the method according to the invention begins in a variant group in step s 10 with obtaining a model of the x - ray imaging , namely in respect of a first string , e . g . for the x - ray source , and in respect of a second string von components , e . g . for the x - ray detector . such a model will be explained with reference to fig2 which shows a six axis articulated arm robot 10 which carries the x - ray source 12 and the x - ray detector 14 . for the per se known components of this x - ray imaging device , the parameters t and k of a model are now specified for kinematics and dynamics . the kinetic parameters can include denavit - hartenberg parameters , denoted by t dh , and hayati - roberts parameters , denoted by t hr . the effect string for the x - ray source therefore contains t and k parameters . the effect string for the x - ray detector 14 is virtually identical to the effect string for the x - ray source , but differs in at least one parameter . when carrying out the method according to the invention , imaging of a calibrating phantom is now performed in step s 12 , i . e . a two - dimensional x - ray image is acquired at a plurality of positions of x - ray source 12 and x - ray detector 14 . in step s 14 , the model parameters of the two models in respect of string 1 and string 2 can be identified on the basis of this plurality of two - dimensional x - ray images . the identifying of model parameters is known per se , parameter identification , also known as mathematical optimization , being described e . g . in the book “ practical methods of optimization ”, published by john wiley and sons , isbn - 10 : 0471494631 . now that the model is completely known , namely all the model parameters have been identified , in a first variant of the method according to the invention the desired trajectory for string 1 , i . e . for the x - ray source , is defined in step s 16 . via a trajectory , it can here be specified which translatory and rotatory movements the x - ray source is to execute . six degrees of freedom are thereby utilized , i . e . all the degrees of freedom available to a six axis articulated robot . on the basis of the desired trajectory , the inverse model for string 1 can now be used to calculate which adjustment parameters must be executed for the individual components of the six axis articulated arm robot , i . e . the positions to which the individual articulations of the device must be moved . this movement to the articulation positions then takes place in step s 18 . as a trajectory includes a plurality of positions for string 1 , the articulation positions are moved to a plurality of times in step s 18 . a three - dimensional x - ray image of the object of interest is acquired , the imaging of the object of interest in step s 20 therefore taking place in a coordinated manner with moving to the articulation positions in step s 18 . now that a plurality of two - dimensional x - ray images have been acquired , the trajectory for the unselected string 2 is calculated in step s 22 . as in this first variant all the degrees of freedom have been utilized , the trajectory traversed by the x - ray detector can be calculated . as , on the one hand , the desired trajectory for the x - ray source and is known , on the other , the associated trajectory for the x - ray detector has been calculated , both the absolute position of x - ray source and x - ray detector in space and their relative position is known , and in this way the parameters for projection matrices can be calculated in step s 24 . after the imaging of the object of interest in step s 20 , with the aid of these parameters filtered back projection , for example , can then be performed in step s 26 and in this way a 3d reconstruction can be carried out to obtain a 3d image dataset for the object of interest . in a second variant of the method described , the desired trajectory is not determined for string 1 , i . e . the x - ray source , but for string 2 , for the x - ray detector , see step s 16 ′. once again the positions can be moved to in step s 18 ′ and the images acquired in step s 20 ′, and in step s 22 ′ the trajectory is calculated not for string 2 as in step s 22 but now for string 1 , i . e . the trajectory of the x - ray source . in running through steps s 16 ′ to s 22 ′, the x - ray source and x - ray detector roles are therefore reversed as compared to steps s 16 to s 22 . in another variant of the method , only a trajectory for translation is specified as the desired trajectory for string 1 , i . e . for the x - ray source , so that only three parameters are defined , and three other degrees of freedom are available in the case of the six axis articulated arm robot . accordingly , aspects of the desired trajectory can likewise be specified for the x - ray detector ( string 2 ), in this case these are preferably rotatory parameters . the desired trajectory in step s 16 ″ is therefore combined . once again individual positions in the desired trajectory are moved to ; in step s 18 ″ an appropriate position is therefore moved to a plurality of times for each articulation , and imaging of the object of interest takes place simultaneously therewith in step s 20 ″. although there is no remaining string in this case , the complementary trajectory must be calculated , i . e . the rotatory portions for string 1 and the translatory for string 2 , step 22 ′. the method then proceeds to step s 24 , after which the filtered back projection 26 is calculated in order to obtain the 3d image dataset . in a variant of the method according to the invention explained below with reference to fig3 , only a model for one of the strings , in the example in the figure only for the x - ray source , is obtained in step s 110 . in step s 112 the calibrating phantom is then imaged , i . e . a plurality of two - dimensional x - ray images are acquired , so that the model parameters can be subsequently identified in step s 114 . in step s 116 the desired trajectory is now defined for string 1 , i . e . for the x - ray source . as is known from s 18 and s 20 in fig1 , the articulation positions can now be moved to in step s 118 ( a plurality of times in each case ) and an x - ray image is recorded in each case , i . e . overall imaging of the object of interest is acquired , see s 120 . as no calibrated model is now available for string 2 , the trajectory for string 2 cannot now be calculated in step s 22 as in fig1 . instead , the position of string 2 , i . e . the x - ray detector , is measured in step s 122 . this measurement is possible if , during imaging of the object of interest as per step s 120 , an appropriate outline is imaged at the same time , i . e . a rectangular aperture b 1 , for example , see fig5 , is disposed in front of the x - ray source 12 which masks out so much x - radiation that unexposed areas remain on the detector 14 . depending on the location of the exposed areas on the x - ray detector 14 , i . e . of the images produced by it , specified by the vectors ( d ) s i emanating from the origin of a coordinate system ( ks ) d of the x - ray detector 14 , a different position of the x - ray detector 14 and therefore of the coordinate system ( ks ) d with respect to the coordinate system ( ks ), of the x - ray source 12 can be specified . typically the outline of a rectangular aperture b 1 is both somewhat offset with respect to the origin , and also distorted , namely forming a trapezium , and because of the position and distortion , the relative position of the x - ray detector 14 with respect to the x - ray source 12 can then be calculated . once this has taken place in step s 122 , the parameters for the projection matrices can be calculated in step s 124 and then , in step s 126 in the example , filtered back projection can be performed on the basis of the imaging acquired in step s 122 , so that even in this variant of the method a good 3d image dataset for the object of interest is obtained .
a method for obtaining a 3d image dataset of an object of interest is proposed . a plurality of 2d x - ray images are captured and a 3d reconstruction is carried out using filtered back projection . the projection parameters have been measured with the aid of a calibrating phantom , possibly using an interpolation or extrapolation of such measurements . a model of effect strings of the components in an x - ray imaging device is obtained , and the model parameters are identified based on imaging of a calibrating phantom . a projection matrix can then be calculated for any positions on any desired trajectories , without having to use imaging of a calibrating phantom at precisely that position and desired trajectory .