Abstract. This paper presents a new algorithm for reconstruction of 3D shapes using a few x-ray views and a statistical model. In many applications of surgery such as orthopedics, it is desirable to define a surgical planning on 3-D images and then to execute the plan using standard registration techniques and image-guided surgery systems. But the cost, time and x-ray dose associated with standard pre-operative Computed Tomography makes it difficult to use this methodology for rather standard interventions. Instead, we propose to use a few x-ray images generated from a C-Arm and to build the 3-D shape of the patient bones or organs intra-operatively, by deforming a statistical 3-D model to the contours segmented on the x-ray views. In this paper, we concentrate on the application of our method to bone reconstruction. The algorithm starts from segmented contours of the bone on the x-ray images and an initial estimate of the pose of the 3-D model in the common coordinate system of the set of x-ray projections. The statistical model is made of a few principal modes that are sufficient to represent the normal anatomy. Those modes are built by using a generalization of the Cootes and Taylor method to 3-D surface models, previously published in MICCAI'98 by the authors. Fitting the model to the contours is achieved by using a generalization of the Iterative Closest Point Algorithm to nonrigid 3D/2D registration. For pathological shapes, the statistical model is not valid and subsequent local refinement is necessary. First results are presented for a 3-D statistical model of the distal part of the femur.

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Abstract. This paper addresses the problem of extrapolating very few range data to obtain a complete surface representation of an antomical structure. A new method that uses statistical shape models is proposed and its application to modeling a few points manually digitized on the femoral surface is detailed, in order to improve visualization of a system developped by TIMC laboratory for computer assisted anterior cruciate ligament (ACL) reconstruction. The model is built from a population of 11 femur specimen digitized manually. Data sets are registered together using an elastic registration method of Szeliski and Lavall6e based on octree-splines. Principal Components Analysis (PCA) is performed on a field of surface deformation vectors. Fitting this statistical model to a few points is performed by non-linear optimisation. Results are presented for both simulated and real data. The method is very flexible and can be applied to any structures for which the shape is stable.

This paper presents an approach to the problem of intraoperative reconstruction of 3D anatomical surfaces. The method is based on the integration of intra-operatively available shape and image data of different dimensionality such as 3D scattered point data, 2.5D ultra sound data, X-ray images etc. by matching them to a statistical shape model, thus providing the surgeon with a complete surface representation of the object of interest. Previous papers of the authors describe the matching of either 3D or 2D data to a statistical model and clinical applications. The here presented work combines former published ideas with a new approach for the complex task of shape analysis required for the computation of the statistical model, thus providing a generic approach for intra-operative surface reconstruction based on statistical models. The method for shape extraction/analysis is based on a generic model of the object and is used to segment training shapes and to establish point to point correspondence simultaneously in a set of CT images. Reconstruction experiments are performed on a statistical model of lumbar vertebrae. Results are provided for 3D/3D, 2D/3D and hybrid matching with simulated data and for 3D/2D matching for a cadaveric spine.

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