Pre-Operative Simulation and Post-Operative Validation of Soft-Tissue Deformations for Breast Implantation Planning

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1 Pre-Operative Simulation and Post-Operative Validation of Soft-Tissue Deformations for Breast Implantation Planning Liesbet Roose a, Wim De Maerteleire b, Wouter Mollemans a, Frederik Maes a, Paul Suetens a a Medical Image Computing, Faculties of Medicine and Engineering, University Hospital Gasthuisberg, Herestraat 49, 3000 Leuven, Belgium; b 3D Medical BV, Keizer Karel V singel 14, 5615 PE Eindhoven, The Netherlands ABSTRACT Virtual surgery simulation plays an increasingly important role as a planning aid for the surgeon. A reliable simulation method to predict the surgical outcome of breast reconstruction and breast augmentation procedures does not yet exist. However, a method to pre-operatively assess the result of the procedure would be useful to ensure a symmetrical and naturally looking result, and could be a practical means of communication with the patient. In this paper, we present a basic framework to simulate a subglandular breast implantation. First, we propose a method to build a model of the patient s anatomy, based on a 3D picture of the skin surface in combination with thickness estimates of the soft tissue surrounding the breast. This approach is cheap, fast and the picture can be taken while the patient is standing upright, which makes it advantageous compared to conventional CTor MR-based methods. Second, a set of boundary conditions is defined to mimic the effect of the implant. Finally, we compute the new equilibrium geometry using the iterative FEM-based Mass Tensor Method, which is computationally more efficient than the traditional FEM approach since sufficient precision can be achieved with a limited number of iterations. We illustrate our approach with a preliminary validation study on 4 patients. We obtain promising results with a mean error between the simulated and the true post-operative breast geometry below 4 mm and maximal error below 10 mm, which is found to be sufficiently accurate for visual assessment in clinical practice. Keywords: Image-Guided Therapy, Procedure Simulation, Soft Tissue Simulation, Mass Tensor Method, Finite Element method, Augmentation Mammoplasty, Surgery Planning 1. INTRODUCTION Breast cancer is the most common cancer in women worldwide, accounting for 1 million new cases annually 1.An operative mastectomy in which the breast is amputated will frequently be part of the treatment, but afterwards, women often choose for a breast reconstruction with a breast implant. Besides this reconstruction surgery, there is also a growing request for breast augmentation because of aesthetic improvement, for instance in the case of congenital asymmetry of the breasts. For these augmenting and reconstructive procedures, a symmetrical and naturally looking result is of utmost importance. Therefore, a wide variety of implant sizes and shapes is available, and preoperative implant selection has become a major issue 2. Our goal is the development of a 3D computer-based interactive planning environment to predict the surgical outcome of augmenting procedures, using a patient-specific representation based on medical images and a physically based tissue model. In this paper, we present a complete framework to simulate a breast augmentation, including image acquisition and model building, selection and placement of the implant, and computation of the new shape of the breast. Moreover, we give validation results for four patients. Since taking a CT or MR scan for every patient undergoing a breast augmentation is hardly feasible in daily clinical practice, we developed a fast and cheap method to build a patient specific geometry out of a 3D picture of the skin surface. This picture is acquired with a 3D camera, a technology which is recently receiving considerable attention in plastic breast surgery as a tool for objective and quantitative analysis of the breast 3. A set of boundary constraints to mimic the effect of the implant is applied to this model of the patient s anatomy Corresponding author: liesbet.roose@esat.kuleuven.ac.be, Telephone: ++32 (0) Medical Imaging 2006: Visualization, Image-Guided Procedures, and Display, edited by Kevin R. Cleary, Robert L. Galloway, Jr., Proc. of SPIE Vol. 6141, 61410Z, (2006) /06/$15 doi: / Proc. of SPIE Vol Z-1

