Image fusion for stereotactic radiotherapy and radiosurgery treatment planning

Image fusion for stereotactic radiotherapy and radiosurgery treatment planning

Int. J. Radiation Pergamon Oncology Biol. Phys., Vol. 28, No. 5, pp. 1229-1234, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in the USA. All r...

1MB Sizes 0 Downloads 85 Views

Int. J. Radiation

Pergamon

Oncology Biol. Phys., Vol. 28, No. 5, pp. 1229-1234, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0360-3016/94 $6.00 + .OO

0360-3016(93)E0065-E

??Physics Original Contribution

IMAGE FUSION FOR STEREOTACTIC RADIOTHERAPY AND RADIOSURGERY TREATMENT PLANNING HANNE M. KOOY, PH.D.,* MARCEL VAN HERK, PH.D.,* PATRICK D. BARNES, M.D.,+ EBEN ALEXANDER III, M.D., *,# SUSAN F. DUNBAR, M.D.,* NANCY J. TARBELL, M.D.,* ROBERT V. MULKERN, PH.D.,+ EDWARD J. HOLUPKA, PH.D.* AND JAY S. LOEFFLER, M.D.*

*Joint Center for Radiation Therapy, and the Stereotactic Radiosurgery and Radiotherapy Program, Departments Oncology, +Radiology, and ‘Surgery, Brigham and Women’s Hospital, The Children’s Hospital, Harvard Medical School, Boston MA

of Radiation

Purpose: We describe an image fusion application that addresses two basic problems that previously limited the use of magnetic resonance imaging (MRI) for geometric localization in stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT). The first limitation is imposed by the use of a relocatable, MRI-incompatible, stereotactic frame for stereotactic radiotherapy. The second limitation is an inherent lack of geometric fidelity in current MRI scanners that invalidates the use of MRI for stereotactic localization. Methods and Materials: We recently developed and implemented a novel automated method for fusing computerized tomography (CT) and MRI volumetric image studies. The method is based on a chamfer matching algorithm, and provides a quality assurance procedure to verify the accuracy of the fused image set. The image fusion protocol removes the need for stereotactic fixation of the patient for the MRI study. Results: The image fusion protocol significantly improves on the spatial accuracy of the MRI study. We demonstrate the effect of distortion and the effectiveness of the fusion with a phantom study. We present two case studies, an acoustic neurinoma treated with SRS. and a pilocytic astrocytoma treated with SRT. Conclusion: The image fusion protocol significantly improves our logistical management of treating patients with radiosurgery and makes conformal therapy practical for treating patients with SRT. The image fusion protocol demonstrates both the superior diagnostic quality and the poor geometric fidelity of MRI. MRI is a required imaging modality in stereotactic therapy. Image fusion combines the superior MRI diagnostic quality with the superior CT geometric definition, and makes the use of MRI in stereotactic therapy possible and practical. Stereotactic distortion.

radiosurgery,

Stereotactic

radiotherapy,

Image fusion, Diagnostic

imaging, Treatment

planning,

MRI

manual input to define analogous surfaces in each modality. A more general fusion technique is based on the chamfer match technique (8, 11, 22). The chamfer tech-

INTRODUCTION

Image fusion is a technique that combines the often complementary information from separate imaging studies into a single coherent study. The combination of MRI and SPECT studies, for example, allows a direct comparison of anatomy and metabolic activity. Popular image fusion techniques are based on fiducial markers (18) or on surface matching between volumes identified on each modality ( 10, 13, 17). The fiducial marker technique re-

nique does not require the identification of individual volumes. Instead, individual, but not identical, sets of points belonging to the same anatomical structures on each study are used. These points can be automatically segmented from each study, thus making the chamfer technique automatic. We recently (spring 1992) commenced SRT treatments based on the Gill-Thomas-Cosman (GTC) stereotactic frame’ (9). Our treatments combine standard fractionation schemes with the precision and treatment planning of SRS (15). The localization accuracy is 0.4 mm in our

quires markers visible on all modalities and permanent implantation for follow-up studies. The rather small number of such markers reduces the precision of the fusion. The surface matching technique, in practice, requires

Accepted for publication 12 November ’Radionics Inc., Burlington, MA.

