Dynamic multi feature-class Gaussian process models.

In model-based medical image analysis, three relevant features are the shape of structures of interest, their relative pose, and image intensity profiles representative of some physical properties. Often, these features are modelled separately through statistical models by decomposing the object's features into a set of basis functions through principal geodesic analysis or principal component analysis. However, analysing articulated objects in an image using independent single object models may lead to large uncertainties and impingement, especially around organ boundaries. Questions that come to mind are the feasibility of building a unique model that combines all three features of interest in the same statistical space, and what advantages can be gained for image analysis. This study presents a statistical modelling method for automatic analysis of shape, pose and intensity features in medical images which we call the Dynamic multi feature-class Gaussian process models (DMFC-GPM). The DMFC-GPM is a Gaussian process (GP)-based model with a shared latent space that encodes linear and non-linear variations. Our method is defined in a continuous domain with a principled way to represent shape, pose and intensity feature-classes in a linear space, based on deformation fields. A deformation field-based metric is adapted in the method for modelling shape and intensity variation as well as for comparing rigid transformations (pose). Moreover, DMFC-GPMs inherit properties intrinsic to GPs including marginalisation and regression. Furthermore, they allow for adding additional pose variability on top of those obtained from the image acquisition process; what we term as permutation modelling. For image analysis tasks using DMFC-GPMs, we adapt Metropolis-Hastings algorithms making the prediction of features fully probabilistic. We validate the method using controlled synthetic data and we perform experiments on bone structures from CT images of the shoulder to illustrate the efficacy of the model for pose and shape prediction. The model performance results suggest that this new modelling paradigm is robust, accurate, accessible, and has potential applications in a multitude of scenarios including the management of musculoskeletal disorders, clinical decision making and image processing.

Reconstruction of full femora from partial bone fragments for anthropological analyses using statistical shape modeling.

OBJECTIVES: Due to taphonomic processes such as burial, fire, or animal activity, bones are often found incomplete, which can pose problematic for establishing the biological profile of the deceased using anthropological methods. The aim of this study is to test the feasibility of using statistical shape modeling (SSM) to reconstruct full femora from simulated partial femora and determine the accuracy of the reconstruction. Moreover, we assess the accuracy of sex estimation and the degree of stature error added based on the reconstructed femur using different anthropological methods. METHODS: A total of 42 (28 female, 14 female) 3D models of left femora extracted from computed tomography (CT) scans were used. We performed a leave-one-out cross-validation (LOOCV) where 41 bones were used to build the SSM and one bone was used for testing. This bone was cut in 1 cm steps proximally, distally and from both ends up to 10 cm, reconstructed using SSM, and tested using the methods established by Stewart and Purkait (2005), Trotter and Gleser (1952), as well as a method based on SSM. with landmarks being automatically identified. RESULTS: The error induced by reconstructing the femur to the length measurements was low, which translated into useful stature estimations (single sided cuts up to 10 cm: 0.4-1.1%, double sided<2% for cuts shorter than 6 cm). Using Purkaits method for sex estimation on reconstructed bones looked promising as well (single sided: 90.5% when compared to applying Purkaits method on the original bone, double sided 78.6% (10 cm cut) to 97.6% (1-3 cm cuts)) Using SSM for sex classification looked promising as well (single sided cut: 81-85.7%, double sided cut: 59.5-85.3%) CONCLUSION: SSM can be used to reconstruct fragmented femora. These reconstructions can be used for sex and stature estimations, at the cost of lower accuracy. Using SSM might give investigators an additional tool to gain information about the biological profile of a deceased in cases where the fragmentation of a femur does not allow for using other anthropological methods.

Model Construction for the Estimation of Healthy Bone Shape and Density Distribution.

Statistical models are widely used within biomedical fields for automated segmentation and reconstruction of healthy geometry. In the absence of contralateral geometry, statistical models are a viable alternative for reconstructing healthy bone anatomy. Therefore, statistical models of shape and appearance were constructed from sample data based on the right femur of South African males, and their use in an automated segmentation and density estimation application was investigated. The models reproduced the shape and density distribution of the population with an average error of 1.3 mm and a 90% density fit. These results fall within the acceptable tolerance limits of reconstructive surgery and appear promising for practical use in implant design.Clinical Relevance- Constructing and validating statistical models and registration algorithms provides the groundwork for further investigation into automating the digital reconstruction of pathological bone for use in implant design.

