a c - arm x - ray device 1 shown in fig1 has components arranged in a known manner , with the differences in accordance with the invention described below . the c - arm x - ray device has a support 2 at which a c - arm 5 provided with an x - ray source 3 and an x - ray receiver 4 is seated . in the exemplary embodiment , the c - arm 5 is isocentrically adjustable ( see the double arrow ‘ a ’) along its circumference around its isocenter iz and its orbital axis o . together with the support 2 , the c - arm 5 is also isocentrically pivotable around its angulation axis a in the directions of the double arrow ‘ b ’. 2d and 3d images of subjects , for example patients , can be acquired with the c - arm x - ray device 1 and presented on a display device 6 . the devices required for this purpose , particularly an image computer , are implemented in a known way and are therefore not shown in fig1 and need not be explicitly described . particularly for medical applications , navigation - guided interventions at a patient ( not shown ) are to be implemented with the c - arm x - ray device 1 . for this reason , it is necessary to determine a coordinate transformation between a coordinate system k m that is allocated to a measurement of the c - arm x - ray device 1 , and has its origin in the isocenter iz of the c - arm x - ray device 1 in the exemplary embodiment , and a coordinate system k p allocated to a position acquisition system 10 ( schematically shown in fig1 ) wherein the coordinates of an instrument 11 to be navigated relative to a patient are defined . to this end , a support mount 20 to which a coordinate system k h1 is allocated is arranged at the support 2 of the c - arm x - ray device 1 . a carrying arm 21 that is removable from the support mount 20 is secured to the support mount 20 . an x - ray calibration phantom 22 is secured to the carrying arm 21 , with a coordinate system k r1 being allocated to the x - ray calibration phantom 22 . the carrying arm 21 is arranged in a defined manner at the support mount 20 and the x - ray calibration phantom 22 is arranged in a defined manner at the carrying arm 21 so that the coordinate transformation between the coordinate system k h1 allocated to the support mount 20 and the coordinate system k r1 allocated to the x - ray calibration phantom 22 is known on the basis of the known dimensions of the carrying arm 21 . for determining the coordinate transformation between the coordinate system k r1 allocated to the x - ray calibration phantom 22 and the coordinate system k m allocated to the measurement volume of the c - arm x - ray device 1 , a series of 2d projections of the x - ray calibration phantom 22 is acquired from different projection directions by movement of the c - arm 5 around its orbital axis o . the x - ray calibration phantom 22 is arranged at the carrying arm 21 so that it is penetrated by an x - ray beam proceeding from the x - ray source 3 to the x - ray receiver 4 . the coordinate transformation between the coordinate system k r1 allocated to the x - ray calibration phantom 22 and the coordinate system k m allocated to the measurement volume of the c - arm x - ray device 1 is determined from the acquired series of 2d projections of the x - ray calibration phantom 22 . to this end , moreover , the x - ray calibration phantom 22 has x - ray - positive marks in a known way that are imaged in the 2d projections . the orientation of the x - ray - positive marks in the coordinate system k r1 allocated to the x - ray calibration phantom 22 is thereby known . since , thus , the coordinate transformation between the coordinate system k h1 allocated to the support mount 20 and the coordinate system k r1 allocated to the x - ray calibration phantom 22 , and the coordinate transformation between the coordinate system k r1 allocated to the x - ray calibration phantom 22 and the coordinate system k m allocated to the measurement volume of the c - arm x - ray device 1 , are known , the coordinate transformation between the coordinate system k h1 allocated to the support mount 20 and the coordinate system k m allocated to the measurement volume can also be determined in a simple way . this latter transformation , for example , is stored in a memory ( not shown in fig1 ) of the c - arm x - ray device 1 . when the c - arm x - ray device 1 is to be utilized for navigation - guided interventions at a patient , the carrying arm 21 provided with the x - ray calibration phantom 22 is removed from the support mount 20 , and a marker plate ( not shown in fig1 but well known ) that is provided with markers is arranged in a defined manner at the support mount 20 of the c - arm x - ray device 1 thus the coordinate system k h1 allocated to the support mount 2 is also allocated to the marker plate in the exemplary embodiment . the coordinate transformation between the coordinate system k h1 allocated to the marker plate 20 and the coordinate system