Reprint requests to: Hanne M. Kooy, Ph.D., Joint Center for Radiation Therapy, 50 Binney St., Boston MA 02 I 15. Acknowledgments-We gratefully acknowledge the assistance of and discussions with Zach Leber and Bob Ledoux from RSA Inc. 1229

1993.

1230

I. J. Radiation

Oncology

0 Biology 0 Physics

experience ( 14) acquired over 1000 individual patient setups, and confirms the original work by Gill et ul. (9). The accuracy of the GTC frame thus approximates the accuracy of the standard SRS frame. The GTC frame can only be used for CT imaging, however, and is incompatible with MRI. The superiority of MRI over CT for diagnostic neuroanatomical imaging and treatment planning is well established (1, 2, 20). Often, it is the only appropriate imaging modality for many brain tumors, especially for tumors that do not enhance with contrast and for tumors in the posterior fossa. The spatial accuracy of MRI for stereotactic localization is, however, unacceptable due to magnetic susceptibility effects. These effects depend critically on the local inhomogeneity in magnetic susceptibility and result in geometric shifts and distortion effects of up to 4 mm (19). These effects are particularly pronounced at bone-tissue and tissue-air interfaces. Corrective pulse sequences are under investigation but not in clinical practice (GE Corp. and RSA, Inc., Brookline, MA, Personal communication and correspondence, 20 November 1992). The image fusion technique thus solves two crucial problems. First, it allows MRI data to be used for SRT patients through a fusion with a CT study obtained under stereotactic conditions. Second, it removes, to first order, the geometric distortions inherent in any MRI study. as the CT study can be used as a calibration of the MRI study.

Volume

28, Number

5, 1994

els. The final set of segmented CT voxels are presented as a flat list of voxel coordinates 7,. The MRI segmentation algorithm identifies a set of voxels that lie on the edges of bony anatomy through a spectral analysis of the MRI voxel values. A histogram of the MRI voxel values consists of a peak representing the majority of soft tissue voxels, and a tail below the peak representing other anatomical features. The bony voxels values typically are in the range of 30-70s of the mean peak voxel value: an observation made through experimentation. All MRI voxels that are identified as lying on the bony edges are given the value 0. A distance transform ( 1 1,2 1) sets the value of the other, nonbony edge, voxels equal to the closest distance to a zero-valued, that is bony-edge, voxel. If we consider Eq. 1, G represents the list of CT bonyedge voxel coordinates P, that need to be matched against the MRI bony-edge template E a CT voxel coordinate T,, transformed by T, is indexed in the distance transformed MRI volume. F( T- 7,) thus yields the distance of the CT bony voxel i to a bony edge in the MRI. If the CT and MRI were perfectly aligned, and if the segmentation were perfect, the resultant sum in Eq. 1 would equal 0. The objective is thus to optimize the cost function Cy 7) to yield to best match under our transformation T. We consider three cost functions (22): (Eq.2)

(Eq. 3) METHODS

AND

MATERIALS Max C(T) = max,F( T. 3,).

CT and MRI irnage,fiuion

The original chamfer matching technique was developed by Barrow et al. (3) and improved by Borgefors (4). Image-based chamfer matching computes a cost function between two image sets where in one image set the feature to be matched is sufficiently sparse to allow a rapid evaluation of the cost function. Consider two image sets, b and G, where G only contains elements i with values 0 or 1. The 1-valued feature elements can be enumerated in a list Y, and a cost function C can be evaluated as a linear function of the transformation T between F and G as: C(T)

= c

F(T X v,).

(I%. 1)

In our application we have a CT volume and a MRI volume. We wish to obtain the geometric transformation T-which includes translation, rotation. and linear scaling in three-dimensions-to correlate the CT coordinate system with the MRI coordinate system. Our technique (22) relies on automated segmentation algorithms for extracting those voxels that lie on edges of bony anatomy in both the CT and MRI volumes. The CT segmentation algorithm relies on simple thresholding on bone CT values and edge detection around those vox-

