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  • Medical Image Analysis 7 (2003) 237–250 www.elsevier.com/ locate/media

    R obust registration for computer-integrated orthopedic surgery: Laboratory validation and clinical experience

    *B. Ma, R.E. Ellis School of Computing, Queen’ s University, Kingston, Ontario, Canada K7L 3N6

    Received 19 July 2001; received in revised form 1 October 2002; accepted 6 November 2002

    Abstract

    In order to provide navigational guidance during computer-integrated orthopedic surgery, the anatomy of the patient must first be registered to a medical image or model. A common registration approach is to digitize points from the surface of a bone and then find the rigid transformation that best matches the points to the model by constrained optimization. Many optimization criteria, including a least-squares objective function, perform poorly if the data include spurious data points (outliers). This paper describes a statistically robust, surface-based registration algorithm that we have developed for orthopedic surgery. To find an initial estimate, the user digitizes points from predefined regions of bone that are large enough to reliably locate even in the absence of anatomic landmarks. Outliers are automatically detected and managed by integrating a statistically robustM-estimator with the iterative-closest-point algorithm. Our in vitro validation method simulated the registration process by drawing registration data points from several sets of densely digitized surface points. The method has been used clinically in computer-integrated surgery for high tibial osteotomy, distal radius osteotomy, and excision of osteoid osteoma.  2003 Elsevier B.V. All rights reserved.

    Keywords: Computer-integrated orthopedic surgery; Validation; Clinical experience

    1 . Introduction registration; the computation speed and registration accura- cy depend on how this initial estimate is chosen. Two

    Registration of a patient to a medical image or model is acknowledged problems with ICP-like algorithms are (1) a fundamental requirement of computer-integrated surgery the requirement of a good initial estimate, and (2) that (CIS) systems that provide intraoperative navigational minimization of the sum of squared errors is optimal only guidance. A registration method for general use in ortho- under the assumption that measurement errors are in- pedic surgery should be effective, fast, and simple to use. dependent and have identical Gaussian distributions. If It should not depend on readily locatable anatomic land- noise in the measurements is non-Gaussian, a least-squares marks because these are often difficult to find or nonexis- error measure can produce poor results. A common source tent such as when performing a percutaneous procedure. of non-Gaussian noise is the presence of statistical outliers

    The iterative-closest-point (ICP) algorithm of Besl and which can be present in the measurements if, for example, McKay (1992) is a well-known method for registering a a measurement is accidentally collected far from the target 3D set of points to a 3D model that minimizes the sum of anatomy or is taken from a point outside the medical squared residual errors between the set and the model, i.e. image. Fig. 1 illustrates the effect of outliers on registra- it finds a registration that is locally best in a least-squares tion accuracy. sense. This algorithm requires an initial estimate of the Two attractive features of ICP are that it is guaranteed to

    converge to a minimum in its objective function, and convergence is very fast when started from a good initial*Corresponding author.

    E-mail address: [email protected](R.E. Ellis). estimate. An efficient implementation by Rusinkiewicz and

    1361-8415/03/$ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S1361-8415(02)00133-0

    mailto:[email protected]

  • 238 B. Ma, R.E. Ellis / Medical Image Analysis 7 (2003) 237–250

    Fig. 1. The effect of outliers on registration accuracy. On the left are 16 measured contact points from a phantom tibia; three of the points are outliers. In the middle is a registration obtained using ICP initialized with a good estimate of a reasonable registration. On the right is a registration obtainedusing our robust implementation of ICP started from the same initial estimate.