Morphological analysis of Gissane's angle utilising a statistical shape model of the calcaneus.

INTRODUCTION: Gissane's crucial angle (GA) facilitates to diagnose calcaneal fractures, and serves as an indicator of the quality of anatomical reduction after fixation. The study aimed to utilise statistical shape models (SSM) for analysing the complex 3D surface anatomy of the calcaneus represented by the simplified GA measurement on lateral radiographs. MATERIALS AND METHODS: SSMs were generated from CT scans of paired adult calcanei from 10 Japanese and 31 Thai specimens. GA measurements in 3D and 2D were obtained for the lateral, central and medial anatomy of the posterior facet and sinus tarsi. The correlation between calcaneal length and GA was analysed. Regression and principal component (PC) analyses were conducted for analysing morphological variability in calcaneal shape relating to GA. The bilateral symmetry of the obtained measurements was analysed. RESULTS: The mean GA (lateral) for the Japanese specimens was 105.1° ± 7.5 and 105.4° ± 8.5 for the Thai. The projected 2D angles of the central and medial measurements were larger (P < 0.00) than the 3D values. The medial projected 2D angles were larger (P ≤ 0.02) compared to the lateral. Despite the bilateral symmetry of GA and calcaneal length, their correlation displayed clear signs of asymmetry, which was confirmed by regression and PC analyses. CONCLUSIONS: Japanese and Thai specimens revealed lower GAs (both range and mean) compared to reported reference values of other ethnicities. As a reduced GA is generally indicative of a calcaneal fracture, our results are important to surgeons for their diagnostic assessment of Japanese and Thai patients. The results indicate that the GA measurement on a plain radiograph is a simplified representation of the lateral-to-central 3D calcaneal anatomy but significantly underestimates the angle measurement on the medial aspects of the respective surface areas.

Review of 2-D/3-D Reconstruction Using Statistical Shape and Intensity Models and X-Ray Image Synthesis: Toward a Unified Framework.

Patient-specific three-dimensional (3-D) bone models are useful for a number of clinical applications such as surgery planning, postoperative evaluation, as well as implant and prosthesis design. Two-dimensional-to-3-D (2-D/3-D) reconstruction, also known as model-to-modality or atlas-based 2-D/3-D registration, provides a means of obtaining a 3-D model of a patient's bones from their 2-D radiographs when 3-D imaging modalities are not available. The preferred approach for estimating both shape and density information (that would be present in a patient's computed tomography data) for 2-D/3-D reconstruction makes use of digitally reconstructed radiographs and deformable models in an iterative, non-rigid, intensity-based approach. Based on a large number of state-of-the-art 2-D/3-D bone reconstruction methods, a unified mathematical formulation of the problem is proposed in a common conceptual framework, using unambiguous terminology. In addition, shortcomings, recent adaptations, and persisting challenges are discussed along with insights for future research.

Restoration of the Patient-Specific Anatomy of the Proximal and Distal Parts of the Humerus: Statistical Shape Modeling Versus Contralateral Registration Method.

BACKGROUND: In computer-assisted reconstructive surgeries, the contralateral anatomy is established as the best available reconstruction template. However, existing intra-individual bilateral differences or a pathological, contralateral humerus may limit the applicability of the method. The aim of the study was to evaluate whether a statistical shape model (SSM) has the potential to predict accurately the pretraumatic anatomy of the humerus from the posttraumatic condition. METHODS: Three-dimensional (3D) triangular surface models were extracted from the computed tomographic data of 100 paired cadaveric humeri without a pathological condition. An SSM was constructed, encoding the characteristic shape variations among the individuals. To predict the patient-specific anatomy of the proximal (or distal) part of the humerus with the SSM, we generated segments of the humerus of predefined length excluding the part to predict. The proximal and distal humeral prediction (p-HP and d-HP) errors, defined as the deviation of the predicted (bone) model from the original (bone) model, were evaluated. For comparison with the state-of-the-art technique, i.e., the contralateral registration method, we used the same segments of the humerus to evaluate whether the SSM or the contralateral anatomy yields a more accurate reconstruction template. RESULTS: The p-HP error (mean and standard deviation, 3.8° ± 1.9°) using 85% of the distal end of the humerus to predict the proximal humeral anatomy was significantly smaller (p = 0.001) compared with the contralateral registration method. The difference between the d-HP error (mean, 5.5° ± 2.9°), using 85% of the proximal part of the humerus to predict the distal humeral anatomy, and the contralateral registration method was not significant (p = 0.61). The restoration of the humeral length was not significantly different between the SSM and the contralateral registration method. CONCLUSIONS: SSMs accurately predict the patient-specific anatomy of the proximal and distal aspects of the humerus. The prediction errors of the SSM depend on the size of the healthy part of the humerus. CLINICAL RELEVANCE: The prediction of the patient-specific anatomy of the humerus is of fundamental importance for computer-assisted reconstructive surgeries.

