Kumar T. Rajamani

Evaluation of 3D Correspondence Methods for Model Building

The correspondence problem is of high relevance in the construction and use of statistical models. Statistical models are used for a variety of medical application, e.g. segmentation, registration and shape analysis. In this paper, we present comparative studies in three anatomical structures of four different correspondence establishing methods. The goal in all of the presented studies is a model-based application. We have analyzed both the direct correspondence via manually selected landmarks as well as the properties of the model implied by the correspondences, in regard to compactness, generalization and specificity. The studied methods include a manually initialized subdivision surface (MSS) method and three automatic methods that optimize the object parameterization: SPHARM, MDL and the covariance determinant (DetCov) method. In all studies, DetCov and MDL showed very similar results. The model properties of DetCov and MDL were better than SPHARM and MSS. The results suggest that for modeling purposes the best of the studied correspondence method are MDL and DetCov.

Statistical deformable bone models for robust 3D surface extrapolation from sparse data

A majority of pre-operative planning and navigational guidance during computer assisted orthopaedic surgery routinely uses three-dimensional models of patient anatomy. These models enhance the surgeons capability to decrease the invasiveness of surgical procedures and increase their accuracy and safety. A common approach for this is to use computed tomography (CT) or magnetic resonance imaging (MRI). These have the disadvantages that they are expensive and/or induce radiation to the patient. In this paper we propose a novel method to construct a patient-specific three-dimensional model that provides an appropriate intra-operative visualization without the need for a pre or intra-operative imaging. The 3D model is reconstructed by fitting a statistical deformable model to minimal sparse 3D data consisting of digitized landmarks and surface points that are obtained intra-operatively. The statistical model is constructed using Principal Component Analysis from training objects. Our deformation scheme efficiently and accurately computes a Mahalanobis distance weighted least square fit of the deformable model to the 3D data. Relaxing the Mahalanobis distance term as additional points are incorporated enables our method to handle small and large sets of digitized points efficiently. Formalizing the problem as a linear equation system helps us to provide real-time updates to the surgeons. Incorporation of M-estimator based weighting of the digitized points enables us to effectively reject outliers and compute stable models. We present here our evaluation results using leave-one-out experiments and extended validation of our method on nine dry cadaver bones.

Accurate and Robust Reconstruction of a Surface Model of the Proximal Femur From Sparse-Point Data and a Dense-Point Distribution Model for Surgical Navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

Bone model morphing for enhanced surgical visualization

We propose a novel method for reconstructing a complete 3D model of a given anatomy from minimal information. This reconstruction provides an appropriate intra-operative 3D visualization without the need for a pre or intra-operative imaging. Our method #ts a statistical deformable model to sparse 3D data consisting of digitized landmarks and bone surface points. The method also allows the incorporation of nonspatial data such as patient height and weight. The statistical model is constructed using principal component analysis (PCA) from a set of training objects. Our morphing method then computes a Mahalanobis distance weighted least square #t of the model by solving a linear equation system. First experimental promising results with model generated from 14 femoral head are presented.

Bone Morphing with statistical shape models for enhanced visualization

This paper addresses the problem of extrapolating extremely sparse three-dimensional set of digitized landmarks and bone surface points to obtain a complete surface representation. The extrapolation is done using a statistical principal component analysis (PCA) shape model similar to earlier approaches by Fleute et al. 1 This extrapolation procedure called Bone-Morphing is highly useful for intra-operative visualization of bone structures in image-free surgeries. We developed a novel morphing scheme operating directly in the PCA shape space incorporating the full set of possible variations including additional information such as patient height, weight and age. Shape information coded by digitized points is iteratively removed from the PCA model. The extrapolated surface is computed as the most probable surface in the shape space given the data. Interactivity is enhanced, as additional bone surface points can be incorporated in real-time. The expected accuracy can be visualized at any stage of the procedure. In a feasibility study, we applied the proposed scheme to the proximal femur structure. 14 CT scans were segmented and a sequence of correspondence establishing methods was employed to compute the optimal PCA model. Three anatomical landmarks, the femoral notch and the upper and the lower trochanter are digitized to register the model to the patient anatomy. Our experiments show that the overall shape information can be captured fairly accurately by a small number of control points. The added advantage is that it is fast, highly interactive and needs only a small number of points to be digitized intra-operatively.

