Stair-case suppression for computed tomograph imaging

A correction algorithm for substantially eliminating "stair case" type artifacts in dental scans is described. In one specific embodiment, all high density object boundaries in the reformatted images are identified. To identify high density object boundaries, structures in the reformatted image are separated into two classes, namely, structure containing teeth and structure not containing teeth. Then, within each class, fuzzy logic is used to define the membership grade of each pixel. Particularly, linear interpolation is utilized to determine the boundary, and to reduce the probability that spike noise will be erroneously considered as high density objects, the N by N neighbors of the boundary candidate are searched to ensure that the number of pixels that belong to the high density object exceeds a certain predefined threshold. Such searching can be performed by summing the N by N neighbors of the membership function, .xi., and comparing the summation against a pre-defined threshold. Once the boundaries of the neighboring rows are located, the difference between the true boundary of the current row and the average boundary location of the two neighboring rows is determined to generate a boundary error candidate, .delta..sub.i,j. Since multiple boundaries can be found within each row, all the error candidates for the row are recorded and tested to determine the consistency among the error candidates within each row. Particularly, the average error candidate, .delta..sub.j and the average of the quantity .vertline..delta..sub.i,j -.delta..sub.i,j .vertline. for all the error candidates for row j is determined to produce .omega..sub.j. If .omega..sub.j is less than a pre-defined threshold, the shift in object boundaries for row j is likely caused by motion, and a simple linear shift of the row by an amount .delta..sub.i,j is performed. Otherwise, each boundary that has significant shift is smoothed along the boundary direction with the neighboring rows.

FIELD OF THE INVENTION 
This invention relates generally to computed tomography (CT) imaging and 
more particularly, to suppressing stair-case artifacts in multi-planar 
reformat CT imaging. 
BACKGROUND OF THE INVENTION 
In at least one known CT system configuration, an x-ray source projects a 
fan-shaped beam which is collimated to lie within an X-Y plane of a 
Cartesian coordinate system and generally referred to as the "imaging 
plane". The x-ray beam passes through the object being imaged, such as a 
patient. The beam, after being attenuated by the object, impinges upon an 
array of radiation detectors. The intensity of the attenuated beam 
radiation received at the detector array is dependent upon the attenuation 
of the x-ray beam by the object. Each detector element of the array 
produces a separate electrical signal that is a measurement of the beam 
attenuation at the detector location. The attenuation measurements from 
all the detectors are acquired separately to produce a transmission 
profile. 
In known third generation CT systems, the x-ray source and the detector 
array are rotated with a gantry within the imaging plane and around the 
object to be imaged so that the angle at which the x-ray beam intersects 
the object constantly changes. A group of x-ray attenuation measurements, 
i.e., projection data, from the detector array at one gantry angle is 
referred to as a "view". A "scan" of the object comprises a set of views 
made at different gantry angles during one revolution of the x-ray source 
and detector. In an axial scan, the projection data is processed to 
construct an image that corresponds to a two dimensional slice taken 
through the object. One method for reconstructing an image from a set of 
projection data is referred to in the art as the filtered back projection 
technique. This process converts that attenuation measurements from a scan 
into integers called "CT numbers" or "Hounsfield units", which are used to 
control the brightness of a corresponding pixel on a cathode ray tube 
display. 
With respect to reformatted dental scans, the reformation is performed 
across slices along a pre-defined curved line, in a similar manner as 
multi-planar reformation. A pronounced "stair case" artifact may appear in 
the reformatted image. This artifact is caused by patient motion and/or by 
irregular table motion. Increasing the amount of motion suppression in the 
tomographic reconstruction reduces the motion effect. For example, and for 
motion suppression, the projection data set is first multiplied by a set 
of "underscan" weighing factors before the reconstruction process. Since 
the underscan weighting reduces the contribution at the beginning and end 
of the projection data set, patient motion related artifacts can be 
substantially reduced. 
The underscan weighting, however, reduces the contribution from the views 
that are closest to the projections used in the generation of the 
neighboring slices. As a result, although the motion effect within each 
tomographic slice is reduced, the discontinuity between slices is 
increased. 
It would be desirable to provide a correction algorithm which is effective 
in correcting images for stair case type artifacts in dental scans. It 
also would be desirable to provide such an algorithm which enables 
reducing the motion effect within each tomographic slice without 
increasing the discontinuity between slices. 
SUMMARY OF THE INVENTION 
These and other objects may be attained by a correction algorithm for 
substantially eliminating "stair case" type artifacts in dental scans. 