k p allocated to the position acquisition system can be determined from camera images acquired with cameras 12 , 13 of the position acquisition system 10 wherein the marker plate is imaged , so that — overall — the coordinate transformation between the coordinate system k m allocated to the c - arm x - ray device 1 and the coordinate system k p allocated to the position acquisition system can be determined , for example with a computer ( not shown in fig1 ). this computer can be allocated to the position acquisition system 10 or can be the image computer ( likewise not shown in fig1 ) of the c - arm x - ray device 1 . camera images are acquired of the instrument 11 , provided with a marker plate 14 having markers during the course of a navigation - guided intervention . the positions of the instrument 11 with respect to the coordinate system k p allocated to the position acquisition system 10 thus can be determined on the basis of the camera images , and these can be can be transformed into coordinates of the coordinate system k m of the measurement volume on the basis of the identified coordinate transformation between the coordinate system k p allocated to the position acquisition system 10 and the coordinate system k m allocated to the measurement volume . for guidance of the instrument 11 relative to a patient , images of the instrument 11 can be mixed into x - ray images of the patient acquired with the c - arm x - ray device 1 . fig2 illustrates a second possibility for determining a coordinate transformation between a coordinate system allocated to a measurement volume of a c - arm x - ray device and a coordinate system allocated to the c - arm x - ray device itself without the use of markers in the registration . the c - arm x - ray device shown in fig2 essentially corresponds to the c - arm x - ray device shown in fig1 , so the components of the c - arm x - ray device are provided with the same reference characters . differing from the c - arm x - ray device 1 shown in fig1 , the c - arm x - ray device 1 shown in fig2 has a support mount 30 arranged at the radiation receiver 4 . the support mount 30 has a coordinate system k h2 allocated to it . a carrying arm 31 at which an x - ray calibration phantom 32 is arranged in a defined way is arranged at the support mount 30 in a defined way . the x - ray calibration phantom 32 is releasably attached to the carrying arm 31 . like the x - ray calibration phantom 22 , the x - ray calibration phantom 32 has x - ray - positive marks ( not shown ). the orientation of these marks relative to a coordinate system k r2 allocated to the x - ray calibration phantom 32 is known . due to the defined arrangements of the carrying arm 31 at the support mount 30 and the x - ray calibration phantom 32 at the carrying arm 31 , as well as due to the known dimensions of the carrying arm 31 , the coordinate transformation between the coordinate system k h2 allocated to the support mount 30 and the coordinate system k r2 allocated to the x - ray calibration phantom 32 is known . as can be seen from fig2 , the x - ray calibration phantom 32 is arranged at a stand 33 standing on the floor in addition to being arranged at the carrying arm 31 . the arrangement of the x - ray calibration phantom 32 at the stand 33 does not ensue until after the fastening of the carrying arm 31 provided with the x - ray calibration phantom 32 to the support mount 30 . in the present exemplary embodiment , the stand 33 is ( in a way not shown in detail ) height - adjustable , and is adjustable around ball - and - socket joints 34 , 35 for this purpose . for acquiring 2d projections of the x - ray calibration phantom 32 from different projection directions , the carrying arm 31 is released from the x - ray calibration phantom 32 and thus from the support mount 30 , but the orientation of the x - ray calibration phantom 32 does not change relative to the support mount 30 nor relative to the c - arm x - ray device 1 , so that the transformation rule between the coordinate system k h2 allocated to the support mount 30 and the coordinate system k r2 allocated to the x - ray calibration phantom 32 , which is known due to the defined arrangement of the x - ray calibration phantom 32 at the carrying arm 31 and of the carrying arm 31 at the support mount 30 , is preserved . for determining the coordinate transformation between the coordinate system k r2 allocated to the x - ray calibration phantom 32 and the coordinate system k m allocated to the measurement volume of the c - arm x - ray device 1 , a series of 2d projections of the x - ray calibration phantom 32 from different projection directions is acquired − after the removal of the carrying arm 31 − by movement of the c - arm 5 around its orbital axis . the coordinate transformation between the coordinate system k r2 allocated to the x - ray calibration phantom 32 and the coordinate system k m allocated to the measurement of the c - arm x - ray device 1 is then determined from the acquired series of 2d projections of the x - ray calibration phantom 32 . since , thus , the coordinate transformation between the coordinate system k h2 allocated to the support mount 30 and the coordinate system k r2 allocated to the x - ray calibration phantom 32 and the coordinate transformation between the coordinate system k r2 allocated to the x - ray calibration phantom 32 and the coordinate system k m allocated to the measurement volume of the c - arm x - ray device 1 are known , the coordinate transformation between the coordinate system k h2 allocated to the support mount 30 and the coordinate system k m allocated to the measurement volume can also be determined in a simple way . this latter transformation can be stored in a memory ( not shown in fig2 ) of the c - arm x - ray device 1 . a marker plate detectable by the position acquisition system 10 is arranged at the support mount 30 in a defined manner so that — as in the exemplary embodiment shown in fig1 — the coordinate system k h2 allocated to the support mount 30 can also be allocated to the marker plate . a transformation rule between the coordinate system k m allocated to the measurement volume and a coordinate system allocated to a position acquisition system thus can be determined . as a result , the pre - conditions are established for mixing images of an instrument into x - ray images of , for example , a patient acquired with the c - arm x - ray device 1 . fig3 illustrates a third possibility for determining a coordinate transformation between a coordinate system allocated to a c - arm x - ray device and a coordinate system allocated to the measurement volume of the c - arm x - ray device . the c - arm x - ray device shown in fig3 corresponds to the c - arm x - ray device 1 shown in fig1 and fig2 , so that the components of the c - arm x - ray device shown in fig3 are provided with the same reference characters as the components of the c - arm x - ray device 1 shown in fig1 and 2 . the c - arm x - ray device 1 shown in fig3 differs from the c - arm x - ray devices 1 shown in fig1 and 2 by virtue of a support mount 40 , to which a coordinate system k h3 is allocated , being arranged at the x - ray source 3 . a carrying arm 41 is arranged at the support mount 40 in a defined way and an x - ray calibration phantom 42 is arranged at the carrying arm 41 in a defined way . like the x - ray calibration phantoms 22 and 32 , the x - ray calibration phantom 42 has x - ray - positive marks whose orientation relative to a coordinate system k r3 allocated to the x - ray calibration phantom 42 is known . due to the defined arrangements of the carrying arm 41 at the support mount 40 and the x - ray calibration phantom 42 at the carrying arm 41 as well as due to the known dimensions of the carrying arm 41 , the coordinate transformation between the coordinate system k h3 allocated to the support mount 40 and the coordinate system k r3 allocated to the x - ray calibration phantom 42 is known . for determining the coordinate transformation between the coordinate system k h3 allocated to the support mount 40 and the coordinate system k m allocated to the measurement volume , and before the carrying arm 41 provided with the x - ray calibration phantom 42 is arranged at the support mount 40 , the x - ray calibration phantom 42 or some other x - ray calibration phantom is arranged relative to the c - arm x - ray device 1 independently of the carrying arm 41 , for example on any kind of substrate , so that an x - ray beam emanating from the x - ray source 3 can penetrate the x - ray calibration phantom . the x - ray calibration phantom 42 is employed in the exemplary embodiment . a first series of 2d projections of the x - ray calibration phantom 42 is acquired from different projection directions by moving the c - arm 5 around the orbital axis o , for example along its circumference . first projection matrices for the c - arm x - ray device 1 are determined therefrom and deposited in a memory of the c - arm x - ray device 1 . subsequently , the carrying arm 41 provided with the x - ray calibration phantom 42 is arranged at the support mount 40 , as shown in fig3 . a 2d projection of the x - ray calibration phantom 42 is now acquired at an arbitrarily selectable but defined position of the c - arm 5 . the only requirement is that c - arm this c - arm position must be a position of the c - arm 5 that this assumed in the acquisition of a 2d projection of the first series of 2d projections . a second projection matrix belonging to this position of the c - arm 5 is determined from this 2d projection . based on the known coordinate transformation between the coordinate system k h3 allocated to the support mount 40 and the coordinate system k r3 allocated to the x - ray calibration phantom 42 as well as based on a first projection matrix that is allocated to the defined position of the