2 in order to simulate and to predict the outcome of the intervention. The simulation of the behavior of the breast tissue under influence of these boundary constraints is a typical example of soft tissue simulation, a rapidly expanding research field in medical engineering. The two most common modeling approaches are Finite Element Models (FEM) and Mass Spring Models (MSM). FEM is based on continuum mechanics and is widely accepted as a very accurate method to model deformations, but it is often expensive in computational cost and memory usage. Most approaches to simulate breast tissue so far use a FEM-based model, for example to register mammographic images with MR-images 4, 5. These models are however specifically designed for tumour detection, which requires a much higher accuracy than the application we are concentrating on. MSM is an attractive alternative to FEM, because of its conceptual simplicity, low computational complexity and simple implementation. In the classical MSM, the tissue is discretized in mass points, which are connected by elastic springs. The movement of the points is described by a set of coupled differential equations. However, in earlier work we showed 6 that the mass spring system is less suited for the very large deformations which occur in breast augmentation, because of the risk of non-physical local minima of the mass spring system. The necessary model extensions to prevent these minima weaken the physical foundation of the method and strongly slow down the computation. In this paper we use the Tensor Mass method 7 which combines both the advantages from MSM and FEM, i.e. this method is physically based and offers the possibility to compute very rapidly an estimate of the exact solution. 2. METHODS 2.1. Data Acquisition and Mesh Building The starting point for the simulation pipeline is the generation of a geometrical model of the individual anatomy of the patient. The developed framework focuses on subglandular placement only, where the implant is placed on top of the pectoralis major muscle 8. Since muscular tissue is very stiff compared to the breast tissue and the silicone or saline implant, the muscle is supposed to maintain its original shape without experiencing any influence of the implant. Therefore all computations are performed on a tetrahedral mesh representation of the implant and the tissue volume enclosed between the outer muscle surface and the skin. Different imaging modalities can be used to extract the 3D patient s anatomy, from which MR and CT are the most obvious acquisition systems to obtain a volumetric model. However, they require an expensive and time-consuming scan for every patient. Moreover, the image is acquired while the patient is lying prone or supine, whereas we want to evaluate the simulation result while the patient is standing upright. We therefore developed an alternative approach, based on pictures taken with a 3D camera, combined with information about AeL!c9I!fl6 W!CI(U6 bloauqoq pa flje eflläeou Figure 1. Left and middle: Frontal and backward view of the three-dimensional skin surface, the estimates of the tissue thickness (distances A, B, C) and the vertical planes (a, b, c) through the points where the thickness is indicated. Right: The underlying CT slice, showing the real anatomy, serves for illustration purposes only and is not used in the procedure. The shaded area will be part of the breast tissue volume. The dotted lines show the intersection of the slice with the skin surface and with the outer muscle surface. Proc. of SPIE Vol Z-2

3 the thickness of the breast tissue. To estimate this tissue thickness, palpation or ultrasound measurements can be used. In the current setup, the surgeon has to provide three thickness estimates between the skin surface and the muscle: one estimate above the sternum, and two estimates lateral to the breast (respectively distances B, A and C in Fig. 1). We assume that the tissue thickness in the breast region is constant in each of the vertical planes perpendicular on the skin surface, going through one of these points (planes a, b and c in Fig. 1). Furthermore, we assume that the curvature of the outer muscle surface is similar to the curvature of the skin surface, except in the region directly underneath the breast (see Fig. 1). Based on these assumptions, we construct an estimate of the muscle surface. To this end, we design a function in three dimensions, which has an isosurface coinciding with the skin surface except for the breast region. If this function has a smooth behavior and we force the known points on the muscle surface to have the same function value, we can expect the muscle surface to be approximately described by the isosurface with this value. Radial Basis Functions (RBF) are known to be an appropriate mathematical model to implicitly describe surfaces 9, and have successfully been employed for smoothly interpolating incomplete surfaces derived from medical graphics 10. A RBF consists of a weighted sum of radially symmetric basic function Φ located at the centres x i and a low degree polynomial p: s(x) =p(x)+ If we consider three dimensional RBF s, the implicit equation N λ i Φ( x x i 2 ), x R, λ i R (1) i=1 s(x) =a, R 3, a R (2) describes a surface in three dimensions. The function value at the isosurfaces coinciding with the skin surface and the muscle surface can be chosen arbitrary, and we choose to describe the skin with the implicit surface s(x) = 0 and the muscle surface with s(x) = 1. To construct the RBF, the skin and muscle points with a known position are used. 1. Firstly the skin surface, which can be used to estimate the curvature, is isolated by removing the breast region, as illustrated in Fig. 2 (2). The positions {x s } of all points on this surface are points on the skin surface, where the function value should be For a second set of points on the muscle surface, the estimates of the tissue thickness are