[ 0062 ] fig4 illustrates a spiral scan cone beam 3d ct imaging system in which an image reconstruction protocol according to the present invention may be implemented for accurately reconstructing a roi image within a long object . in a preferred embodiment , the imaging system 40 of fig4 is preferably constructed and operates substantially in accordance with the principles described in the above - incorporated u . s . pat . nos . 5 , 257 , 183 and 6 , 018 , 561 , except as to be specifically described herein with respect to implementation of an image reconstruction process according to the present invention . in particular , as explained in detail below , a preferred embodiment of the present invention comprises an extension of the image reconstruction protocol described in the above - incorporated u . s . pat . no . 6 , 018 , 561 to enable accurate image reconstruction of an roi within a long object . referring now to fig4 in response to control signals from an appropriately programmed computer 43 , a computer controlled manipulator 44 causes a source 42 of a cone or pyramid shaped beam of energy ( such as x - rays ) and a two - dimensional pixelated detector array 41 to cooperate ( scan ) at a plurality of discreet , sequentially occurring , adjacent source positions along a pre - defined source scanning path . in the illustrated embodiment the scanning path is shown as a spiral scan path 48 of a roi 49 a , which is centered on a predetermined axis 49 b of a long object 49 . the figure assumes an upward counterclockwise rotation of the scan path 48 with a beginning portion b near the bottom of the roi 49 a and an ending portion e near the top of the roi 49 a . further , the spiral scan path 48 is shown as being just big enough to cover the roi 49 a of the long object 49 . other types of scan paths that encircle and traverse object 49 can also be used , however , as will become apparent later , a scan path 48 exhibiting a high degree of symmetry in its parallel projection is preferred . as a result of the source / detector cooperation under control of computer 43 and manipulator 44 , at each of the source positions along path 48 , x - ray energy passes through the field of view of the imaging apparatus , is attenuated by object 49 a , and a set of projection data corresponding to the sensed x - ray energy falling on the elements ( pixels ) within detector 212 is developed . each set of projection data is supplied to a data acquisition system ( das ) 45 which , like the previously described portions of fig4 may operate in a fashion well known to those of ordinary skill in this technology for digitizing and storing of the acquired projection data . an image reconstruction model 46 implements protocols described herein for reconstruction a 3d image from the acquired projection data , which reconstructed 3d image can be displayed on display 47 . as noted above , one embodiment for image reconstruction described in u . s . pat . no . 6 , 018 , 561 comprises the “ short object algorithm ,” wherein image reconstruction processing is applied to a plurality of sets of 2d cone beam projection data , each set being acquired on a 2d detector at a corresponding plurality of scan path source positions . in a preferred embodiment of the present invention , the short object algorithm ( which is described in more detail below ) is extended for accurately reconstruction an roi image within a long object . a first image reconstruction processing step comprises applying a mask to each set of the projection data so that data inside the boundaries of each mask form a corresponding plurality of masked 2d data sets . as described in more detail in the above - incorporated u . s . pat . no . 6 , 018 , 561 , the step of applying a mask comprises applying a spiral mask ( such as shown in fig5 ) to each set of the projection data so that data inside the boundaries of each mask form a corresponding plurality of masked 2d data sets . the mask 50 comprises a top curve 51 and a bottom curve 52 , each curve being formed by cone beam projections of the spiral scan path turn above and the spiral scanpath turn below the current source position . we shall refer to this mask as a data - combination mask . more specifically , as noted above , fig4 illustrates a cone beam spiral scan 48 of a region of interest 49 a of a long object 49 . for a flat detector 41 located at the rotation axis 49 b such that the line connecting a source 42 to an origin of the detector 41 is normal to the detector plane , the equation for the top curve for the spiral scan is given by : v = h 2  π  tan - 1  ( r u )  ( 1 + u 2 r 2 ) u ≥ 0 v = h 2  π  [ π + tan - 1  ( r u ) ]  ( 1 + u 2 r 2 ) u & lt ; 0 ( 1 ) where u and v are the cartesian coordinate axes of the detector ( as shown in fig5 ) with the v axis coinciding with the rotation axis , r is the radius of the spiral , and h is the distance between adjacent spiral turns ( the pitch ). the bottom curve is the reflection of the top curve about the origin , i . e . ( u , v )-& gt ;(− u ,− v ). the shape of the spiral mask is shown in fig5 . in accordance with the general principles of masking , data in the set that is outside the mask is changed to a zero value , while data that is inside the mask is left unchanged . after a set of projection data is appropriately masked , it is referred to as a masked set of projection data , or more simply as a masked data set . since the masks are formed by cone beam projection of the spiral turn above and the turn below the current source position , the masked data set corresponds exactly to the angular range bound by the prior and the subsequent source positions , as required by the data combination principles . a second step comprises 1d ramp filtering