Reconstruction of 3D Vertebral Models from a Single 2D Lateral Fluoroscopic Image

Accurate three-dimensional (3D) models of lumbar vertebrae are required for image-based 3D kinematics analysis. MRI or CT datasets are frequently used to derive 3D models but have the disadvantages that they are expensive, time-consuming or involving ionizing radiation (e.g., CT acquisition). In this chapter, we present an alternative technique that can reconstruct a scaled 3D lumbar vertebral model from a single two-dimensional (2D) lateral fluoroscopic image and a statistical shape model. Cadaveric studies are conducted to verify the reconstruction accuracy by comparing the surface models reconstructed from a single lateral fluoroscopic image to the ground truth data from 3D CT segmentation. A mean reconstruction error between 0.7 and 1.4 mm was found.

Fully Automatic CT Segmentation for Computer-Assisted Pre-operative Planning of Hip Arthroscopy

Extraction of both pelvic and femoral surface models of a hip joint from CT data for computer-assisted pre-operative planning of hip arthroscopy is addressed. We present a method for a fully automatic image segmentation of a hip joint. Our method works by combining fast random forest (RF) regression based landmark detection, atlas-based segmentation, with articulated statistical shape model (aSSM) based hip joint reconstruction. The two fundamental contributions of our method are: (1) An improved fast Gaussian transform (IFGT) is used within the RF regression framework for a fast and accurate landmark detection, which then allows for a fully automatic initialization of the atlas-based segmentation; and (2) aSSM based fitting is used to preserve hip joint structure and to avoid penetration between the pelvic and femoral models. Validation on 30 hip CT images show that our method achieves high performance in segmenting pelvis, left proximal femur, and right proximal femur surfaces with an average accuracy of 0.59 mm, 0.62 mm, and 0.58 mm, respectively.

FACTS: Fully Automatic CT Segmentation of a Hip Joint

Extraction of surface models of a hip joint from CT data is a pre-requisite step for computer assisted diagnosis and planning (CADP) of periacetabular osteotomy (PAO). Most of existing CADP systems are based on manual segmentation, which is time-consuming and hard to achieve reproducible results. In this paper, we present a Fully Automatic CT Segmentation (FACTS) approach to simultaneously extract both pelvic and femoral models. Our approach works by combining fast random forest (RF) regression based landmark detection, multi-atlas based segmentation, with articulated statistical shape model (aSSM) based fitting. The two fundamental contributions of our approach are: (1) an improved fast Gaussian transform (IFGT) is used within the RF regression framework for a fast and accurate landmark detection, which then allows for a fully automatic initialization of the multi-atlas based segmentation; and (2) aSSM based fitting is used to preserve hip joint structure and to avoid penetration between the pelvic and femoral models. Taking manual segmentation as the ground truth, we evaluated the present approach on 30 hip CT images (60 hips) with a 6-fold cross validation. When the present approach was compared to manual segmentation, a mean segmentation accuracy of 0.40, 0.36, and 0.36 mm was found for the pelvis, the left proximal femur, and the right proximal femur, respectively. When the models derived from both segmentations were used to compute the PAO diagnosis parameters, a difference of 2.0 ± 1.5°, 2.1 ± 1.6°, and 3.5 ± 2.3% were found for anteversion, inclination, and acetabular coverage, respectively. The achieved accuracy is regarded as clinically accurate enough for our target applications.

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Statistical finite element model for bone shape and biomechanical properties

We present a framework for statistical finite element analysis combining shape and material properties, and allowing performing statistical statements of biomechanical performance across a given population. In this paper, we focus on the design of orthopaedic implants that fit a maximum percentage of the target population, both in terms of geometry and biomechanical stability. CT scans of the bone under consideration are registered non-rigidly to obtain correspondences in position and intensity between them. A statistical model of shape and intensity (bone density) is computed by means of principal component analysis. Afterwards, finite element analysis (FEA) is performed to analyse the biomechanical performance of the bones. Realistic forces are applied on the bones and the resulting displacement and bone stress distribution are calculated. The mechanical behaviour of different PCA bone instances is compared.

Statistical inference for the optimal approximating model

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008, 1989). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral χ2-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one.

Beyond the tree of texts: Building an empirical model of scribal variation through graph analysis of texts and stemmata

Stemmatology, or the reconstruction of the transmission history of texts, is a field that stands particularly to gain from digital methods. Many scholars already take stemmatic approaches that rely heavily on computational analysis of the collated text (e.g. Robinson and O’Hara 1996; Salemans 2000; Heikkilä 2005; Windram et al. 2008 among many others). Although there is great value in computationally assisted stemmatology, providing as it does a reproducible result and allowing access to the relevant methodological process in related fields such as evolutionary biology, computational stemmatics is not without its critics. The current state-of-the-art effectively forces scholars to choose between a preconceived judgment of the significance of textual differences (the Lachmannian or neo-Lachmannian approach, and the weighted phylogenetic approach) or to make no judgment at all (the unweighted phylogenetic approach). Some basis for judgment of the significance of variation is sorely needed for medieval text criticism in particular. By this, we mean that there is a need for a statistical empirical profile of the text-genealogical significance of the different sorts of variation in different sorts of medieval texts. The rules that apply to copies of Greek and Latin classics may not apply to copies of medieval Dutch story collections; the practices of copying authoritative texts such as the Bible will most likely have been different from the practices of copying the Lives of local saints and other commonly adapted texts. It is nevertheless imperative that we have a consistent, flexible, and analytically tractable model for capturing these phenomena of transmission. In this article, we present a computational model that captures most of the phenomena of text variation, and a method for analysis of one or more stemma hypotheses against the variation model. We apply this method to three ‘artificial traditions’ (i.e. texts copied under laboratory conditions by scholars to study the properties of text variation) and four genuine medieval traditions whose transmission history is known or deduced in varying degrees. Although our findings are necessarily limited by the small number of texts at our disposal, we demonstrate here some of the wide variety of calculations that can be made using our model. Certain of our results call sharply into question the utility of excluding ‘trivial’ variation such as orthographic and spelling changes from stemmatic analysis.