employed. The points on the skin surface are projected behind the skin surface, over the tissue depth estimated in this point. This depth is computed by interpolating the known depth estimates over the skin surface. For these newly constructed points {x m } the function value is imposed to be 1. To find the coefficients of p(x) and the weights λ i, the following system of equations has to be solved: { 0=p(x)+ N i=1 λ iφ( x x i 2 ) x {x s } 1=p(x)+ N i=1 λ iφ( x x i 2 ) x {x m } Ii (3) (1) (2) (3) (4) (5) Figure 2. Overview of the method to build a volume model. (1) Original skin surface acquired with the 3D camera. (2) Skin surface without breast regions. (3) Skin surface without breast regions, combined with the isosurface of the RBF at the depth of the outer muscle surface. (4) Final volume. (5) Final volume after tetrahedral meshing. Proc. of SPIE Vol Z-3

4 The Matlab FastRBF toolbox (Farfield Technology, Christchurch, New Zealand) provides methods for a fast approximate solution of this system of equations. We use this toolbox to construct the RBF with basic function Φ(r) =r and a polynomial p(x) of degree 1. The implicit surface s(x) = 1 is our estimate for the muscle surface, as shown in Fig. 2 (3). The volume between the skin surface and the estimated outer muscle surface is the tissue volume we will use in our computations (Fig. 2 (4)). For the finite element computation, an unstructured tetrahedral mesh is chosen as input, because of its flexibility in representing irregularly shaped, non-layered geometries. The Amira software (ZIB, Berlin, Germany) is used to compute a triangular mesh over the surface, and Netgen 11 is used to build a tetrahedral volume mesh, starting from this triangular surface mesh. A possible drawback of this cheap and fast method is the lack of information about the internal tissue distribution of fatty and glandular tissue in the breast. However, earlier research 6, 12 showed that the distinction between fat and glandular tissue has only a minor impact on the final simulation result. The behavior of the breast tissue is modeled as homogeneous, isotropic, linear elastic material with a Young s modulus of 48 kpa and a Poisson coefficient of ) Implant placement n Different shapes of implants are available for the surgeon to create a suitable form of the breast 8. The classic sphere segment shaped implants are commonly called a round implant, in contrast to the anatomic, shaped or teardrop implants. The latter have a vertical axis that is different in dimension from the horizontal axis. We built a library of tetrahedral mesh representations for a set of frequently used silicone breast implant from both groups, as shown in figure 3. In our interactive planning tool, one can select the preferred implant and place it on its right position. Since the implant is placed on the muscle surface during the surgery, the movement of the implant is restricted to positions on this surface. After placement of the implant, it is deformed to let the ground plane of the implant coincide with the muscle surface (see next section). Figure 3. Three examples of implants. Left: round implant. Middle: medium sized anatomical implant. Right: large anatomical implant Boundary conditions To deform the implant and the breast tissue, boundary conditions are assigned to certain points of the tissue mesh in order to mimic the effect of the implant on the breast. We distinguish between four different types of points: Free points: the movement of these points is completely governed by the forces acting on them. Proc. of SPIE Vol Z-4

5 Border points: border points are not allowed to move. Target points: these points are forced to reach a prescribed (target) position, regardless of the force acting on it. Sliding points: sliding points are connected to a certain surface, they cannot leave this surface, but they are able to slide over it. The movement of these points is therefore only governed by the force component tangential to this surface. The assignment of the boundary conditions is carried out in two steps. First, appropriate boundary conditions are chosen for the implant, to enforce it to lie on the muscle surface. Then the implant is deformed with the computational method described in the next section. Based on the new shape of the implant, the boundary conditions for the mesh representation of the breast tissue are determined and the breast tissue is deformed, as illustrated in Fig. 4. In the first step, the points on the ground plane of the implant are marked as target points positioned on the muscle surface (their target position is the projection of their original position on the muscle surface, along the normal of the ground plane of the implant). After calculation of the new equilibrium position of the implant with these boundary conditions, the implant is deformed as shown in Fig. 4 (c). After this deformation, the implant is assumed to be incompressible and rigid, so it does not change its position or shape anymore. In the second step, this new and definitive shape of the implant is used to assign the boundary conditions to the breast tissue. First, the points on the interface between muscle and