Geometric Image Correction and Iso-Center Calibration at Oblique Biplane Angiographic Views

Dietrich G. W. Onnasch and Guido P. M. Prause Clinic for Pediatric Cardiology, Section Biomedical Engineering

University of Kiel, Germany

Abstract I n the X-ray image intensifier TV system there are

geometric image distortion which can be subdivided in pincushion distortions, S-shaped warping, image twist- ing and shifting. These errors depend partly on the direction of the geomagnetic field relative to the im- age intensifier axis and are to be corrected for each view specifically. For caudal or cranial views there is the additional problem that in biplane images the slices of an object are projected o n oblique lines. Based on four small bronze washers marking a centered square on each image intensifier screen, a dewarping pro- gram automatically calculates a non-lanear polynomial transformation. Then all points of the image or the study are dewarped and centered accordingly. At the same time the geometric calibration factors are de- rived. From the registered viewing angles, those angles are calculated by which both images have to be rotated f o r biplane alignment. Both, optimal biplane visual- ization and the base for further analyses are achieved.

1 Introduction

Exact image pairing in biplane angiocardiography has to be made for quantitative analyses as biplane ven- tricular volume determination, the 3D reconstruction of the coronary artery tree [l], or the binary recon- struction of ventricular cross-sections [2]. In princi- ple, this is feasible for isocenteric biplane multiaxial C- or L-arm units which allow to read the projection angles and viewing distances by a computer interface [3]. However, there are geometrical image degrada- tions and relative image rotations which both depend on the projection angles from which the angiocardio- graphy was taken. Therefore we developed dewarp- ing and alignment procedures that are applied to the recorded angiocardiogram before further evaluations are performed.

(On8/1) 'Supported by the Deutsche Forschungsgemeinschaft

2 Geometric image distortions 2.1 Distortions due to magnetic fields

Due to the concave shape of input screen of the image intensifier (11), X-ray angiograms are distorted like a pincushion. In new 11s this distortion is compensated largely by a convex shaped output phosphor screen.

Figure 1. A difference image of a grid imaged with the 17cm field of the image intensifier at the lateral (in white) and frontal view (in black). There is a twisting of the image by about 2.5' around a point outside the center of the input screen. Pincushion distortion is negligible for this reduced field of view.

However, additional degradations arise from the in- teraction of the geomagnetic field with the electrons accelerated inside the image intensifier. As dependent on the direction of that external field relative to the image plane, unsymmetrical S-shaped warping arise as well as a displacement and twisting of the complete image [4,5]. For our equipment (11s Optilux 27HD Triplex and BICOR support system from Siemens) the geometric distortions can be assessed from fig. 1.

We found a systematic change of image twisting (f2.5') and varying center displacement (up to 5") depending on the orientation of the gantry.

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2.2 Correction method To correct these distortions the following procedure was developed. Four small bronze washers (3” 8) are sticked steadily to the corners of a 60“ centered vertical square on the I1 screen (see fig. 4). Because they are semi-transparent, they do not disturb the an- giocardiogram and disappear in DSA images.

Figure 2. Distorted (ti, vi) and true coordinates (ti, y:) of the four markers used to calculate the eight coefficients (or,bk, & = 0,. . . ,3) of the given non-linear polynomial transformation.

Within one image of the sequence these markers are located automatically. Then the ideal positions are calculated such that they form a centered verti- cal square with the same area as the imaged warped quadrangle. Fkom these data, the eight parameters of a global transformation to dewarp and center the square are calculated [5] (fig. 2). That transformation is then applied to each point of the image or to the complete study.

2.3 Automatic marker detection Although the four markers are hard to be seen in the angiocardiogram, they are detected fully automat- ically, normally within a pre-injection frame of the recorded angiocardiography [6].

The algorithm is based on the convolution of the im- age with a kernel adapted to the ring shaped markers. To increase the reliability and computational speed only small areas around the guessed locations are con- sidered, first assuming the large (27cm) field of view (FOV). After filtering, the markers are located apply- ing the maximum operator to the sub-images (fig. 3). If the detected positions do not form the corner points of a shifted and rotated square (within possible defor- mations, deviations up to 5% are allowed), it is as- sumed that a smaller FOV was used and the procedure is repeated. If the “square” condition is not fulfilled for any of the three FOVs, it is assumed that one of the

four markers was detected wrong - probably because it was imaged close to the catheter or another dominant structure. In this case the fourth point is searched within the immediate vicinity of the guessed position as derived from the other three detected markers.

Figure 3. To detect the markers in an image (upper left panel) four subimages covering the guessed locations are filtered (right) such that a maximum operator can be ap- plied (lower left panel). Finally it is tested whether the de- tected markers form a slightly rotated and shifted square.

2.4 Geometric calibration The markers are not only used to dewarp and center the image but also to calibrate geometric measure- ments. By comparing the true and the imaged size of the square in the dewarped image the calibration factor is derived. The distance X-ray focus to the I1 is taken from the gantry control circuit and is registered during image acquisition [3]. The object distance is assumed to be the isocenter distance or taken from the second view.

