffic-relevant objects. As explained above, one and the same object in road traffic, in particular, is observed at a very large number of combinations of distance and observation angle and must nevertheless be correctly classified each time. The method in this example embodiment may, in particular, also include the physical recording of the radar data for the purpose of providing, for example. 
     An activation signal may be generated as a function of the at least one class provided by the classifier, and the vehicle may be activated using this activation signal. For example, the trajectory of the vehicle may be changed by this activation signal in such a way that it no longer intersects the trajectory of another object and thus a collision with this object is avoided. 
     In one further particularly advantageous embodiment of the present invention, radar data are selected, which have been detected by irradiating an area to be monitored with radar radiation from a stationary transmitter and by measuring the reflected radiation using at least one stationary detector. Classes of the predefined classification then represent persons, animals, vehicles, tools and/or other objects relevant for the safety of the area to be monitored. When monitoring areas as well, objects at multiple different combinations of distance and observation angle are presented to one or multiple stationary radar sensors. This applies, in particular, if radar sensors or other detectors are indeed stationary, but pivotably mounted. One and the same location in the area to be monitored may then be selectively observed by various sensors at various angles. The method in this embodiment may encompass, in particular, also the physical recording of the radar data for the purpose of providing, for example. 
     An activation signal may be generated as a function of the at least one class provided by the classifier, and a system for monitoring the area may be activated using this activation signal. For example, an alarm physically perceptible in the monitored area, and/or a silent alarm to a location responsible for the safety of the area may be triggered in response to an object identified as a threat to the safety of the monitored area. 
     As explained above, eliminating the necessity of presenting to a classifier within the scope of its training one and the same object at multiple different combinations of distance and observation angle, simplifies the training significantly and improves the training result. The present invention therefore also relates to a method for training a classifier, which encompasses a neural network including one convolution layer, for use in the above-described method. 
     In accordance with an example embodiment of the present invention, within the scope of this method, learning radar data are provided with learning observations. Setpoint classes of a predefined classification are provided, which are assigned to each of the learning observations. Each learning observation is assigned those setpoint classes onto which the classifier should ideally map this learning observation in its fully trained state. 
     At least one two-dimensional representation each of at least one part of each learning observation is transformed into logarithmic polar coordinates, one fixed point being established as the origin. This fixed point is selected as a point around which observations in the intended operation of the classifier probably appear rotated and/or scaled as compared to the learning observations. 
     The transformed two-dimensional representations are mapped by the classifier onto one or multiple classes of the predefined classification. Parameters that characterize the behavior of the classifier are optimized with the aim that the classes provided by the classifier to the transformed representations of the learning observations coincide as much as possible with the setpoint classes according to a predefined cost function. 
     The transformation of the representations of the learning observations into logarithmic polar coordinates has the effect, similar to that described above, that during the subsequent use of the classifier, observations, which are rotated and/or scaled around the selected fixed point as compared to the learning observations, produce the same results at the output of the convolution layer as the learning observations. Such scalings and rotations thus do not influence the result provided by the classifier. As a result of the transformation with the correct choice of the fixed point, the classifier is thus virtually “prepared” against scalings and/or rotations occurring in the radar data during subsequent use. 
     The methods may, in particular, be wholly or partially computer-implemented. The present invention therefore also relates to a computer program including machine-readable instructions which, when they are executed on one or on multiple computers, prompt the computer or computers to carry out one of the described methods. In this context, control units for vehicles and embedded systems for technical devices, which are also capable of executing machine-readable instructions, are also to be considered as computers. 
     Similarly, the present invention also relates to a machine-readable data medium and/or to a download product including the computer program. A download product is a digital product transmittable via a data network, i.e., downloadable by a user of the data network, which may, for example, be offered for sale in an online shop for immediate download. 
     Furthermore, a computer including a computer program may be equipped with the machine-readable data medium or with the download product. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further measures improving the present invention are described in greater detail below together with the description of the preferred exemplary embodiments of the present invention with reference to the figures. 
         FIG. 1  shows one exemplary embodiment of method  100  for classifying radar data  2 , in accordance with the present invention. 
         FIG. 2  shows the effect of a scaling in representations  4   a  through  4   c  of observations  2   a  through  2   c  on the transformed representations  4   a ′ through  4   c ′, in accordance with the present invention. 
         FIG. 3  shows the effect of a rotation in representations  4   a  through  4   c  of observations  2   a  through  2   c  on the transformed representations  4   a ′ through  4   c ′, in accordance with the present invention. 