breast tissue which lie underneath the implant, are marked as target points and projected to the upper surface of the implant. Second, the other points on the interface become border points, since they are supposed to be connected to the muscle. The result of the calculation of the breast shape with these boundary conditions is shown in Fig. 4 (d). Two extensions to this set of constraints are considered. The first additional boundary condition states that some points on the interface between breast tissue and muscle are actually disconnected from the muscle, namely the points which surround the implant within a radius of 3 cm. This is a better approximation of the real anatomy, since a large part of the fatty tissue layer is separated from the muscle during the surgical procedure to make enough place to bring in the implant easily. As a second additional boundary condition, the target points can be changed to sliding points after they have reached their target position, to mimic the sliding contact between the implant and the muscle surface on the one hand, and between the implant and the tissue on the other hand Tensor Mass method The equilibrium configuration of a finite element system is described by a set of equations K U = F, where K denotes the stiffness matrix, U the displacement of the node points and F the external forces applied to the system. In the classical solution schemes, this equation is solved with a direct method (based on Gaussian elimination). For 3D problems, this approach is very time-consuming, and Cotin et al. 7 introduced an alternative solution scheme, using an iterative procedure, comparable to the classical solution method of the mass spring system. Combined with a quasi-static steepest descent approach in each iteration 14, the Mass Tensor method offers the possibility to stop the computations if a sufficient degree of accuracy is reached, without the need to compute the exact solution. If the required accuracy is not too high, this results in a dramatic reduction of the computational cost. 3. VALIDATION PROCEDURE To validate our simulation method, we have pre- and postoperative 3D pictures of 4 patients at our disposal, for both the left and the right breast. The post-operative pictures are taken approximately three months after surgery, to ensure that the tissue had recovered from the surgical intervention and that swelling due to the surgery has disappeared. All images are taken with the Rainbow 3D camera (Genex Technologies, Kensington, USA). To evaluate our methods, the simulation results are compared with the real post-operative image data. To this end, the pre- and post-operative images have to be registered, which is a difficult task, because of the lack of common rigid structures in these pictures. The only information available for registration is the skin Proc. of SPIE Vol Z-5

6 caudial-cranial view backward view lateral view (a) (b) (c) (d) Figure 4. (a) Original breast volume. (b) Original breast volume with implant superposed. The white points of the implant visible in the backward view, are sliding points. (c) Original breast with deformed implant. (d) Deformed breast volume. surrounding the breast, parts of the belly and the skin around the clavicle, as far as these structures are visible in the images. The arm and the shoulder are not useful for the registration, since there are mostly slight differences in the position of the arm during the pre- and post-operative acquisition. To register the images, we isolate the common parts of the skin in the post-operative image, as shown in Fig. 5. This surface is then registered with the pre-operative surface, using the well-known Iterative Closest Point (ICP) algorithm 15, and the resulting transformation is applied to the original post-operative surface. However, it can be seen in Fig. 5 (d) that the alignment of the two surfaces is far from perfect. There are different reasons for this poor quality of registration. First, the skin surface of the patient can change considerably during the three months betweens the two acquisitions, for example when the patient gains or loses weight. Second, there are slight deviations in the patients position, mostly due to breathing and the positioning of the arm. This makes the region of the shoulder not suitable to use for the registration. The remaining area to be used for the registration is thus limited and lacks salient features for registration. As can be seen in Fig 5 (b) the remainder of the post-operative surface has little variation in the cranio-caudal direction, which makes the registration badly conditioned. As a consequence, it is important to start the ICP computation with a manual initialization. However, for some cases, the resulting registration is clearly incorrect, which can for instance be seen if the position of the nipple is manifestly different in the pre-operative and registered post-operative picture. This was the case for patient 3 and patient 4, and for these cases we had to register the two surfaces manually. To qualify the difference between a simulation and the real post-operative result we visually compare the postoperative picture with the skin surface of the volume after simulation, and measure the maximum distance d max and the mean distance µ d between both surfaces, computed over the breast surface. Proc. of SPIE Vol Z-6