(Eq. 4)

and two general purpose optimization procedures: (a) Downhill Simplex with restart from the first found optimum ( 16); and (b) Powell’s method discarding the direction of largest decrease (5). We used a Monte Carlo study to vary the fitting parameters around an u priori established “true” match. Our results (22) show that the mean cost function in Eq. 3 combined with the Simplex method yielded the lowest rate of false positives (where the final match did not agree with the “true” match) equal to 1.896, an accuracy of < 1.O mm, and a capture range (the initial separation between the two coordinate systems) of < 6 cm for CT-MRI correlations. These results only required 5000 CT voxel coordinates, with only a small decrease in accuracy to 1.3 mm when the number of points is lowered to 1000 points. The false positive rate. however, increases more significantly to 4.3% with 1000 points. We typically use on the order of 10,000 points in a matching session. The false positive rate was significantly higher for the other cost functions in combination with the Simplex or Powell methods. Figure 1 illustrates the matching procedure data flow. The two image studies are segmented, voxel coordinates are extracted in the CT study, and a chamfer is created from the MRI study. The matching procedure takes these

Image fusion 0 H. M. KOOY ef al.

1231

Stereotactic MRI localization

CT Segmentation I Extract Voxel Positions I

I MR Segmentation 1 Chamfer Definition L

1

Transform

MR

Fig. I. Functional flow diagram of the fusion procedure. The CT and MRI image studies are segmented for analogous structures. The CT segmentation results in a set of voxels coordinates, and the MRI segmentation results in a chamfer in which the

voxels are matched. The resultant match transformations are applied to the MRI study to transform it into the CT coordinate system. A subsequent comparison of the two studies, the original CT and the transformed MRI, verifies the fusion result. coordinates and chamfer as input, and produces a translation, rotation, and scaling that is applied to the MRI study to transform it into the position of the CT study. The comparison of the CT and fused MRI allows a detailed comparison of the goodness of the transformation on a per patient basis and forms the basis for our quality assurance protocol. The current system is implemented in the AVS software environment.2 The use of a geometrically accurate CT volume and a geometrically distorted MRI volume allows for a global and linear correction of the distortion averaged over the intra-cranial volume. Since we apply linear scaling along the axes, either image set can be used as the chamfer: the transformations from one volume to the other are symmetric. The choice of the MR image as the chamfer is necessitated by the relatively poor segmentation of the bone in MRI compared to CT. This results in additional edges to be extracted in the MRI compared to the CT. The application of the distance transform on the MRI reduces the effect of these additional edges. We do not expect the linear scaling to adequately compensate for all distortion effects. Since the chamfer matching relies on the bony anatomy-where a significant distortion is possible-we do expect the conditions for linear scaling to be optimal. In practice, we confirm the appropriateness of the match against many soft-tissue and bony landmarks, and do not observe significant (> 1 mm ) shifts except at the tissue-air interface. Thus, a matching on the external surface of the patient can be expected to yield poor results.

’ AVS Inc., Waltham, MA. 3 RSA Inc., Brookline, MA. 4 Radionics Inc., Burlington,

Stereotactic localization in combination with a stereotactic frame (6) relies on fiducial markers, calibrated with respect to the frame, which are imaged with the patient. These fiducial markers are used to generate a transformation from the image modality coordinate system to the stereotactic coordinate system. Stereotactic localization based on CT is a highly accurate procedure with submillimeter accuracy in our experience. Stereotactic localization using MRI, however, greatly suffers from lack of geometric fidelity in the MRI reconstructed images. The manufacturer, in fact, advises against the use of MRI for applications demanding geometric precision, and states the overall accuracy as 2% of the field-of-view (GE Corp. and RSA, Inc., Brookline, MA, Personal communication and correspondence, 20 November 1992); this is confirmed in our experience.

Patient protocol We treat patients with SRS using a single high-dose focal irradiation and SRT using standard fractionation protocols. Both protocols require a CT study with the stereotactic localization frame attached to the patient to reconstruct the 3-D geometric definition of the patient in the stereotactic treatment coordinate space. Patients that require a MRI study for their radiological workup are scanned before the CT study without such a stereotactic frame. The MRI study consists of a sagittal T,-weighted localizer, followed by the acquisition of axial proton-density and T2-weighted images. Slice thicknesses are 3 or 5 mm with no gaps. Fast spin echo sequences are used to collect the axial images with an average scan-time of 35 min ( 12). Axial images-as compared to coronal or sagittal images-fused to the axial CT images show little image quality degradation inherent in the interpolation required to accomplish the fusion with the axial CT images. The chamfer match technique requires volume sets to be within a certain distance of each other. The CT and MRI image sets are thus acquired with the couch and field-of-view appropriately centered approximately in the center of the cranium. RESULTS

Phantom study Figure 2 shows the fusion result based on a CT and MRI compatible phantom.3 The phantom consists of a plastic skull inside a plastic waterproof container, with additional geometric objects placed at precisely defined positions. The phantom was scanned with a MRI compatible localizer4 in both a CT scanner’ and a MRI scanner.h The fusion accurately aligns the two studies based

5 Somatom Plus, Siemens Corp., Concord, ’ GE Signa, GE Corp., Schenectady, NY. MA.

CA.