Gaussian Process Morphable Models.

Models of shape variations have become a central component for the automated analysis of images. An important class of shape models are point distribution models (PDMs). These models represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of PDMs, which we refer to as Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loève expansion. To compute the expansion, we make use of an approximation scheme based on the Nyström method. The resulting model can be seen as a continuous analog of a standard PDM. However, while for PDMs the shape variation is restricted to the linear span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, a PDM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics but is flexible enough to explain shapes that cannot be represented by the PDM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes, including methods for multi-scale or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modeling from the fitting process, this is all achieved without changes to the fitting algorithm. To demonstrate the applicability and versatility of GPMMs, we perform a set of experiments in typical usage scenarios in medical image analysis and computer vision: The model-based segmentation of 3D forearm images and the building of a statistical model of the face. To complement the paper, we have made all our methods available as open source.

Prediction of normal bone anatomy for the planning of corrective osteotomies of malunited forearm bones using a three-dimensional statistical shape model.

Corrective osteotomies of the forearm based on 3D computer simulation using contralateral anatomy as a reconstruction template is an approved method. Limitations are existing considerable differences between left and right forearms, and that a healthy contralateral anatomy is required. We evaluated if a computer model, not relying on the contralateral anatomy, may replace the current method by predicting the pre-traumatic healthy shape. A statistical shape model (SSM) was generated from a set of 59 CT scans of healthy forearms, encoding the normal anatomical variations. Three different configurations were simulated to predict the pre-traumatic shape with the SSM (cross-validation). In the first two, only the distal or proximal 50% of the radius were considered as pathological. In a third configuration, the entire radius was assumed to be pathological, only the ulna being intact. Corresponding experiments were performed with the ulna. Accuracy of the prediction was assessed by comparing the predicted bone with the healthy model. For the radius, mean rotation accuracy of the prediction between 2.9 ± 2.2° and 4.0 ± 3.1° in pronation/supination, 0.4 ± 0.3° and 0.6 ± 0.5° in flexion/extension, between 0.5 ± 0.3° and 0.5 ± 0.4° in radial-/ulnarduction. Mean translation accuracy along the same axes between 0.8 ± 0.7 and 1.0 ± 0.8 mm, 0.5 ± 0.4 and 0.6 ± 0.4 mm, 0.6 ± 0.4 and 0.6 ± 0.5 mm, respectively. For the ulna, mean rotation accuracy between 2.4 ± 1.9° and 4.7 ± 3.8° in pronation/supination, 0.3 ± 0.3° and 0.8 ± 0.6° in flexion/extension, 0.3 ± 0.2° and 0.7 ± 0.6° in radial-/ulnarduction. Mean translation accuracy between 0.6 ± 0.4 mm and 1.3 ± 0.9 mm, 0.4 ± 0.4 mm and 0.7 ± 0.5 mm, 0.5 ± 0.4 mm and 0.8 ± 0.6 mm, respectively. This technique provided high accuracy, and may replace the current method, if validated in clinical studies. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2630-2636, 2017.

Evaluation of segmentation methods on head and neck CT: Auto-segmentation challenge 2015.