         FIG. 4  shows one exemplary embodiment of method  200  for training classifier  5 , in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
       FIG. 1  is a schematic flowchart of one exemplary embodiment of method  100  for classifying radar data  2 . 
     In step  110 , radar data  2  are provided, which contain observations  2   a  through  2   c  of a setting  1  recorded at different points in time. In step  120 , at least one portion  2 ′ of radar data  2  is ascertained which, as compared to observations  2   a  through  2   c  among one another, has experienced a rotation and/or scaling. A fixed point  3  of this rotation and/or scaling is ascertained in step  130 . 
     In step  140 , this fixed point  3  is utilized as an origin in order to transform at least one two-dimensional representation  4   a  through  4   c  of at least one part of observations  2   a  through  2   c  into logarithmic polar coordinates. The at least one transformed representation  4   a  through  4   c  is mapped with a classifier  5 , which encompasses a neural network including at least one convolution layer, onto at least one class  6   a  through  6   d  of a predefined classification  6 . 
     Two examples are specified in  FIG. 1 , as to how classes  6   a  through  6   d  ascertained in this manner may be used in technical applications. In step  160 , an activation signal  160   a  is generated as a function of class  6   a  through  6   d  provided by classifier  5 , and a vehicle  50  is activated in step  170  using this activation signal  160   a . In step  180 , an activation signal  180   a  is generated as a function of class  6   a  through  6   d  provided by classifier  5 , and a system  60  for monitoring an area is activated in step  190  using activation signal  180   a.    
     Different embodiments are specified by way of example within box  110 , as to how radar data  2  may be provided with observations  2   a  through  2   c . Radar data  2  are formed, in general, by registering radar radiation  20  emitted from a transmitter and reflected by at least one object using at least one detector. 
     According to block  111 , two-dimensional or three-dimensional spatial distributions  21 ′ through  24 ′ of at least two measured variables  21  through  24  resulting from reflected radar radiation  20  may be combined in one multi-dimensional tensor  25 . According to block  112 , two or three dimensions of this tensor  25  represent the spatial dimensions of distributions  21 ′ through  24 ′. In the example shown in  FIG. 1 , distributions  21 ′ through  24 ′ are two-dimensional. According to block  113 , a further dimension of tensor  25  represents the number of available measured variables  21  through  24 . There are four measured variables  21  through  24  in the example shown in  FIG. 1 . 
     According to block  114 , radar data  2  may be selected, which have been detected with a detector mounted at or in a vehicle  50 . According to block  115 , classes  6   a  through  6   d  of predefined classification  6  may then represent traffic signs, other road users, traffic lane boundaries, obstacles and/or other traffic-relevant objects  11 . 
     According to block  116 , radar data  2  may be selected, which have been detected by irradiating an area to be monitored with radar radiation  20  from a stationary transmitter and by measuring reflected radiation  20  using at least one stationary detector of a system  60  for monitoring the area. According to block  117 , classes  6   a  through  6   d  of the predefined classification  6  may then represent persons, animals, vehicles, tools and/or other objects  11  relevant for the safety of the area to be monitored. 
     Different embodiments are specified by way of example within box  130  as to how fixed point  3  required for transformation  140  may be ascertained. 
     According to block  131 , multiple candidate fixed points  3   a  through  3   d  may be assessed using a quality function  7  in terms of how well they conform to observations  2   a  through  2   c . Fixed point  3  may then be selected according to block  132  based on these assessments  8   a  through  8   d.    
     According to block  131   a , a parametric approach  31  including free parameters  31   a  through  31   c  may, in particular, be established for candidate fixed points  3   a  through  3   d , for example. Free parameters  31   a  through  31   c  may then be optimized in block  132   a  with the aim of quality function  7  assuming an extremum. 
     According to block  133 , multiple observations  2   a  through  2   c  may be fed to a classifier and/or regressor  9 . According to block  134 , this classifier and/or regressor  9  maps/map observations  2   a  through  2   c  onto sought fixed point  3 . 
       FIG. 2  shows three two-dimensional representations  4   a  through  4   c  of one and the same object  11  in a setting  1 . Representations  4   a  through  4   c  belong to observations  2   a  through  2   c , which have been recorded at different points in time. All three representations  4   a  through  4   c  show the same vehicle as object  11 , but in different sizes. Object  11  may, for example, appear larger from one observation  2   a  through  2   c  to the next if the distance to object  11  is successively reduced. 
     In  FIG. 2 , it is delineated in a stylized manner that the change of size in representations  4   a  through  4   c  impacts transformed representations  4   a ′ through  4   c ′ obtained in each case by transformation  140  in the form of a translation from right to left. 