1232

1. J. Radiation

Oncology

0 Biology 0 Physics

on the segmentation of the skull edges in CT and the corresponding high contrast regions defined by the water surrounding the plastic skull in MRI. Although the internal anatomy is well aligned in the fusion process, the fiducial markers prove to be grossly misaligned. The fiducial markers in the MRI localizer frame consist of hollow plastic tubes filled with petroleum jelly. Other materials will alter the distortion phenomena (Dr. L. Desoto. University of Washington, Seattle, Personal communication, December 1992). We find that the reconstruction of the CT fudicial markers yields submillimeter precision. A stereotactic reconstruction based on the localization fiducial markers in the MRI study is thus clearly unreliable. The stereotactic reconstruction algorithms constrain the imaged positions of the fiducials to their known positions in the stereotactic coordinate system. The large distortion will thus cause the internal anatomy to significantly “stretch” to force the MRI fiducial rod positions in their correct (CT) position. Note that this stretching would primarily affect the anterior and posterior image components, while centrally located structures are less affected.

Volume

28. Number

5, 1994

Fig. 3. Transverse image comparison between CT (lower part) and MRI (upper part). The neurinoma (A.N.) is clearly visible on the MRI. The CT window and level are set to show the bony structure. Note how the acoustic canal (B) forms a clear continuation of the neurinoma. Also note how the posterior skull on CT matches the corresponding dark areas on MRI.

The patient is a 59 year old white female who presented with a 10 year history of grand ma1 seizures. She also suffered gradual hearing loss over 2 years that accelerated over the last few months. Examination revealed an arteriovenous malformation (AVM) in the Sylvian fissure and a left intracanalicular acoustic neurinoma. The treatment of choice for the AVM was stereotactic radiosurgery (SRS), and both lesions were treated with SRS in a single treatment session.

Figure 3 shows a transverse image through the acoustic neurinoma. The image is bisected at the level of the canal, with the top part showing the MRI image component, and the lower part showing the CT image component thresholded for bone. The bisection level can be interactively moved across the image, both horizontal and vertical, and allows a detailed comparison evaluation. Note how the acoustic neurinoma as visible on MRI clearly continuous on the canal visible on CT. Thus, on this transverse image section, the fusion is accurate. In addition, the sphenoid and occipital bones as visible on CT, align with their corresponding regions on MRI. Figure 4 shows a coronal reconstructed image through the acoustic neurinoma. Again, the acoustic neurinoma is in excellent alignment with the corresponding bony landmarks from

Fig. 2. Fusion result for a phantom scanned with a stereotactic localizer in both CT and MRI. Note the distorted positions of the MRI fiducial rod positions vs. the correct CT rod positions. Also note the excellent alignment of the internal geometric structures.

Fig. 4. Coronal image comparison with CT and MRI. The neurinoma (A.N.) matches the bony anatomy (CT bone). Also note how the bony anatomy conforms with the corresponding MRI anatomy throughout the image section, and the contra-lateral canal without an enhancement.

Case 1: Acoustic neurinoma

Image fusion 0 H. M.

KOOY

1233

et d.

as imaged on the CT section. Thus we combine the positional accuracy of CT with the image definition of MRI. We also extract the edges from the bony structures in CT and add those to the fused image. This allows a visual verification of the fusion accuracy on a per slice basis. The overall accuracy of the procedure is limited by the fusion accuracy, equal to about + 1 pixel. DISCUSSION

Fig. 5. Transverse section through the thalamus. Note the continuation of the bony anatomy (A) and the continuation of the internal anatomy (B). The patient was diagnosed with a pilocytic astrocytoma growing into the thalamus. The MRI clearly shows the enhancing mass (C).