Use of a dense surface point distribution model in a three-stage anatomical shape reconstruction from sparse information for computer assisted orthopaedic surgery: a preliminary study

Constructing anatomical shape from extremely sparse information is a challenging task. A priori information is often required to handle this otherwise ill-posed problem. In the present paper, we try to solve the problem in an accurate and robust way. At the heart of our approach lies the combination of a three-stage anatomical shape reconstruction technique and a dense surface point distribution model (DS-PDM). The DS-PDM is constructed from an already-aligned sparse training shape set using Loop subdivision. Its application facilitates the setup of point correspondences for all three stages of surface reconstruction due to its dense description. The proposed approach is especially useful for accurate and stable surface reconstruction from sparse information when only a small number of a priori training shapes are available. It adapts gradually to use more information derived from the a priori model when larger number of training data are available. The proposed approach has been successfully validated in a preliminary study on anatomical shape reconstruction of two femoral heads using only dozens of sparse points, yielding promising results.

A novel and stable approach to anatomical structure morphing for enhanced intraoperative 3D visualization

The use of three dimensional models in planning and navigating computer assisted surgeries is now well established. These models provide intuitive visualization to the surgeons contributing to significantly better surgical outcomes. Models obtained from specifically acquired CT scans have the disadvantage that they induce high radiation dose to the patient. In this paper we propose a novel and stable method to construct a patient-specific model that provides an appropriate intra-operative 3D visualization without the need for a pre or intra-operative imaging. Patient specific data consists of digitized landmarks and surface points that are obtained intra-operatively. The 3D model is reconstructed by fitting a statistical deformable model to the minimal sparse digitized data. The statistical model is constructed using Principal Component Analysis from training objects. Our morphing scheme efficiently and accurately computes a Mahalanobis distance weighted least square fit of the deformable model to the 3D data model by solving a linear equation system. Relaxing the Mahalanobis distance term as additional points are incorporated enables our method to handle small and large sets of digitized points efficiently. Our novel incorporation of M-estimator based weighting of the digitized points enables us to effectively reject outliers and compute stable models. Normalization of the input model data and the digitized points makes our method size invariant and hence applicable directly to any anatomical shape. The method also allows incorporation of non-spatial data such as patient height and weight. The predominant applications are hip and knee surgeries.

A comparison study assessing the feasibility of ultrasound-initialized deformable bone models

This article presents a feasibility and evaluation study for using 2D ultrasound in conjunction with our statistical deformable bone model within the scope of computer-assisted surgery. The final aim is to provide the surgeon with enhanced 3D visualization for surgical navigation in orthopedic surgery without the need for preoperative CT or MRI scans. We unified our earlier work to combine several automatic methods for statistical bone shape prediction and ultrasound segmentation and calibration to provide the intended rapid and accurate visualization. We compared the use of a tracked digitizing pointer and ultrasound for acquiring landmarks and bone surface points for the estimation of two cast proximal femurs.

A Novel Approach to Anatomical Structure Morphing for Intraoperative Visualization

In computer assisted surgery 3D models are now routinely used to plan and navigate a surgery. These models enhance the surgeon’s capability to decrease the invasiveness of surgical procedures and increase their accuracy and safety. Models obtained from specifically acquired CT scans have the disadvantage that they induce high radiation dose to the patient. In this paper we propose a novel method to construct a patient-specific model that provides an appropriate intra-operative 3D visualization without the need for a pre or intra-operative imaging. The 3D model is reconstructed by fitting a statistical deformable model to minimal sparse 3D data consisting of digitized landmarks and surface points that are obtained intra-operatively. The statistical model is constructed using Principal Component Analysis from training objects. Our morphing method then computes a Mahalanobis distance weighted least square fit of the model by solving a linear equation system. The refined morphing scheme has better convergence behaviour because of the additional parameter that relaxes the Mahalanobis distance term as additional points are incorporated. We present leave-one-out experiments with model generated from proximal femors and hippocampi.