       FIG. 3  shows three further representations  4   a  through  4   c  of identical object  11  in setting  1 . In contrast to  FIG. 2 , representations  4   a  through  4   c  show object  11  here in each case in the same size but rotated at different angles. Object  11  may, for example, appear rotated from one observation  2   a  through  2   c  to the next if the relative orientation of the observer to object  11  successively changes. 
     In  FIG. 3 , it is delineated in a stylized manner that the rotation in representations  4   a  through  4   c  impacts transformed representations  4   a ′ through  4   c ′ obtained in each case by transformation  140  in the form of a translation from top to bottom. 
       FIG. 4  shows one exemplary embodiment of method  200  for training classifier  5 . In step  210  of this method  200 , learning radar data  2 * are provided with learning observations  2   a * through  2   c *. In step  230 , at least one two-dimensional representation  4   a  through  4   c  each of at least one part of every learning observation  2   a * through  2   c * is transformed into logarithmic polar coordinates. In this case, a fixed point  3  is used as the origin, around which observations  2   a  through  2   c  in the intended area of classifier  5  probably appear rotated and/or scaled as compared to learning observations  2   a * through  2   c *. As explained above, this has the effect that classifier  5  is “immunized” against rotations and/or scalings around precisely this fixed point  3 . 
     In step  240 , transformed two-dimensional representations  4   a  through  4   c  are mapped by classifier  5  onto one or multiple classes  6   a  through  6   d  of predefined classification  6 . Parameters  5   a , which characterize the behavior of classifier  5 , are optimized in step  250  with the aim that the classes provided by classifier  5  to transformed representations  4   a ′ through  4   c ′ of learning observations  2   a  through  2   c  coincide preferably well with predefined setpoint classes  6   a * through  6   d * (provided in step  220 ) according to a predefined cost function  5   b.    
     If the optimization is converged according to a predefined criterion, the result of the training produced are the finished optimized parameters  5   a *, which characterize the behavior of classifier  5  in the state usable in method  100 . 
     Example embodiments of the present invention are also set forth in the numbered paragraphs below. 
     Paragraph 1. A method ( 100 ) for classifying radar data ( 2 ), which have been obtained by registering radar radiation ( 20 ) emitted from a transmitter and reflected by at least one object using at least one detector, including the steps:
         providing ( 110 ) radar data ( 2 ), which include observations ( 2   a  through  2   c ) of a setting ( 1 ) recorded at different points in time;   ascertaining ( 120 ) at least one portion ( 2 ′) of the radar data ( 2 ), which is rotated and/or scaled in at least one of the observations ( 2   a  through  2   c ) as compared to at least one other of the observations ( 2   a  through  2   c );   ascertaining ( 130 ) a fixed point ( 3 ) of the rotation and/or scaling;   transforming ( 140 ) at least one two-dimensional representation ( 4   a  through  4   c ) of at least one part of the observations ( 2   a  through  2   c ) into logarithmic polar coordinates using the ascertained fixed points ( 3 ) as the origin;   mapping ( 150 ) the at least one transformed two-dimensional representation ( 4   a ′ through  4   c ′) onto at least one class ( 6   a  through  6   d ) of a predefined classification ( 6 ) via at least one classifier ( 5 ), which encompasses a neural network that includes at least one convolution layer.       

     Paragraph 2. The method ( 100 ) as recited in Paragraph 1, wherein two-dimensional or three-dimensional spatial distributions ( 21 ′ through  24 ′) of at least two measured variables ( 21  through  24 ) resulting from the reflected radar radiation ( 20 ) are combined ( 111 ) in a multi-dimensional tensor ( 25 ), two or three dimensions of the tensor ( 25 ) representing ( 112 ) the spatial dimensions of the distributions ( 21 ′ through  24 ′) and a further dimension of the tensor ( 25 ) representing ( 113 ) the number of available measured variables ( 21  through  24 ). 
     Paragraph 3. The method ( 100 ) as recited in Paragraph 2, wherein the measured variables ( 21  through  24 ) encompass
         the intensity of the reflected radar radiation ( 20 ), and/or   the radar cross section of objects ( 11 ) in the setting ( 1 ) and/or   a velocity component of objects ( 11 ) in the propagation direction of the radar radiation ( 20 ).       

     Paragraph 4. The method ( 100 ) as recited in one of Paragraphs 1 through 3, wherein the ascertainment ( 130 ) of the fixed point ( 3 ) encompasses assessing ( 131 ) multiple candidate fixed points ( 3   a  through  3   d ) using a quality function ( 7 ) in terms of how well they conform to the observations ( 2   a  through  2   c ), and selecting ( 132 ) the fixed point ( 3 ) based on these assessments ( 8   a  through  8   d ). 