More particularly, and in one specific embodiment, all high density object 
boundaries in the reformatted images are identified. To identify high 
density object boundaries, structures in the reformatted image are 
separated into two classes, namely, structure containing teeth and 
structure not containing teeth. To perform such classification, and for 
each row in the reformatted image (and therefore, each slice in the 
reconstructed image), the maximum intensity is identified. If the maximum 
intensity exceeds a predefined threshold, the row is classified as the 
"teeth" class. Otherwise, the row is classified as not containing teeth, 
i.e., formed with bones only. 
Then, within each class, fuzzy logic is used to define the membership grade 
of each pixel. Particularly, linear interpolation is utilized to determine 
the boundary, and to reduce the probability that spike noise will be 
erroneously considered as high density objects, the N by N neighbors of 
the boundary candidate are searched to ensure that the number of pixels 
that belong to the high density object exceeds a certain predefined 
threshold. Such searching can be performed by summing the N by N neighbors 
of the membership function, .xi., and comparing the summation against a 
pre-defined threshold. 
Once the boundaries of the neighboring rows are located, the difference 
between the true boundary of the current row and the average boundary 
location of the two neighboring rows is determined to generate a boundary 
error candidate, .delta.i,j. Since multiple boundaries can be found within 
each row, all the error candidates for the row are recorded and tested to 
determine the consistency among the error candidates within each row. 
Particularly, the average error candidate, .delta..sub.j and the average 
of the quantity .vertline..delta..sub.j -.delta..sub.i,j .vertline. for 
all the error candidates for row j is determined to produce .omega..sub.j. 
If .omega..sub.j is less than a pre-defined threshold, the shift in object 
boundaries for row j is likely caused by motion, and a simple linear shift 
of the row by an amount .delta..sub.j is performed. Otherwise, each 
boundary that has significant shift is smoothed along the boundary 
direction with the neighboring rows. 
The above described algorithm is believed to be effective in correcting 
images for stair case type artifacts in dental scans. Particularly, such 
algorithm enables reducing the motion effect within each tomographic slice 
without increasing the discontinuity between slices.

DETAILED DESCRIPTION 
Referring to FIGS. 1 and 2, a computed tomography (CT) imaging system 10 is 
shown as including a gantry 12 representative of a "third generation" CT 
scanner. Gantry 12 has an x-ray source 14 that projects a beam of x-rays 
16 toward a detector array 18 on the opposite side of gantry 12. Detector 
array 18 is formed by detector elements 20 which together sense the 
projected x-rays that pass through a medical patient 22. Each detector 
element 20 produces an electrical signal that represents the intensity of 
an impinging x-ray beam and hence the attenuation of the beam as it passes 
through patient 22. During a scan to acquire x-ray projection data, gantry 
12 and the components mounted thereon rotate about a center of rotation 
24. 
Rotation of gantry 12 and the operation of x-ray source 14 are governed by 
a control mechanism 26 of CT system 10. Control mechanism 26 includes an 
x-ray controller 28 that provides power and timing signals to x-ray source 
14 and a gantry motor controller 30 that controls the rotational speed and 
position of gantry 12. A data acquisition system (DAS) 32 in control 
mechanism 26 samples analog data from detector elements 20 and converts 
the data to digital signals for subsequent processing. An image 
reconstructor 34 receives sampled and digitized x-ray data from DAS 32 and 
performs high speed image reconstruction. The reconstructed image is 
applied as an input to a computer 36 which stores the image in a mass 
storage device 38. 
Computer 36 also receives commands and scanning parameters from an operator 
via console 40 that has a keyboard. An associated cathode ray tube display 
42 allows the operator to observe the reconstructed image and other data 
from computer 36. The operator supplied commands and parameters are used 
by computer 36 to provide control signals and information to DAS 32, x-ray 
controller 28 and gantry motor controller 30. In addition, computer 36 
operates a table motor controller 44 which controls a motorized table 46 
to position patient 22 in gantry 12. Particularly, table 46 moves portions 
of patient 22 through gantry opening 48. 
The correction algorithm described below may be implemented in computer 36 
and practiced using the image generated by image reconstructor 34. It will 
be apparent to those skilled in the art, of course, that such algorithm 
could be practiced in other components. In addition, the correction 
algorithm is described below as being performed in the reformatted image 
space for computational simplicity. Of course, such correction could be 
performed on the original reconstructed images. In addition, the term 
"high density" objects refers to objects having significantly different 
densities as compared to soft tissue. 
As described above, and with reformatted dental scans, most stair-case 
artifacts appear near the edge of high density objects, e.g., bones and 
teeth. If the artifact is caused by simple motion, e.g., patient or table 
motion, the motion artifact can be easily removed from the image by simple 
geometric transformation. Particularly, since the bony structure is rigid, 
the motion will likely appear as a simple one dimensional translation of 
the slice. 