of each masked 2d data set along a plurality of parallel lines formed therein , to generate a corresponding plurality of filtered 2d data sets . each filtered 2d data set is a calculation of a first estimate of radon derivative data determined from a given set of the 2d cone beam projection data . more specifically , a feldkamp ramp filtering technique is applied to the masked sets of projection data , wherein each set of masked data is ramp filtered along a plurality of parallel lines ( t ) formed therein , which lines are parallel with and in the direction of a parallel projection into the data set of a line that is tangent to the scan path at the source position that acquired that data set and in the direction of the next source position . ramp filtering of each masked data set along lines ( t ) generates a corresponding plurality of filtered data sets , where the data at each point along each line represents a summation of the radon data at that point . a third step comprises developing 2d correction data for each of the first estimates of radon derivative data by processing portions of the given set of cone beam projection data that are adjacent boundaries of the mask . a fourth step comprises combining each filtered 2d data set and the 2d correction data calculated therefore , in a weighted 3d backprojection manner into a 3d space , thereby reconstructing a 3d image of the roi in the object . in accordance with the principles of the present invention , an extension to the “ short object algorithm ” described above is implemented to eliminate / mitigate data contamination . in a preferred embodiment , step 3 of the above process is modified to achieve roi reconstruction in the spiral scan of a long object , wherein those source positions near both ends of the spiral scan path ( e . g ., portions b and t of the spiral scan path 48 shown in fig4 ) which see the overlaying objects are first identified , and step 3 is skipped in processing the associated cone beam data . a process for identifying contamination data will now be described in detail , with references to fig7 - 12 . [ 0073 ] fig7 is an exemplary diagram that illustrates a local region of interest ( roi ) 71 ( of long object 70 ) defined by a spiral path projection 72 . fig8 a and 8 b illustrate a correspondence between an integration line segment on a detector and line integral interval on a n plane . a “ n plane ” as defined herein is a plane in radon space that contains the z axis oriented at an azimuthal angle n . [ 0074 ] fig8 a specifically illustrates a n plane = n i , wherein the illustrated sine curve 80 comprises a projection of the spiral path 72 on the n plane from a source position s . in particular , the parallel projection of the spiral path 72 on a n plane is in the form of a sinusoidal curve 80 bound between the projection of the two side edges ( 73 and 74 ) of a spiral cylinder effectively defined by the spiral scan path 72 . the phase of the sinusoidal 80 is dependant on the orientation of the n plane . the dotted lines in fig8 a from s ( source position ) represent all line integral intervals on the n i plane that intersect s on the spiral scan path ( the line integral intervals represent the data generated on the n i plane the source position s . [ 0075 ] fig8 b illustrates a detector plane , representing an image generated at source position s . the term c i ( s ) corresponds to plane n = n i at source position s . the dotted lines on the detector in fig8 b are integration line segments that correspond to the line integral intervals in fig8 a . in fig7 various portions of the sinusoidal partitioned by the side edges 73 , 74 are referred to herein as “ sinusoidal stages ”. as shown in fig7 a sinusoidal stage is deemed “ complete ” if both ends of the sinusoidal state are in touch with the side edges 73 , 74 , otherwise the sinusoidal stage is deemed “ incomplete ”. a “ complete ” sinusoidal stage contains source positions covering an angular range of b . in accordance with the present invention , on each n plane , the top and the bottom edges of a local roi are defined by the uppermost and the lowermost “ complete ” sinusoidal stages of the spiral path projection , as illustrated in fig7 . a reconstructed ( global ) roi is formed by the intersection of all local roi &# 39 ; s . from a theoretical point of view , the filtering steps ( step 2 and step 3 ) of the above - described “ short object ” algorithm are essentially equivalent to a filtering process involving all integration line segments on the detector ( fig8 b ). as noted above , fig8 a and 8 b show the correspondence between line integral intervals on a n plane an integration line segment on the detector . accordingly , the filtering processes applied to the set of line segments that intersect at a common point on the u axis ( of the detector ) ( fig8 b ) generates a corresponding set of line integral intervals on a n plane ( fig8 a ). this correlation between a n plane and a location on the u axis is described in detail , for example , in the above incorporated u . s . pat . no . 