3 Rotated biplane projections 3.1 Within an arbitrary orientated biplane gantry there is just one orientation of the stack of slices of the imaged object such that corresponding lines coincide. In the special case of no caudocranial angulation the scan lines of both images coincide with the horizontal

Image rotation at oblique views

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plane of the patient. In general however, both pro- jected images A and B must be rotated to be com- bined slice by slice (fig. 4). Tools to calculate the an- gle between oblique views have already been derived by Wollschlager et al. [7] and Dodge et al. [l]. How- ever, the rotational angles of the projected images for correct biplane alignment have not been calculated for combined C- and L-arm equipment and not for non- orthogonal orientated views.

Figure 4. A square plane is positioned in the isocenter perpendicular to both I1 input screens for an oblique or- thogonal projection (system A: 45’ left anterior oblique, 40’ cranial; system B: 120’ left posterior oblique, 17’ cau- dal). The direction of the video scan lines is indicated by copper rulers fixed on both image intensifiers. The pro- jections of the imaged plane appear m lines in both views indicating exact orthogonal projection. They are inclined by P A = 22’ and p~ = 53’, respectively.

3.2 Mathematical correction Here we calculate the rotational angles from the four projection angles. The solution depends on the way the support system is turned to a certain oblique po- sition P” (fig. 5). We present the mathematical tools for the geometric properties of the Siemens BICOR system.

3.2.1 Spatial rotations

The rotation of a Cartesian coordinate system C = (O,x, y, z ) around line g through the origin 0 into the system C’ = (0, d, y’, 2’) is given in mathemat- ical handbooks [8]. For C-arm units it is performed in two steps. For the system A (Coroskop C) of the BICOR, the standard position of which is in the pa position, there is first a rotation around g = x by the angle a, describing the left anterior rotation (left- ward positive), and second around the inclined y-axis (0, cos a, - sin cy) by the angle p to achieve the cran- iocaudal angulation (caudal positive) (fig. 5, upper

anterior Sysfem A

Figure 5. Definition of the axes and angles. The move- ments to achieve a certain left anterior and caudal angula- tion P” are different for the two sub-systems A and B of the BICOR.

panel). This leads to

211 = xcosp + zsinp (1) y“ = -xsina s i n p + y c o s a + z s i n a cosp z’l = -xcoscy sin0 - ysincy+zcoscy cos@

For the system B (Coroscop L), mounted on the ceiling, the rotational axes are different (fig. 5, lower panel). While the left- or rightward orientation is also described by a rotation around the x-axis by y, the craniocaudal angulation is achieved by a rotation around the z-axis by 6. Thus

x” = xcos6 + ycosy sin6 + zsiny sin6 y” = -zsinb+ycosy cosS+zsiny cos6 2’ = -ysiny+zcosy (2)

Though the movement is different for both systems A and B, the displayed angles are the same for the

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same view. The angles 7 and 5 of the system B are converted to the corresponding angles CYB and PB as defined for system A. The conversion can be derived by describing the position of a certain point PIr as defined both by (7,6) and by ( a g , P ~ ) . This yields

cos7 = Co8(Yg CosBB (3)

41 - cos2 ag COS2PB

s h (YB CO8 OB cos6 =

h r t h e r we use the displayed patient angles (YA (=a), P A (=P), a B and PE.

3.2.2 To compute the angle E between two projections the point P = (O,O, 1) is rotated according to eq. (1) by ( (YA, PA) and (ag, PE). The dot product of the result-

Spatial angle between two projections

ing vectors P i and Pfl yields [7] (4)

COS E = sin P A sin PB + COS P A COS Pg COS(C~A - ( Y E )

3.2.3 To compute the rotation of the TV image we follow the movement of the scan lines - in the standard posi- tion bcing parallel to the y-axis (0,1,0) - by applying eqs. (1) or (2) to this vector. The cross product of the rotated axes P i and Pfs. defines the direction perpen- dicular to both planes. From the dot product of the inclined scan line vectors and the cross product one gets cos(90°-pA) and COS(go"-pB). The final terms to calculate the inclinations are

Alignment of the video images

( 5 )

COS P A sin Pg - sin PA COS PB COS( (YA -(YE SlnpA =

sinpg = sin E J1 - cos2 a g cos2 PB

For an orthogonal projection sine is equal to 1. Then, using eq. (4) the first equation reduces to s i n p ~ = sin P B / COSPA as derived by Dodge et al. [l] for a C- arm unit.

4 Discussion The presented tools for optimal image pairing can eas- ily be implemented at the cardiac workstation and used in the routine clinical setting. Both the correc- tion of the distortions due to the magnetic field and the alignment of the rotated images can be applied to any biplane recorded angiocardiogra". At the same time a different enlargement of the two planes can be adapted.

For the images presented in fig. 4, using (YA = 45', PA = -40', CYB = 120' and = 170, we get = 89.9', PA = 22.5' and PB = 51.9' from eqs. (4) and (5). This is in close agreement to the measured angles.

In the event that the isocenter of the gantry is not adjusted accurately, the images may be displaced ver- tically by some lines. This error can be fixed by com- paring one certain landmark being identified in both corrected images.

In conclusion, from the knowledge of the biplane projection angles, the optimal image rotation is cal- culated such that corresponding lines match the same slice. The resulting dewarped, centered, and rotated images offer both the basis for quantitative biplane im- age analyses, and a better visual biplane presentation of complex anatomical structures.

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We gratefully acknowledge the technical assistence of Jene Redmer and Klaus Moldenhauer.

Address for correspondence: Dietrich Onnasch, Pediatric Cardiology, Biomedical Engi- neering, Schwanenweg 20, 2300 Kiel, Germany

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