If the artifact is caused by other factors, e.g., as a result of the 
interpolation algorithm or calibration errors, the mis-alignment of the 
boundaries probably will not be consistent for all structures. That is, 
there will be inconsistency among boundary shifts within each slice. When 
an inconsistency among boundary shifts within each slice is present, no 
geometric transformations are performed on the image slice. Rather, the 
edges along the object boundaries are smoothed or no operation is 
performed on the boundaries. 
In accordance with one embodiment of the correction algorithm, and to 
eliminate the "stair case" artifact, all high density object boundaries in 
the reformatted images are identified. Significant density variations can 
exist, however, even among dense objects. For example, the CT number for 
teeth is much higher than the CT number for bones. As a result, a simple 
threshold method is not sufficient for identifying object boundaries. 
Therefore, to identify high density object boundaries, structures in the 
reformatted image are separated into two classes, namely, structure 
containing teeth and structure not containing teeth. To perform such 
classification, and for each row in the reformatted image (and therefore, 
each slice in the reconstructed image), the maximum intensity is 
identified. If the maximum intensity exceeds a predefined threshold, the 
row is classified as the "teeth" class. Otherwise, the row is classified 
as not containing teeth, i.e., formed with bones only. 
Then, within each class, fuzzy logic is used to define the membership grade 
of each pixel. The relationship between the membership grade and its pixel 
intensity are defined as: 
##EQU1## 
where 
##EQU2## 
where P.sub.hi and P.sub.lo are empirically determined parameters for each 
class. The "rough" boundaries are defined as the location where the 
membership value is closest to 0.5. The true boundary, .gamma..sub.i,j, is 
defined as the location where the membership value equals 0.5. The indexes 
i,j indicate the i.sup.th boundary identified for the j.sup.th row in the 
reformatted image. Linear interpolation is performed for the true boundary 
determination. The true boundary .gamma..sub.i,j, in general, is not an 
integer. 
To reduce the probability that spike noise will be erroneously considered 
as high density objects, the N by N neighbors of the boundary candidate 
are searched to ensure that the number of pixels that belong to the high 
density object exceeds a certain predefined threshold. Such searching can 
be performed by summing the N by N neighbors of the membership function, 
.xi., and comparing the summation against a pre-defined threshold. 
A boundary search for the slices that are immediately above and below the 
current slice is then performed. The search is centered around the 
boundary candidate to the left and right of M pixels. An exemplary search 
is shown in FIG. 3, and this search, M=3. Limiting the boundary search for 
the neighboring rows to the nearby pixels avoids the situation where the 
boundaries of other high density objects are included in the current 
boundary. Since the scan is taken with thin slice thickness and the high 
density objects are, in general, continuous, this search strategy is 
believed to be reliable. 
Once the boundaries of the neighboring rows are located, the difference 
between the true boundary of the current row and the average boundary 
location of the two neighboring rows is determined to generate a boundary 
error candidate, .delta..sub.ij. Specifically: 
##EQU3## 
Since multiple boundaries can be found within each row, all the error 
candidates for the row are recorded and no correction is made until 
further testing is performed. 
Specifically, the following test determines the consistency among the error 
candidates within each row. The average error candidate, .delta..sub.j 
and the average of the quantity .vertline..delta..sub.j -.delta..sub.i,j 
.vertline. for all the error candidates for row j is determined to produce 
.omega..sub.j. If .omega..sub.j is less than a pre-defined threshold, the 
shift in object boundaries for row j is likely caused by motion, and a 
simple linear shift of the row by an amount .delta..sub.j is performed. 
Otherwise, each boundary that has significant shift is smoothed along the 
boundary direction with the neighboring rows. 
The above described algorithm is believed to be effective in correcting 
images for stair case type artifacts in dental scans. Particularly, such 
algorithm enables reducing the motion effect within each tomographic slice 
without increasing the discontinuity between slices. Further, the 
algorithm is not limited to use in only dental scans but can be used to 
remove stair-case artifacts in bone or air pocket images. Generally, 
images of object pairs which have a significant density difference can be 
corrected using the above described algorithm. For example, images for 
object pairs such as soft tissue/air and soft tissue/bone have 
significantly different densities and can be corrected using the above 
described algorithm. 
From the preceding description of various embodiments of the present 
invention, it is evident that the objects of the invention are attained. 
Although the invention has been described and illustrated in detail, it is 
to be clearly understood that the same is intended by way of illustration 
and example only and is not to be taken by way of limitation. Accordingly, 
the spirit and scope of the invention are to be limited only by the terms 
of the appended claims.