5 , 257 , 183 . since the set of line segments on the detector ( fig8 b ) are limited at the mask boundary , the set of line integral intervals on the n plane ( fig8 a ) are limited at the next sinusoidal stage above and below the current source position . furthermore , a line segment on the detector bounded between the u axis and the upper / lower the mask boundary corresponds to a line integral interval on the n plane bounded between the current source position and the upper / lower sinusoidal stage . consider a source position s in the views [ 0 , b ] ( i . e ., a first half of a spiral circle ) measured from the end t of the spiral path , as shown in fig7 . the source position s projects onto some n planes onto the uppermost complete stage of the spiral path projection . the line integral intervals on the n planes below s illuminate the local roi 71 , whereas the line integral intervals on the n plane above s illuminate the objects outside the local roi 71 . due to the correspondence between integration line segment on the detector and line integral interval on a n plane ( as illustrated in fig8 ) to reconstruct the local roi on these n planes , only the portion of cone beam data below the u axis on the detector are utilized because the portion of cone beam data above the u axis illuminate the objects outside the local roi and , thus , contribute to the contamination of the roi . thus , for these n planes , step 3 of the short object algorithm is applied to only the lower mask boundary in filtering the cone beam data at s . on the other n planes , s 1 projects outside the uppermost complete stage of the spiral path projection . for these n planes , all the cone beam data of s illuminate the objects outside the local roi and therefore contribute to the contamination of the roi . thus for these n planes , step 3 of the short object algorithm is skipped entirely in filtering the cone beam data at s 1 . consider a source position s in the views [ b , 2b ] measured from the end of the spiral path . s projects onto some n planes onto the uppermost complete stage of the spiral path projection . the line integral intervals on the n planes below s illuminate the local roi , and the line integral intervals on the n plane above s illuminate the objects outside the local roi . due to the correspondence between integration line segment on the detector and line integral interval on a n plane as illustrated in fig8 for the reconstruction of the local roi on these n planes , only the portion of cone beam data below the u axis on the detector are needed ; the portion of cone beam data above the u axis illuminate the objects outside the local roi and therefore contribute to the contamination of the roi . thus , for these n planes , step 3 is applied to only the lower mask boundary in filtering the cone beam data at s . on the other n planes , s projects inside the uppermost complete stage of the spiral path projection . for these n planes , all the cone beam data of s illuminate the local roi and therefore do not contribute to the contamination of the roi . thus , for these n planes , no modification of step 3 is needed in filtering the cone beam data at s . in the following description of preferred embodiments , a detailed discussion will be provided regarding the grouping processes for the source positions in the view angular range [ 0 , b ] and those in the view angular range [ b , 2b ], both measured from the end of the spiral path ( e . g ., t in fig7 ). the grouping processes for the source positions near the start of the spiral path ( e . g ., b in fig7 ) is similar except for obvious modifications . in the following analysis , it is assumed that the sense of the rotation of the source along the spiral is anticlockwise up . the analysis can be readily modified for the opposite sense of source rotation . referring now to fig9 a diagram illustrates various source positions in the angular range [ 0 , b ]. more specifically , fig9 illustrates a top view wherein circle 90 represents of an object 90 being imaged from a source position s i in the view angular range [ 0 , b ] measured from a spiral end source position s 0 . the circle 91 represents the spiral path traversed by the x ray source s . in fig9 a line l 1 starting from ending source position s o is tangential to spiral scan circle 91 . the radon space n plane that forms an orthogonal intersection with line l 1 defines the radon space n o plane . assuming anti - clockwise rotation of the source , source position s i is marked on circle 91 . a line l 2 that passes through s i is parallel with l 1 and , therefore , bears an orthogonal relationship with the radon space n o plane . the point c o is defined as the point at which the line l 2 intersects the u - axis of the detector that acquires the cone beam data at source position s i the detector plane 93 that acquires the cone beam data at s i is determined by its orthogonal relationship to line l 3 that extends from source position si to the center of the object 90 . [ 0086 ] fig1 a , 10 b and 10 c respectively illustrate projections of the spiral path on n + , n o and n − planes shown in fig9 ( viewing the spiral path in fig9 from three different angles ). as shown in fig1 b , in the direction n 0 , the end source position s 0 projects onto the edge of the spiral cylinder . also shown in fig9 and 10 are two directions n + and n − incrementally rotated from n 0 in the opposite directions . as shown in fig1 a , in the direction n + , the spiral path portion containing s i and ending at s 0 does not touch the tangent to the spiral cylinder on the right hand side . therefore on the n = n + plane , the sinusoidal stage on which the current source position s i projects does not reach both edges of the spiral cylinder projection , as illustrated in fig1 a , and thus this sinusoidal stage is incomplete . in other words , since s o does not touch the edge of the spiral cylinder on the right side , the top segment of the spiral turn is incomplete ( i . e ., less than b ) consequently , on this plane , the uppermost complete sinusoidal stage which defines the top edge of the local roi is the stage beneath , as shown in fig1 a . since the projection of s i lies outside the local roi , s i contributes to the contamination of the local roi on the n = n + plane . in other words , because s i is located on an incomplete segment , the data from s i is not