    Levoy (2001) that was not robust to outliers has been required by ICP, and discussed how to choose an optimal shown to register 2000 data points to models comprised of set of points to use for registration. Cuchet et al. (1995) 100 000 points in tens of milliseconds. The computational used a chamfer map to accelerate the nearest-neighbor efficiency of ICP makes it an attractive starting point for a search. robust registration algorithm. Rusinkiewicz and Levoy (2001) studied several varia-

    We have previously described a robust registration tions of ICP for model-based tracking and 3D scanning. algorithm in (Ma et al., 1999). In this article, we describe Greenspan and Godin (2001) have described ICP variants our experiences using this algorithm for orthopedic pro- that use nearest-neighbour search methods which are cedures. In Section 2 we present a brief summary of significantly faster thank–d tree methods for surfaces ICP-like methods and robust registration methods. In represented by point sets. Section 3 we describe our registration algorithm. In Rangarajan et al. (1997) extended the Procrustes method Section 4 we describe our in vitro experiments used to to matching point sets of different cardinality with un- validate registration accuracy. In Section 5 we describe the known correspondences. Their Softassign method jointly clinical application of our algorithm for high tibial os- solves for the rotation and point correspondances, treating teotomy, distal radius osteotomy, and excision of osteoid non-homologies as outliers. There is empirical evidence in osteoma. We conclude by discussing the results and (Rangarajan et al., 1999) suggesting that the Softassign limitations of our work. objective function is much smoother than the root mean

    squared error function minimized by ICP. Chui and Rangarajan (2000) re-interpreted their previous work as a

    2 . Related work maximum likelihood problem and used an approach simi- lar to expectation maximization to solve the feature

    ´Lavallee (1995) and Maintz and Viergever (1998) have registration problem. Their expectation-like step updates extensively reviewed the literature on general registration the feature correspondences and the maximization step algorithms. Here, we will review the literature of ICP-like updates the registration transformation. Similar methods methods and robust registration methods. were independently developed by Granger et al. (2001).

    Several research groups have reported using ICP in CIS Dellaert (2001) argued that the feature correspondences applications. Palombara et al. (1997), who used ICP for in were actually nuisance parameters and that one needs to vitro experiments related to total knee arthroplasty, re- compute the probability distribution of the transformation ported that outliers were detrimental to the accuracy of the parameters over all possible correspondences. Since there computed registrations. Betting et al. (1995) used a are a combinatorial number of correspondences, the exact modified version of ICP that took into account surface- solution is computationally intractable and was approxi- normal information and that used ak–d tree to accelerate mated using Monte Carlo sampling. All of these methods the nearest-neighbor search. Maurer et al. (1996) also used can be made robust against outliers. a k–d tree to accelerate ICP, and discussed how to Zhang (1994) independently described an algorithm that decompose a set of surface primitives into a weighted is very similar to ICP. He attempted to identify outliers by point-set representation. Applications of their algorithm examining the standard deviation of the residual matching have also been reported in (Herring et al., 1998) and errors and removing those points that had errors greater (Maurer et al., 1998). Simon et al. (1995) used ak–d tree than some multiple of the standard deviation. We can and other techniques to decrease the computation time identify three problems with this thresholding approach.

  • B. Ma, R.E. Ellis / Medical Image Analysis 7 (2003) 237–250 239

    First, there is no mathematically sound way of choosing found that obtaining a good solution with their Tukey- the threshold value as some multiple of the standard based algorithm depended critically on the quality of the deviation. Second, a least-squares solution assumes a initial estimate of the registration. Gaussian distribution of the residual errors, yet an outlier Masuda and Yokoya (1995) reported a statistically may have asmaller residual error than a valid observation robust version of ICP. Their algorithm used the LMS after a least-squares procedure. Finally, thresholding does estimator, and it was applied to the segmentation and not address the issue of the true underlying distribution of matching of range images. They claimed that, for range the measurement errors. Despite these limitations, other images of size 2563256 and larger, their method could researchers Blais and Levine (1995) and Feldmar and segment and register images with up to 50% outlier Ayache (1994) have applied thresholding in an attempt to contamination. remove outliers in their registration methods. Luck et al. (2000) recently reported a robust version of

    Robust registration is a process of attempting to dimin- ICP that uses simulated annealing in an attempt to find the ish or eliminate the effects of outliers in estimating the registration that produces the global minimum mat

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