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Institute
3D Morphable Models (MM) are a popular tool for analysis and synthesis of facial expressions. They represent plausible variations in facial shape and appearance within a low-dimensional parameter space. Fitted to a face scan, the model's parameters compactly encode its expression patterns. This expression code can be used, for instance, as a feature in automatic facial expression recognition. For accurate classification, an MM that can adequately represent the various characteristic facets and variants of each expression is necessary. Currently available MMs are limited in the diversity of expression patterns. We present a novel high-quality Facial Expression Morphable Model built from a large-scale face database as a tool for expression analysis and synthesis. Establishment of accurate dense correspondence, up to finest skin features, enables a detailed statistical analysis of facial expressions. Various characteristic shape patterns are identified for each expression. The results of our analysis give rise to a new facial expression code. We demonstrate the advantages of such a code for the automatic recognition of expressions, and compare the accuracy of our classifier to state-of-the-art.
We present an efficient GPU-based method to generate virtual X-ray images from tetrahedral meshes which are
associated with attenuation values. In addition, a novel approach is proposed that performs the model deformation
on the GPU. The tetrahedral grids are derived from volumetric statistical shape and intensity models (SSIMs) and describe anatomical structures. Our research targets at reconstructing 3D anatomical shapes by comparing virtual X-ray images generated using our novel approach with clinical data while varying the shape and density of the SSIM in an optimization process. We assume that a deformed SSIM adequately represents an anatomy of interest when the similarity between the virtual and the clinical X-ray image is maximized. The OpenGL implementation presented here generates accurate (virtual) X-ray images at interactive rates, thus qualifying it for its use in the reconstruction process.
We propose a novel GPU-based approach to render virtual X-ray projections of deformable tetrahedral meshes. These meshes represent the shape and the internal density distribution of a particular anatomical structure and are derived from statistical shape and intensity models (SSIMs). We apply our method to improve the geometric reconstruction of 3D anatomy (e.g.\ pelvic bone) from 2D X-ray images. For that purpose, shape and density of a tetrahedral mesh are varied and virtual X-ray projections are generated within an optimization process until the similarity between the computed virtual X-ray and the respective anatomy depicted in a given clinical X-ray is maximized. The OpenGL implementation presented in this work deforms and projects tetrahedral meshes of high resolution (200.000+ tetrahedra) at interactive rates. It generates virtual X-rays that accurately depict the density distribution of an anatomy of interest. Compared to existing methods that accumulate X-ray attenuation in deformable meshes, our novel approach significantly boosts the deformation/projection performance. The proposed projection algorithm scales better with respect to mesh resolution and complexity of the density distribution, and the combined deformation and projection on the GPU scales better with respect to the number of deformation parameters. The gain in performance allows for a larger number of cycles in the optimization process. Consequently, it reduces the risk of being stuck in a local optimum. We believe that our approach contributes in orthopedic surgery, where 3D anatomy information needs to be extracted from 2D X-rays to support surgeons in better planning joint replacements.
We present a novel method to derive the surface distance of an osteosynthesis plate w.r.t. the patientspecific surface of the distal femur based on 2D Xray images. Our goal is to study from clinical data, how the platetobone distance affects bone healing. The patientspecific 3D shape of the femur is, however, seldom recorded for cases of femoral osteosynthesis since this typically requires Computed Tomography (CT), which comes at high cost and radiation dose. Our method instead utilizes two postoperative Xray images to derive the femoral shape and thus can be applied on radiographs that are taken in clinical routine for followup. First, the implant geometry is used as a calibration object to relate the implant and the individual Xray images spatially in a virtual Xray setup. In a second step, the patientspecific femoral shape and pose are reconstructed in the virtual setup by fitting a deformable statistical shape and intensity model (SSIM) to the images. The relative positioning between femur and implant is then assessed in terms of displacement between the reconstructed 3D shape of the femur and the plate. A preliminary evaluation based on 4 cadaver datasets shows that the method derives the platetobone distance with a mean absolute error of less than 1mm and a maximum error of 4.7 mm compared to ground truth from CT. We believe that the approach presented in this paper constitutes a meaningful tool to elucidate the effect of implant positioning on fracture healing.