considered . on the other hand , in the direction n − , the spiral path portion containing s i and ending at s 0 touches the tangent to the spiral cylinder on the right hand side . therefore , on the n = n − plane , the sinusoidal stage on which the current source position s i projects reaches both edges of the spiral cylinder projection , as illustrated in fig1 c , and thus this sinusoidal stage is complete . consequently , on this plane , the projection of s i lies on the uppermost complete sinusoidal stage which defines the top edge of the local roi on the n = n − plane , as shown in fig1 c . referring again to fig9 let the points c 0 , c + , and c − on the u axis respectively denote the projection on the detector of the current source position in the direction n 0 , n + , and n − . the points c + and c − are respectively to the left and to the right of c 0 . all the radon derivative data generated on the n = n + plane using the cone beam data detected at s i come from integration line segments that intersect c + . as discussed above for fig1 a , since s i contributes to the contamination of the local roi on the n = n + plane , to avoid contamination , the boundary / correction term at both the upper and lower mask boundary is preferably skipped for integration line segments intersecting c + and by extension of step 3 of the short object algorithm , the boundary / correction term at both the upper and lower mask boundary is preferably skipped for integration line segments intersecting to the left of c 0 on the u axis . on the other hand , all the radon derivative data generated on the n = n − plane using the cone beam data detected at s i come from integration line segments that intersect c 31 . as discussed above for fig1 c , since the projection of s i lies on the uppermost complete sinusoidal stage which defines the top edge of the local roi on the n = n − plane , the portion of the cone beam data above the u axis contributes to the contamination of the local roi . consequently to avoid contamination , the boundary / correction term at the upper mask boundary is preferably skipped for integration line segments that intersect c − , and by extension , the boundary / correction term at the upper mask boundary is preferably skipped for integration line segments that intersect to the right of c 0 on the u axis . [ 0090 ] fig1 is a diagram that illustrates a portion of a mask boundary to which a filtering step ( step 3 ) is applied for source positions in the angular range [ 0 , b ] from the spiral end . in other words , the diagram of fig1 summarizes how the boundary / correction term is skipped for the cone beam images in the view angular range [ 0 , b ] measured from the spiral end . integration line segments are shown for an arbitrary projection angle 2 . more specifically , in fig1 , a set of cone bean data 100 acquired at a given source position si , the point co is marked on the u axis of detector . the data combination mask 101 is applied to the cone beam data 100 , and a plurality of lines 102 are formed in the set of cone beam data 100 ( as discussed above ). generally , the endpoints ( and thus length ) of the lines 102 are determined by the outer boundaries of the data combination mask 101 for all source positions that are internal of the top and bottom 2b angular range in the scan path that are near the top and bottom edges , respectively , of the roi . however , as shown in fig1 , the line segments that which cross the u axis to the right of point co ( corresponding to fig1 c ) have their endpoints determined by one of lower boundary of the mask and the u axis , and all of the line segments crossing the u axis to the left of co ( corresponding to fig1 a ) are not used . in other words , the boundary / correction term at the upper mask boundary is skipped for line segments which intersect the u axis to the right of c 0 , and the boundary / correction term at both the upper and lower mask boundary is skipped for line segments which cross the u axis to the left of c 0 . the process is repeated for all 2 . the above analysis can be made in a similar manner as in the case of view angular range [ b , 2b ], and a detailed analysis is not necessary to understanding the invention . fig1 summarizes how the boundary / correction term is skipped for the cone beam images in the view angular range [ b , 2b ] measured from the spiral end . the point c 0 is constructed as illustrated in fig9 . integration line segments are shown for an arbitrary projection angle 2 . the boundary / correction term at the upper mask boundary is skipped for line segments that intersect the u axis to the left of c 0 . the process is repeated for all 2 . although illustrative embodiments of the present invention have been described herein with reference to the accompanying drawings , it is to be understood that the invention is not limited to those precise embodiments , and that various other changes and modifications may be affected therein by one skilled in the art without departing from the scope or spirit of the invention . all such changes and modifications are intended to be included within the scope of the invention as defined by the appended claims .
a system and method for accurately reconstructing an image of a roi within a long object by removing components associated with data contamination . in one aspect , an image reconstruction method comprises collecting a set of image data along a spiral scan path of a roi portion of an object , identifying contaminated data within the collected set of image data , the contaminated data corresponding to image data associated with an object outside the roi , and reconstructing an image of the roi using the set of image data less the contaminated data .