     Paragraph 5. The method ( 100 ) as recited in Paragraph 4, wherein a parameterized approach ( 31 ) including free parameters ( 31   a  through  31   c ) is established ( 131   a ) for the candidate fixed points ( 3   a  through  3   d ), and the free parameters ( 31   a  through  31   c ) being optimized ( 132   a ) with the aim of the quality function ( 7 ) assuming an extremum. 
     Paragraph 6. The method ( 100 ) as recited in one of Paragraphs 4 through 5, wherein multiple observations ( 2   a  through  2   c ) are fed ( 133 ) to a trained classifier and/or regressor ( 9 ), which maps ( 134 ) these observations ( 2   a  through  2   c ) onto the sought fixed point ( 3 ). 
     Paragraph 7. The method ( 100 ) as recited in one of Paragraphs 1 through 6, wherein radar data ( 2 ) are selected ( 114 ), which have been detected using a detector mounted at or in a vehicle ( 50 ), and classes ( 6   a  through  6   d ) of the predefined classification ( 6 ) representing ( 115 ) traffic signs, other road users, traffic lane boundaries, obstacles and/or other traffic-relevant objects ( 11 ). 
     Paragraph 8. The method ( 100 ) as recited in Paragraph 7, wherein an activation signal ( 160   a ) is generated ( 160 ) as a function of the at least one class ( 6   a  through  6   d ) provided by the classifier ( 5 ), and the vehicle ( 50 ) being activated ( 170 ) using this activation signal ( 160   a ). 
     Paragraph 9. The method ( 100 ) as recited in one of Paragraphs 1 through 6, wherein radar data ( 2 ) are selected ( 116 ), which have been detected by irradiating an area to be monitored with radar radiation ( 20 ) from a stationary transmitter and by measuring the reflected radiation ( 20 ) using at least one stationary detector, and classes ( 6   a  through  6   d ) of the predefined classification ( 6 ) representing ( 117 ) persons, animals, vehicles, tools and/or other objects ( 11 ) relevant for the safety of the area to be monitored. 
     Paragraph 10. The method ( 100 ) as recited in Paragraph 9, wherein an activation signal ( 180   a ) is generated ( 180 ) as a function of the at least one class ( 6   a  through  6   d ) provided by the classifier ( 5 ), and a system ( 60 ) for monitoring the area being activated using this activation signal ( 180   a ). 
     Paragraph 11. A method ( 200 ) for training a classifier ( 5 ), which encompasses a neural network including at least one convolution layer, for use in the method ( 100 ) as recited in one of Paragraphs 1 through 10, including the steps:
         providing ( 210 ) learning radar data ( 2 *) with learning observations ( 2   a * through  2   c *);   providing ( 220 ) setpoint classes ( 6   a * through  6   d *) of a predefined classification ( 6 ), which are assigned to each of the learning observations ( 2   a * through  2   c *);   transforming ( 230 ) at least one two-dimensional representation ( 4   a  through  4   c ) each of at least one part of each learning observation ( 2   a * through  2   c *) into logarithmic polar coordinates including a fixed point ( 3 ) as the origin, this fixed point ( 3 ) being selected as a point around which observations ( 2   a  through  2   c ) in the intended area of the classifier ( 5 ) probably appear rotated and/or scaled as compared to the learning observations ( 2   a * through  2   c *);   mapping ( 240 ) the transformed two-dimensional representations ( 4   a ′ through  4   c ′) onto one or multiple classes ( 6   a  through  6   d ) of the predefined classification ( 6 ) via the classifier ( 5 );   optimizing ( 250 ) parameters ( 5   a ), which characterize the behavior of the classifier ( 5 ), with the aim that the classes provided by the classifier ( 5 ) to the transformed representations ( 4   a ′ through  4   c ′) of the learning observations ( 2   a  through  2   c ) coincide preferably well with the setpoint classes ( 6   a * through  6   d *) according to a predefined cost function ( 5   b ).       

     Paragraph 12. A computer program, containing machine-readable instructions which, when they are executed on one or on multiple computers, prompt the computer(s) to carry out a method ( 100 ,  200 ) as recited in one of Paragraphs 1 through 11. 
     Paragraph 13. A machine-readable data medium and/or download product including the computer program as recited in Paragraph 12. 
     Paragraph 14. A computer, equipped with the computer program as recited in Paragraph 12 and/or with the machine-readable data medium and/or download product as recited in Paragraph 13.