in the set - up for automatic registration using a reference body as shown in fig1 , the geometric relationships between the reference body 5 and the ct scanner 1 are shown in a partially perspective representation . the ct scanner 1 is shown in a linear top view onto the ct ring , whereas the reference body 5 is shown in the form of a cuboid which shows perspective . this serves to simplify the representation . the cuboid reference body 5 comprises two different marker systems : on the one hand , the reference body has three ct markers 4 which can be identified when imaging by means of the ct scanner ( so - called specific imaging markers ). these three ct markers 4 are situated in a plane 6 which is indicated by the dotted line of a section in the reference body 5 . in a ct recording by means of a fan - shaped imaging ray , this plane 6 is detected by the fanned ray , such that all the ct markers 4 are imaged . the reference body 5 also comprises three markers 3 of a marker device which are visible to a camera system . in the present example , they are passive markers which reflect radiation of a certain wavelength ( in this case , infrared ). the three markers 3 which can be identified by the camera system ( not shown ) are referred to in the following as position markers , in order to distinguish them from the specific imaging markers 4 . the position markers 3 are attached on a facing area of the cuboid reference body and , in the example embodiment , define an area parallel to the area spanned by the imaging - specific markers 4 . the relative distance between the position markers 3 and the imaging - specific markers 4 is known . in the example embodiment described , the distance between the facing area and the sectional area 6 is also in particular known . the position of the position markers 3 relative to each other is also known , as is the position of the imaging - specific markers 4 relative to each other . the position of at least one position marker 3 relative to at least one imaging - specific marker 4 is also known . ultimately , enough parameters are available to allow the position of the imaging - specific markers 4 relative to the position markers 3 and the reference frame spanned by them to be described . in the example embodiment described , markers 2 are attached to the ct scanner 1 which can also be identified by a camera system . in the example embodiment described , they are again passive markers , i . e . markers which reflect a certain type of radiation ( in this case : infrared radiation ). on the basis of the markers 2 , it is possible to describe any points in a coordinate system of the ct scanner 1 , wherein it is possible to specify absolute position data of points in said reference frame of the ct scanner 1 . however , it is also possible to specify relative positions of points in this reference frame and to store them in the form of data . the markers 2 which are attached to the ct scanner 1 , and the position markers 3 which are attached to the reference body 5 , are orientated such that they can be simultaneously identified by a single camera system ( not shown ). if the position of the markers 2 on the ct scanner 1 is then known , and if the position of the position markers 3 on the reference body 5 is determined within the framework of the automatic registration method which is known in its own right , then with the aid of the position determined in this way , it is also possible to deduce the spatial position of the specific imaging markers 4 in the reference frame of the imaging apparatus ( i . e . with respect to the markers 2 on the ct scanner 1 ). the function which links the position of the specific imaging markers 4 to the reference frame of the ct scanner 1 is the spatial transformation function already described . fig2 shows the geometric relationships in a fanned ray projection in comparison with a conical ray projection . in the present example , x - rays are used as the imaging rays and are shown in a comparison . the fan - shaped imaging rays such as are used in a ct pre - scan are shown on the left in fig2 ; the so - called topograms or scout views ( two - dimensional representations ) are generated . the conical imaging ray of a conventional x - ray source , which generates a conventional fluoroscopic image , is shown in the right - hand half of the figure . the fan - shaped imaging rays on the left in fig2 are shown in an idealized form . they are also treated as idealized in the image registration method in accordance with the invention . the fan - shaped imaging ray exhibits fanning in the fanning direction x . the fan - shaped imaging ray is also detected in this direction x . however , the fan - shaped imaging ray exhibits almost no extension in the orthogonal direction z , i . e . in the direction orthogonal to the fanning direction x . a two - dimensional image data set is assembled from a number of individual images in the x direction . the individual images are spatially shifted parallel to each other by the amount δz . each of the fan - shaped imaging rays exhibits the same planar fanning angle α . the distance between the starting point of the rays ( for practical purposes , this corresponds to the radiation source ) and the detection unit in the x direction is indicated by d . the right - hand half of fig2 shows the geometric relationships in a fluoroscopic recording . proceeding from the radiation source 9 , a conical ray is emitted . the aperture angle of the conical ray is a spatial angle . the main ray direction runs in the direction of the y axis . a conical spatial portion is irradiated with the x - rays . the image is inherently two - dimensional in nature ; all the points are imaged in or projected into a circular segment 10 in the xz plane . the comparison between the ct fanned ray geometry and the conical ray geometry of the fluoroscopic recording very clearly shows that the projection in the ct fanned ray recording is lower in dimensions . in the ct fanned ray recording , the projection is performed along a straight line ( in the direction of the x axis ); in the projection exhibiting a conical ray profile , the projection is performed into a two - dimensional plane , the xz plane . fig3 shows the geometric relationships when imaging and / or projecting individual points , when a fan - shaped imaging ray is used . the ct scanner 1 is again shown , to which an x - ray radiation source 7 is attached in a fixed position . said x - ray radiation source 7 emits a fan - shaped x - ray 11 , wherein the flaring of the ray in the direction orthogonal to the fanning direction x is shown in a significant exaggeration . the flaring of the ray in the z direction is exceedingly small and is indicated here by ε . the two - dimensional image data set , composed of a number of individual recordings using one fan - shaped imaging ray each which are shifted parallel to each other in the z direction , includes entries in the x and z directions . in the example embodiment , the xz plane is the plane in which a ct table 8 is situated which can be moved relative to the x - ray radiation source 7 . a system of points p 1 , p 2 , p 3 and p 4 is then considered in fig3 . the points p 1 and p 2 are situated at a certain height above the detection plane ( the xz plane ), i . e . they have the same y coordinate . if the origin of the xyz coordinate system is set at the imaging point 13 , into which a