We presented the application of a novel image fusion technique to SRS and SRT. The fusion technique addresses the limitations in the use of MRI in stereotactic localization due to the lack of geometric fidelity in the current generation of MRI scanners and the current lack of a MRI localization frame for the radiotherapy. The image fusion protocol is an essential component of our treatment planning effort. Image fusion is used in the majority of SRT patients, in all patients presenting with acoustic neurinomas, arterio-venous malformations, peri-sellar tumors, posterior-fossa tumors, and in about 20% of our general patient population. These cases trans-

CT. (Note the position of the canal on the contra-lateral side as visible on CT.) The CT bony landmarks also show good alignment throughout the coronal image section.

Case 2: Pilocytic astrocytoma The patient is a 9-year old boy who developed headaches and intermittent nausea and vomiting with progressive lethargy. A head CT scan revealed an enhancing mass in the right temporal lobe. The tumor was grossly resected, except for tumor extension into the thalamus. The patient was followed, when a MRI scan 6 months following surgery demonstrated tumor progression. Figure 5 shows a transverse section through the thalamus. The MRI portion on the section clearly shows the pilocytic astrocytoma enhancement not visible on the CT. Again, visible landmarks quantitatively demonstrate the fusion accuracy. The treatment planning CT shows the occipital support of the GTC stereotactic repeat localizer frame used for SRT. Figure 6 shows the isodose distribution on a transverse CT section through the target volume.’ Our treatment planning protocol always relies on the CT study for the geometric definition. In a fusion study, we continue to rely on the spatial definition from CT. For each voxel in a CT section, we use the fusion transformations to obtain the MRI signal value at that voxel, and replace the CT density value of the voxel with the MRI signal value. We then transform the CT section to its position in the stereotactic coordinate system using the fiducial markers

’ Image obtained with the XKnife treatment RSA Inc., Brookline, MA.

planning

system,

Fig. 6. Treatment

isodose distribution showing the 40, 60, 80, and 100% isodose levels. The transverse image plane is a CT plane with the CT image pixels replaced by the corresponding MRI pixels. The bony edges from CT have been added to the resultant image to allow a per slice documentation ofthe fusion result. The isodose distribution shows the rapid fall-off of dose possible with stereotactic therapy. The 40% isodose has a plumed appearance as a consequence of the target volume shape below this slice.

1234

1. J. Radiation Oncology 0

Biology0 Physics

late to approximately two patients/week at our current treatment planning levels. Image fusion has completely replaced the use of MRI stereotactic localization. The out-patient nature of most SRS treatments means that the CT image data obtained with the stereotactic localizer is not available until the actual day of treatment, and the fusion must be accomplished within a short time span. The actual computer time required for a fusion is about 1 minute.8 The real effort and time, however, is consumed by the verification process and possible iterations on the fusion parameters due to MRI pulse-sequence variations. The overall process takes about 1 h. The verification process involves critical evaluation of the fusing results on transverse, coronal, and sagittal planes. The

Volume 28. Number

5, I994

image reconstruction on these planes requires interactive operations on two image sets and the mapping of one image set into the other. The whole process is only feasible because of the current generation of computer workstations. The treatment of brain tumors with conformal stereotactic therapy poses severe demands on the ability to accurately define the target volume. The localization precision offered by stereotactic technology has a standard deviation of approximately 1.3 mm when considering all aspects of the process, and may exceed the diagnostic precision. The latter is limited by both the actual image quality and the ability of the physician to discriminate the abnormal tissues from the image.