PURPOSE: Automated delineation of structures and organs is a key step in medical imaging. However, due to the large number and diversity of structures and the large variety of segmentation algorithms, a consensus is lacking as to which automated segmentation method works best for certain applications. Segmentation challenges are a good approach for unbiased evaluation and comparison of segmentation algorithms. METHODS: In this work, we describe and present the results of the Head and Neck Auto-Segmentation Challenge 2015, a satellite event at the Medical Image Computing and Computer Assisted Interventions (MICCAI) 2015 conference. Six teams participated in a challenge to segment nine structures in the head and neck region of CT images: brainstem, mandible, chiasm, bilateral optic nerves, bilateral parotid glands, and bilateral submandibular glands. RESULTS: This paper presents the quantitative results of this challenge using multiple established error metrics and a well-defined ranking system. The strengths and weaknesses of the different auto-segmentation approaches are analyzed and discussed. CONCLUSIONS: The Head and Neck Auto-Segmentation Challenge 2015 was a good opportunity to assess the current state-of-the-art in segmentation of organs at risk for radiotherapy treatment. Participating teams had the possibility to compare their approaches to other methods under unbiased and standardized circumstances. The results demonstrate a clear tendency toward more general purpose and fewer structure-specific segmentation algorithms.

Spatially varying registration using Gaussian processes.

In this paper we propose a new approach for spatially-varying registration using Gaussian process priors. The method is based on the idea of spectral tempering, i.e. the spectrum of the Gaussian process is modified depending on a user defined tempering function. The result is a non-stationary Gaussian process, which induces different amount of smoothness in different areas. In contrast to most other schemes for spatially-varying registration, our approach does not require any change in the registration algorithm itself, but only affects the prior model. Thus we can obtain spatially-varying versions of any registration method whose deformation prior can be formulated in terms of a Gaussian process. This includes for example most spline-based models, but also statistical shape or deformation models. We present results for the problem of atlas based skull-registration of cone beam CT images. These datasets are difficult to register as they contain a large amount of noise around the teeth. We show that with our method we can become robust against noise, but still obtain accurate correspondence where the data is clean.

Three-dimensional analysis of the correlation between anterior tooth form and face shape.

Traditional esthetic guidelines and denture-tooth selection protocols suggest a correlation between a patient's face and anterior tooth shapes. This study examined the correlation between face shape, maxilla shape, and maxillary anterior tooth form with fully automated algorithms. Three-dimensional digital datasets of the faces and maxillae were obtained from 117 people. Correlation was analyzed using canonical correlation analysis, ridge regression, and the Hausdorff-distance. A weak but not statistically significant correlation between face and tooth shape could be identified. However, a good prediction of tooth shape from the facial data was not possible. The described approach revealed a weak correlation between face shape and tooth shape, but the outcome was not accurate enough for clinical use.

Finite element surface registration incorporating curvature, volume preservation, and statistical model information.

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models.

Posterior shape models.

We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a "posterior shape model", which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness.

The correlation between anterior tooth form and gender - a 3D analysis in humans.

This study examined the correlation between maxillary anterior tooth form and gender with three-dimensional data. Three-dimensional digital models of the area between the maxillary right central incisor and the maxillary right canine were obtained from 120 Caucasian subjects (60 males and 60 females) with healthy dentitions. Correlation between gender and tooth form was assessed applying logistic regression, with and without size standardization. Success rates were estimated using 10-fold cross-validation. Principal components that correlated with gender were evaluated with a Wald test. Values for the significance of the predictors were provided with a likelihood ratio test (P < 0.05). Significant correlation between gender and tooth shape was found for the maxillary central incisor (P = 0.003), lateral incisor (P ≤ 0.001), and canine individually (P ≤ 0.001), and for the three teeth combined (P ≤ 0.001) without size standardization. For the maximillary right lateral incisor (P=0.004), canine (P ≤ 0.001), and a correlation of the teeth (P ≤ 0.001), a correlation was also established after size standardization. Prediction of gender was not possible without information on tooth size for the maxillary right central incisor (P =0.15). maxillary anterior teeth have gender-specific differences. Differences in tooth size account for part of the correlation. However, tooth shapes are also gender specific.

Building shape models from lousy data.

Statistical shape models have gained widespread use in medical image analysis. In order for such models to be statistically meaningful, a large number of data sets have to be included. The number of available data sets is usually limited and often the data is corrupted by imaging artifacts or missing information. We propose a method for building a statistical shape model from such "lousy" data sets. The method works by identifying the corrupted parts of a shape as statistical outliers and excluding these parts from the model. Only the parts of a shape that were identified as outliers are discarded, while all the intact parts are included in the model. The model building is then performed using the EM algorithm for probabilistic principal component analysis, which allows for a principled way to handle missing data. Our experiments on 2D synthetic and real 3D medical data sets confirm the feasibility of the approach. We show that it yields superior models compared to approaches using robust statistics, which only downweight the influence of outliers.