ray is imaged along the main axis 12 of the fan - shaped imaging ray , then the points p 1 and p 2 have the same x coordinates in terms of magnitude . it may also be assumed that p 1 and p 2 exhibit the same z coordinate . the points p 1 and p 2 are then imaged into the points p 1 ′ and p 2 ′, which in turn exhibit identical y and z coordinates ( in the present case , y = z = 0 ), and the x coordinates of p 1 ′ and p 2 ′ are identical in terms of magnitude . for imaging the points p 1 and p 2 onto p 1 ′ and p 2 ′, the following relationship applies : p 1 p 2 = c · p 1 ′ p 2 ′ . the distance p 1 p 2 and the distance p 1 ′ p 2 ′ are linked together via the proportionality factor c . the same type of linking via the proportionality constant c applies to all the distances between points pa and pb which exhibit the same y coordinate and x coordinates which are identical in terms of magnitude . if the points pa and pb to be imaged are situated at a different height above the detection plane ( the xz plane ), i . e . they have a different y coordinate than in the example just described , then the proportionality factor c changes . the proportionality factor c is thus a function of the height ( the y coordinate in fig3 ) and / or the distance between the point to be imaged and the radiation source . in accordance with a preferred embodiment , the proportionality factor c is not explicitly determined ; instead , the law of imagery is ascertained . to this end , an imaging matrix is determined . such an imaging matrix has a simpler form for the fanned ray image used than for example for fluoroscopic images . the imaging matrix for a fanned ray image is in particular lower in dimensions . since the geometric relationships in a projection onto the x direction have been described , the geometric relationships in the much more strongly focused and / or barely flared ray direction z shall now be briefly discussed . the points p 3 and p 4 , which exhibit the same x and y coordinate and are to be imaged , are considered . the points p 3 and p 4 do , however , differ slightly in their z coordinate . when imaging the points p 3 and p 4 onto the points p 3 ′ and p 4 ′ in the xz plane , it may be seen that the x and y positions of the points p 3 ′ and p 4 ′ are again identical , but that the z coordinate differs slightly . this difference in the z coordinate of the points p 3 ′ and p 4 ′ is , however , extremely small and is below the resolution of the detector which is used in the embodiment described by way of example . the maximum distance between imaged points p 3 ′ and p 4 ′ in the z direction is ε . however , the resolution of the line detector used is greater than or equal to ε , i . e . when detected , the points p 3 ′ and p 4 ′ are in any case assigned to the same z value . thus , the following relationship approximately applies : distance p 3 p 4 = p 3 ′ p 4 ′ . although imaging the points p 1 , p 2 , p 3 and p 4 onto the points p 1 ′, p 2 ′, p 3 ′ and p 4 ′ has been described in fig3 , it is clear that also when projecting three points , as for example represented by the specific imaging markers 4 of the reference body 5 , the geometric relationships are in principle the same . it is thus possible to deduce the imaging transformation function from the geometric relationships when imaging the specific imaging markers 4 by means of a fan - shaped imaging ray 11 . in order to more simply describe the geometric ray relationships , the origin of the coordinate system xyz was set on the detection plane xz . alternatively , it is possible for the position of the x - ray radiation source 7 to be chosen as the coordinate origin . it is easily possible to convert the positions of the points to be imaged and the locations of their projection from one coordinate system into another coordinate system . computer program elements of the invention may be embodied in hardware and / or software ( including firmware , resident software , micro - code , etc .). the computer program elements of the invention may take the form of a computer program product which may be embodied by a computer - usable or computer - readable storage medium comprising computer - usable or computer - readable program instructions , “ code ” or a “ computer program ” embodied in said medium for use by or in connection with the instruction executing system . within the context of this application , a computer - usable or computer - readable medium may be any medium which can contain , store , communicate , propagate or transport the program for use by or in connection with the instruction executing system , apparatus or device . the computer - usable or computer - readable medium may for example be , but is not limited to , an electronic , magnetic , optical , electromagnetic , infrared or semiconductor system , apparatus , device or medium of propagation such as for example the internet . the computer - usable or computer - readable medium could even for example be paper or another suitable medium on which the program is printed , since the program could be electronically captured , for example by optically scanning the paper or other suitable medium , and then compiled , interpreted or otherwise processed in a suitable manner . the computer program product and any software and / or hardware described here form the various means for performing the functions of the invention in the example embodiments . although the invention has been shown and described with respect to one or more particular preferred embodiments , it is clear that equivalent amendments or modifications will occur to the person skilled in the art when reading and interpreting the text and enclosed drawings of this specification . in particular with regard to the various functions performed by the elements ( components , assemblies , devices , compositions , etc .) described above , the terms used to describe such elements ( including any reference to a “ means ”) are intended , unless expressly indicated otherwise , to correspond to any element which performs the specified function of the element described , i . e . which is functionally equivalent to it , even if it is not structurally equivalent to the disclosed structure which performs the function in the example embodiment or embodiments illustrated here . moreover , while a particular feature of the invention may have been described above with respect to only one or some of the embodiments illustrated , such a feature may also be combined with one or more other features of the other embodiments , in any way such as may be desirable or advantageous for any given application of the invention .
the present invention relates to a method for registering a two - dimensional image data set , generated using fan - shaped imaging rays , in the medical field , wherein the method comprises : processing the two - dimensional image data on the basis of a spatial transformation function which describes a spatial relative position between points which have been imaged using a fan - shaped imaging ray , and the imaging apparatus used for imaging ; and processing the two - dimensional image data on the basis of an imaging transformation function which describes an imaging function of the imaging apparatus used for generating the two - dimensional image data set , which describes a spatial relationship between the actual spatial position of imaged points and their imaging location in a recording .