7 (a) (b) C (c) (d) Figure 5. (a) Post-operative picture. (b) Selection of useful structures in the post-operative surface, frontal and caudalcranial view. (c) Registration of the selection of the post-operative picture with the pre-operative picture. (e) Combination of post-operative picture (wireframe) and pre-operative picture, frontal and lateral view. 4. RESULTS 4.1. Required accuracy An interesting issue is the accuracy which is needed for this application. We strive for a realistic looking result, and we have to investigate which simulation error is acceptable to obtain a convincing simulation result, compared to the real result after surgery, assessed by visual inspection. To estimate this, we used post-operative 3D pictures of 5 patients, where the breasts were qualified as being symmetric, both by the patient and the surgeon. We compared the skin surface of the left breast with the mirrored skin surface of the right breast. The mean error µ d between two breasts of the same patient was in the range between 2.7 mm and 3.5 mm and the maximal distance d max was found to be between 5.2 mm and 9.4 mm Data acquisition and model building To estimate the accuracy of our estimation of the muscle surface, we tested our method with a CT scan of a patient. Instead of using a 3D picture of the skin, the skin surface was segmented from this CT image to replace the 3D picture. The muscle surface was the constructed following the procedure in section 4.2 and compared with the real muscle surface as segmented from the CT images. The error consists of two factors: the error on the tissue thickness estimate and the error on the orientation of the normal on the muscle surface. The first one influences the amount of tissue to be deformed, the latter one influences the orientation of the implant. In the region where the implant is placed, the error on the tissue thickness was below 5 mm, and the orientation of the normal differed with maximum 3.5. We measured the effect of this approximation error by performing a breast implant simulation with our approximated tissue volume, and with the real tissue volume as segmented from the CT-scan. The maximal error between both simulations is 6.8 mm and the mean error is 1.7 mm, where this maximal error is situated laterally from the breast Different boundary conditions We have experimented with the different boundary conditions described in paragraph 2.3, simulating the implantation of a 245 cc silicone-filled implant. If no additional free points are added around the ground plane of Proc. of SPIE Vol Z-7

8 the implant, large errors are present at the boundaries of the breast, where our simulation lies underneath the real post-operative surface. Adding extra free points clearly has a positive influence on the position of the skin in this region, as can be seen in Fig. 6. Using sliding points instead of target points does not have an unequivocal effect on the maximal and mean error. Typically, the error on the side of the breast becomes slightly smaller, but the error on top of the breast becomes slightly larger, because of the contraction of the implant in the lateral direction. without extra free points with extra free points I/c) µ d =3.1 mm (over the whole breast surface) µ d =2.9 mm (over the whole breast surface) 0mm 10 mm Figure 6. The simulation result of an augmentation with and without extra free points on the muscle-fat interface. The color of the breast surface shows the distance to the real post-operative skin surface. In the simulation with extra free points, the error on the boundary of the breast becomes slightly smaller Efficiency and stopping criterion In each iteration, the points move under influence of the forces acting on it. The maximal displacement over all points turns out to be a good stopping criterion to decide in which iteration the optimization process can be stopped to reach a certain accuracy (see Fig. 7). For a set of simulations with different mesh resolutions and for different implants, we computed the exact FEM solution and compared this with the estimate of the solution in each iteration of the Mass Tensor method. In the iteration where a maximal error of 1 mm is reached (compared to the final FEM solution), the maximal movement of an individual point lies between 0.1 mm and 0.01 mm. A solution with a precision of 1 mm is sufficient for this application, so we stop the iterations when all points move for less than 0.01 mm. For a grid with approximately 3500 tetrahedra (mean edge length of the tetrahedra is 13 mm) the entire numerical solution takes about 20 seconds (Pentium M, 1.7 GHz, 1Gb RAM), if there are no sliding points involved. If sliding points are part of the boundary constraints, the solution time is doubled Validation on Patient Data We used our method to simulate the breast augmentation of 4 patients. The results are presented in Table 1 and Fig. 8. Our results achieve the desired accuracy of a maximal error below 1 cm. The mean error is still