c - arm 5 , determined during the course of determining the first projection matrices , and based on the second projection matrix that is allocated to the defined position of the c - arm 5 , the coordinate transformation between the coordinate system k h3 allocated to the support mount 40 and the coordinate system k m allocated to the measurement of the c - arm x - ray device 1 is calculated . the calculation thereby ensues on the basis of the following equation : p 1 = p 2 * t ( k h3 ; k r3 ) * t ( k h3 ; k m ), wherein p 1 is the first projection matrix that is allocated to the defined position of the c - arm 5 , p 2 is the second projection matrix that is allocated to the defined position of the c - arm 5 , and t ( k h3 ; k r3 ) is the known transformation rule between the coordinate systems k h3 and k r3 . t ( k h3 ; k m ) is the sought transformation rule between the coordinate systems k h3 and k m . by resolution of the projection matrix p 1 into an extrinsic component and an intrinsic component as well as by resolution of the projection matrix that proceeds from a matrix multiplication of the projection matrix p 2 by the transformation rule t ( k h3 ; k r3 ) into an intrinsic component and extrinsic component , the transformation rule t ( k h3 ; k m ) can be composed of a rotary component and a translational component that are formed from the extrinsic components of the resolutions of the projection matrices . accordingly , the transformation rule between the coordinate system k h3 allocated to the support mount 40 and the coordinate system k m allocated to the measurement volume can be determined in this way , so that the preconditions are established for being able to mix images of an instrument into x - ray images of , for example , a patient acquired with the c - arm x - ray device 1 , with the assistance of a position acquisition system , for example the position acquisition system 10 of fig1 . in the exemplary embodiment shown in fig3 , moreover , second projection matrices can be acquired in a number of defined positions of the c - arm 5 on the basis of 2d projections of the x - ray calibration phantom 42 acquired at these position in order to determine the transformation rule between the coordinate system k h3 allocated to the support mount 40 and the coordinate system k m allocated to the measurement volume . it must be noted , however , that the second projection geometries of the c - arm x - ray device 1 may possibly be modified by the weight of the carrying arm 41 and of the x - ray calibration phantom 42 . this would then require an additional calibration of the c - arm x - ray device 1 with the carrying arm and the x - ray calibration phantom 42 arranged thereat . in the exemplary embodiments , the c - arm 5 is moved around its orbital axis o in order to acquire 2d projections of the x - ray calibration phantom . the c - arm 5 alternatively can be moved around its angulation axis a for acquiring 2d projections . further , the x - ray device need not necessarily be a c - arm x - ray device . the arrangements of the support mounts 20 , 30 and 40 as described in the exemplary embodiments are examples . in the exemplary embodiment shown in fig1 , for example , the support mount 20 alternatively can be arranged in a component of the c - arm x - ray device 1 that is immobile during the acquisition of the 2d projections . in the case of the exemplary embodiment shown in fig2 , further , the support mount 30 alternatively can be arranged at the x - ray source 3 or at the c - arm 5 . the situation is the same in the exemplary embodiment shown in fig3 . although modifications and changes may be suggested by those skilled in the art , it is the intention of the inventors to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of their contribution to the art .
a registration method and an apparatus for navigation - guided interventions employing an x - ray device and a position acquisition system and avoid the use of patient - associated markers . by means of a defined arrangement of a carrying arm proceeding from a support mount at the x - ray device and a defined arrangement of an x - ray calibration phantom at the carrying arm , the coordinate transformation between a coordinate system allocated to the support mount and a coordinate system allocated to the x - ray calibration phantom is known . on the basis of the acquisition and evaluation of 2d projections of the x - ray calibration phantom with the x - ray device , a coordinate transformation between the coordinate system allocated to the support mount and a coordinate system allocated to a measurement volume of the x - ray device is produced . by arranging a device detectable by the position acquisition system at the support mount , a coordinate transformation between the coordinate system allocated to the measurement volume and a coordinate system allocated to the calibration phantom is determined for the navigation .