This study provides normative coverage data and a reproducible method for evaluating acetabular coverage. Cranial acetabular retroversion (crossover sign) and a positive posterior wall sign were frequent findings in a young asymptomatic cohort and might be a normal variant rather than pathologic in a significant number of cases.

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The accurate matching of 3D anatomical surfaces with sensory data such as 2D X-ray projections is a basic problem in Computer and Robot Assisted Surgery. In model-based vision, this problem can be formulated as the estimation of the spatial pose (position and orientation) of a 3D smooth object from 2D video images. We present a new method for determining the rigid body transformation that describes this match. Our method perform a least squares minimization of the energy necessary to bring the set of the camera-contour projection lines tangent to the surface. To correctly deal with projection lines that penetrate the surface, we consider the minimum signed distance to the surface along each line (i.e., distances inside the object are negative), To quickly and accurately compute distances to the surface, we introduce a precomputed distance map represented. using an octree spline whose resolution increases near the surface. This octree structure allows us to quickly find the minimum distance along each line using best-first search. Experimental results for 3D surface to 2D projection matching are presented for both simulated and real data. The combination of our problem formulation in 3D, our computation of line to surface distances with the octree-spline distance map, and our simple minimization technique based on the Levenberg-Marquardt algorithm results in a method that solves the 3D/2D matching problem for arbitrary smooth shapes accurately and quickly.

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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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This paper presents a new method for determining the minimal non-rigid deformation between two 3-D surfaces, such as those which describe anatomical structures in 3-D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3-D surfaces.

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