slightly higher than the desired error derived in Par Discussion One source of remaining errors in our validation is the limited information about the exact position of the implant and the difficult registration of the pre- and post-operative skin surface. Secondly, our method to estimate the muscle surface introduces an extra error, as shown in section 4.2. However, this error is partly compensated by the other errors in the simulation method. Thirdly, in the current framework, the implant is deformed prior to the deformation of the breast tissue and does not experience any influence from the pressure of the breast tissue. It would be more realistic to fully couple the implant and the tissue mesh, and to let them deform simultaneously. Another source of errors is the lack of gravity forces. Furthermore, in the time between taking Proc. of SPIE Vol Z-8

9 distance (mm) iteration number Figure 7. Convergence behavior of the simulation. Solid line: maximal distance to exact FEM solution, over all points. Dashed line: maximal displacement over all points in one iteration. A maximal error of 1 mm compared to the exact FEM solution, corresponds to a maximal displacement of 0.02 mm. Table 1. Maximal error and mean error for the simulation of a breast enlargement by 5 patients, both for left and right breast. left breast right breast implant d max (mm) µ d (mm) implant d max (mm) µ d (mm) Patient1 295 cc cc Patient2 280 cc cc Patient3 245 cc cc Patient4 255 cc cc Patient1 (right) Patient2 (left) Patient3 (right) Patient4 (left) 0mm 10 mm Figure 8. Top: original breast (solid) and simulation result (wireframe). Bottom: error distribution on the skin surface. Proc. of SPIE Vol Z-9

10 the pre- and post-operative picture, some biological effects (tissue growth and atrophy) occur which we do not take into account. However, the current results already reach an acceptable accuracy to assess the post-operative result. We plan to implement the simultaneous simulation of the implant and tissue, and we will add gravity forces to our model. Moreover, we want to extend our simulation framework with the possibility to simulate subpectoral implantation, where the implant is placed partly under the muscle. 5. CONCLUSION We presented a prototype planning system to predict the outcome of a breast augmentation, needing only a 3D picture of the skin surface and an estimate of the tissue thickness as input. We developed a set of boundary constraints to mimic the effect of an implantation, taking into account the size and shape of the implant, and we use the Tensor Mass method to compute a new equilibrium solution. The first results of our approach are promising, reaching an acceptable accuracy with a maximal error of 10 mm and a mean error below 4.0 mm. ACKNOWLEDGMENTS This work is part of the Flemish government IWT GBOU project. Liesbet Roose is Research Assistant of the Research Foundation - Flanders (FWO - Vlaanderen). REFERENCES 1. B. Stewart and P. Kleihues, World cancer report, Oxford University Press, D. Hudson, Factors determining shape and symmetry in immediate breast reconstruction, Annals of Plastic surgery 52, pp , January G. M. Galdino, M. Nahabedian, M. Chiaramonte, J. Z. Geng, S. Klatsky, and P. Manson, Clinical applications of three-dimensional photography in breast surgery, Plastic and Reconstructive Surgery 110, pp , July A. Samani, J.Bishop, M. Yaffe, and D. Plewes, Biomechanical 3-D finite element modeling of the human breast for mr/x-ray using mri data, IEEE transactions on medical imaging 20, pp , April N. Ruiter, Registration of X-ray mammograms and MR-volumes of the female breast based on simulated mammographic deformation. PhD thesis, Universitaet Mannheim, L. Roose, W. D. Maerteleire, W. Mollemans, and P. Suetens, Validation of different soft tissue simulation methods for breast augmentation, in Computer assisted radiology and surgery, H. U. Lemke, ed., ICS 1281, S. Cotin, H. Delingette, and N. Ayache, A hybrid elastic model allowing real-time cutting, deformations and force-feedback for surgery training and simulation, The Visual Computer 16(7), pp , S. L. Spear, E. J. Bulan, and M. L. Venturi, Breast augmentation, Plastic and Reconstructive surgery 114(5), R. Franke, Scattered data interpolation: tests of some methods, Mathematics of computation 38, pp , January J. C. Carr, W. R. Fright, and R. K. Beatson, Surface interpolation with radial basis functions for medical imaging, IEEE Transactions on Medical Imaging 16, p , February Netgen C. Tanner, A. Degenhard, C. Hayes, L. Sonoda, M. Leach, D. Hose, D. Hill, and D. Hawkes, Comparison of biomechanical breast models: A case study, in Medical Imaging: Image Processing, Proc. SPIE 4683, pp , P. Bakic, Breast Tissue Description and Modeling in Mammography. PhD thesis, Lehigh University, USA, W. Mollemans, F. Schutyser, N. Nadjmi, and P. Suetens, Very fast soft tissue predictions with mass tensor model for maxillofacial surgery planning systems, in Computer assisted radiology and surgery, H.U.Lemke, ed., ICS 1281, P. J. Besl and N. D. McKay, A method for registration of 3-D shapes, IEEE Trans. Pat. Anal. and Mach. Intel. 14, pp , February Proc. of SPIE Vol Z-10