We present a novel method to derive the surface distance of an osteosynthesis plate w.r.t. the patient-specific surface of the distal femur based on postoperative 2D radiographs. In a first step, the implant geometry is used as a calibration object to relate the implant and the individual X-ray images spatially in a virtual X-ray setup. Second, the patient-specific femoral shape and pose are reconstructed by fitting a deformable statistical shape and intensity model (SSIM) to the X-rays. The relative positioning between femur and implant is then assessed in terms of the displacement between the reconstructed 3D shape of the femur and the plate. We believe that the approach presented in this paper constitutes a meaningful tool to elucidate the effect of implant positioning on fracture healing and, ultimately, to derive load recommendations after surgery.
Towards Robust Measurement of Pelvic Parameters from AP Radiographs using Articulated 3D Models
(2015)
Patient-specific parameters such as the orientation of the acetabulum or pelvic tilt are useful for custom planning for total hip arthroplasty (THA) and for evaluating the outcome of surgical interventions. The gold standard in obtaining pelvic parameters is from three-dimensional (3D) computed tomography (CT) imaging. However, this adds time and cost, exposes the patient to a substantial radiation dose, and does not allow for imaging under load (e.g. while the patient is standing). If pelvic parameters could be reliably derived from the standard anteroposterior (AP) radiograph, preoperative planning would be more widespread, and research analyses could be applied to retrospective data, after a postoperative issue is discovered. The goal of this work is to enable robust measurement of two surgical parameters of interest: the tilt of the anterior pelvic plane (APP) and the orientation of the natural acetabulum. We present a computer-aided reconstruction method to determine the APP and natural acetabular orientation from a single, preoperative X-ray. It can easily be extended to obtain other important preoperative and postoperative parameters solely based on a single AP radiograph.
Der Artikel gibt einen Einblick in das reiche Feld der Zusammenarbeit zwischen Mathematik und Medizin. Beispielhaft werden drei Erfolgsmodelle dargestellt: Medizinische Bildgebung, mathematische Modellierung und Biosignalverarbeitung im Bereich der Dynamik des Herzens sowie mathematische Modellierung und Simulation in der Krebstherapie Hyperthermie und der Mund-Kiefer-Gesichts-Chirurgie. In allen Fällen existiert ein Gleichklang der Interessen von Medizin und Mathematik: Beide Disziplinen wollen die Resultate schnell und zuverlässig. Für die Klinik heißt das, dass notwendige Rechnungen in möglichst kurzer Zeit, und zwar auf dem PC, ablaufen müssen und dass die Resultate so genau und belastbar sein müssen, dass medizinische Entscheidungen darauf aufbauen können. Für die Mathematik folgt daraus, dass höchste Anforderungen an die Effizienz der verwendeten Algorithmen und die darauf aufbauende Software in Numerik und Visualisierung zu stellen sind. Jedes Kapitel endet mit einer Darstellung der Perspektive des jeweiligen Gebietes. Abschließend werden mögliche Handlungsoptionen für Politik und Wirtschaft diskutiert.
We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. We evaluate the performance of our model w.r.t. shape-based classification of pathological malformations of the human knee and show that it outperforms the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model's ability of capturing natural biological shape variability, we carry out an analysis of specificity and generalization ability.
We describe a novel nonlinear statistical shape model basedon differential coordinates viewed as elements of GL+(3). We adopt an as-invariant-as possible framework comprising a bi-invariant Lie group mean and a tangent principal component analysis based on a unique GL+(3)-left-invariant, O(3)-right-invariant metric. Contrary to earlier work that equips the coordinates with a specifically constructed group structure, our method employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences. We demonstrate this in experiments on two anatomical datasets including comparison to the standard Euclidean as well as recent state-of-the-art nonlinear approaches to statistical shape modeling.