REFERENCES I. Barnes, P. D.; Kupsky. W.; Strand, R. Cranial and intracranial tumors. In: Wolpert, S., Barnes, P. D., eds. MRI in pediatric neuroradiology. St. Louis: Mosby Yearbook: 1992: 204-2 1I. 2. Barnes. P. D.; Lester, P.: Yamanashi, W. MR imaging in childhood intracranial masses. Mag. Res. Im. 4:41; 1986. 3. Barrow, H. G.: Tenenbaum, J. M.: Bolles, R. C.; Wolf, H. C. Parametric correspondence and chamfer matching. Proceedings of the 5th International Joint Conference on Artificial Intelligence, Cambridge, MA. 1977:659-663. 4. Borgefors, G. Hierarchical chamfer matching: A parametrical edge matching algorithm. IEEE Trans. Patt. Recog. Machine Intel. 10:849-865; 1988. 5. Brent, R. P. Algorithms for minimization without derivatives. Englewood Cliffs, NJ: Prentice Hall; 1973. 6. Brown, R. A.; Roberts, T. S.: Osborn, A. G. Simplified CTguided stereotaxic biopsy. Am. J. Neuro. Rad. 2: I8 1- 184; 1981. 7. Cline. H. E.; Lorensen, W. E.; Kikinis, R.; Jolesz, F. Threedimensional segmentation of MR images of the head using probability and connectivity. J. Comp. Assist. Tomog. 14: 1037-1045; 1990. 8. Gilhuijs, K.; van Herk, M. Automatic on-line inspection of patient set-up in radiation therapy using digital portal images. Med. Phys. 20:667-677: 1993. 9. Gill, S. S.; Thomas, D. G. T.; Warrington, A. P.; Brada, M. Relocatable frame for stereotactic external beam radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 20:599-603; 199 I. IO. Holupka, E. J.: Kooy, H. M. A geometrical algorithm for medical imaging correlations. Med. Phys. 19:433-438; 1992. 1I. Hongjian, J.; Holton, K.; Robb, R. A. A new approach to 3D registration of multi-modality medical images by surface matching. In: Robb, R. A., ed. Visualization in biomedical computing. Proc. SPIE 1808. San Jose, CA: 1992: 197-2 13. 12. Jones, K. M.: Mulkern, R. V.; Schwartz, R. B.: Oshio. K.: Barnes, P. D.; Jolesz. F. A. Fast spin-echo MR imaging of the brain and spine: Current concepts. Am. J. Roentgenol. 158:1313-1320: 1992. 13. Kessler. M. L.: Pitluck. S.; Petti, P.: Castro. J. R. Integration

’ Result for a Hewlett-Packard Packard, Palo Alto, CA.

9000/755 workstation.

Hewlett

14.

15.

16. 17.

18.

19.

20.

2 1.

22.

of multimodality imaging data for radiotherapy treatment planning. Int. J. Radiat. Oncol. Biol. Phys. 21: 1653-1667; 1991. Kooy, H. M.: Dunbar. S. F.; Tarbell, N. J.; Mannarino, E.; Fcrarro. N.: Shusterman, S.; Bellerive. M.; Finn. L.; McDonough. C. V.; Loeffler, J. S. Adaptation and verification of the relocatable Gill-Thomas-Cosman frame in stereotactic radiotherapy. (Submitted for publication.). Kooy, H. M.; Nedzi, L. A.; Loeffler. J. S.; Alexander III. E.: Cheng, C. W.; Mannarino. E.; Holupka. E. J.: Siddon. R. L. Treatment planning for stereotactic radiosurgery of intra-cranial lesions. Intl. J. Radiat. Oncol. Biol. Phys. 21: 683-693: 1991. Nelder, J. A.: Mead. R. A simplex method for function minimization. Comp. J. 7:308-3 13; 1965. Pelizzari, C. A.; Chen. G. T. Y. Registration of multiple diagnostic imaging scans using surface fitting. In: The use of computers in radiation therapy. North Holland: Elsevier: 1987:437-440. Schad, L. R.; Boesecke, R.; Schlegel, W.; Hartmann, G. H.: Sturm. V.: Strauss, L. G.; Lorentz, W. J. Three-dimensional image correlation of CT, MR. and PET studies in radiotherapy treatment planning of brain tumors. J. CAT 11: 948-954; 1987. Tien, R. D.; Buxton, R. B.; Schwaighofer, B. W.; Chu. P. K. Quantitation of structural distortion of the cervical neural foramina in gradient-echo MR imaging. J. Mag. Res. Im. 1:683-687: 1991. Thornton, A. F.; Sandier, H. M.; Ten, Haken, R. K.; McShan, D. L.; Fraass, B. A.; LaVigne, M. L.; Yanke, B. R. The clinical utility of magnetic resonance imaging in 3-dimensional treatment planning of brain neoplasms. Int. J. Radiat. Oncol. Biol. Phys. 24:767-775; 1992. van Herk, M. A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernels. Pan. Recog. Lett. 13:517-521; 1992. van Herk, M.; Kooy, H. M. Automatic three-dimensional correlation of CT-CT, CT-MR. and CT-SPECT using chamfer matching. (Accepted for publication.)