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

Active nonrigid ICP algorithm

© 2015 IEEE.The problem of fitting a 3D facial model to a 3D mesh has received a lot of attention the past 15-20 years. The majority of the techniques fit a general model consisting of a simple parameterisable surface or a mean 3D facial shape. The drawback of this approach is that is rather difficult to describe the non-rigid aspect of the face using just a single facial model. One way to capture the 3D facial deformations is by means of a statistical 3D model of the face or its parts. This is particularly evident when we want to capture the deformations of the mouth region. Even though statistical models of face are generally applied for modelling facial intensity, there are few approaches that fit a statistical model of 3D faces. In this paper, in order to capture and describe the non-rigid nature of facial surfaces we build a part-based statistical model of the 3D facial surface and we combine it with non-rigid iterative closest point algorithms. We show that the proposed algorithm largely outperforms state-of-the-art algorithms for 3D face fitting and alignment especially when it comes to the description of the mouth region

Gaussian Process Morphable Models

Statistical shape models (SSMs) 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 SSMs, called Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loeve expansion. To compute the expansion, we make use of an approximation scheme based on the Nystrom method. The resulting model can be seen as a continuous analogon of an SSM. However, while for SSMs the shape variation is restricted to the 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, an SSM 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 SSM. 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, spatially-varying or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modelling from the fitting process, this is all achieved without changes to the fitting algorithm. We show the applicability and versatility of GPMMs on a clinical use case, where the goal is the model-based segmentation of 3D forearm images

Improved image registration by sparse patch-based deformation estimation

Despite of intensive efforts for decades, deformable image registration is still a challenging problem due to the potential large anatomical differences across individual images, which limits the registration performance. Fortunately, this issue could be alleviated if a good initial deformation can be provided for the two images under registration, which are often termed as the moving subject and the fixed template, respectively. In this work, we present a novel patch-based initial deformation prediction framework for improving the performance of existing registration algorithms. Our main idea is to estimate the initial deformation between subject and template in a patch-wise fashion by using the sparse representation technique. We argue that two image patches should follow the same deformation towards the template image if their patch-wise appearance patterns are similar. To this end, our framework consists of two stages, i.e., the training stage and the application stage. In the training stage, we register all training images to the pre-selected template, such that the deformation of each training image with respect to the template is known. In the application stage, we apply the following four steps to efficiently calculate the initial deformation field for the new test subject: (1) We pick a small number of key points in the distinctive regions of the test subject; (2) For each key point, we extract a local patch and form a coupled appearance-deformation dictionary from training images where each dictionary atom consists of the image intensity patch as well as their respective local deformations; (3) A small set of training image patches in the coupled dictionary are selected to represent the image patch of each subject key point by sparse representation. Then, we can predict the initial deformation for each subject key point by propagating the pre-estimated deformations on the selected training patches with the same sparse representation coefficients. (4) We employ thin-plate splines (TPS) to interpolate a dense initial deformation field by considering all key points as the control points. Thus, the conventional image registration problem becomes much easier in the sense that we only need to compute the remaining small deformation for completing the registration of the subject to the template. Experimental results on both simulated and real data show that the registration performance can be significantly improved after integrating our patch-based deformation prediction framework into the existing registration algorithms

Metodología probabilística para la segmentación de estructuras cerebrales basada en procesos Gaussianos

Con el desarrollo de este proyecto de investigación, se busca avanzar en el estudio de los métodos para la segmentación de formas 3D relacionadas a estructuras cerebrales utilizando modelos probabilísticos de variables latentes, los cuales a partir de un conocimiento a-priori de las estructuras 3D permitan contemplar determinados descriptores y así encontrar nuevas posibles deformaciones sintéticas de la estructura que permitan al modelo mayor flexibilidad y especificidad para capturar las variaciones de una estructura dada. Esto, con el fin de darle más robustez al desarrollo de sistemas de apoyo al especialista para la identificación de estructuras cerebrales en un determinado procedimiento de cirugía guiada por imagen y brindar un apoyo al especialista a la hora de dar un diagnostico..

A global-to-local model for the representation of human faces

In the context of face modeling and face recognition, statistical models are widely used for the representation and modeling of surfaces. Most of these models are obtained by computing Principal Components Analysis (PCA) on a set of representative examples. These models represent novel faces poorly due to their holistic nature (i.e.\ each component has global support), and they suffer from overfitting when used for generalization from partial information. In this work, we present a novel analysis method that breaks the objects up into modes based on spatial frequency. The high-frequency modes are segmented into regions with respect to specific features of the object. After computing PCA on these segments individually, a hierarchy of global and local components gradually decreasing in size of their support is combined into a linear statistical model, hence the name, Global-to-Local model (G2L). We apply our methodology to build a novel G2L model of 3D shapes of human heads. Both the representation and the generalization capabilities of the models are evaluated and compared in a standardized test, and it is demonstrated that the G2L model performs better compared to traditional holistic PCA models. Furthermore, both models are used to reconstruct the 3D shape of faces from a single photograph. A novel adaptive fitting method is presented that estimates the model parameters using a multi-resolution approach. The model is first fitted to contours extracted from the image. In a second stage, the contours are kept fixed and the remaining flexibility of the model is fitted to the input image. This makes the method fast (30 sec on a standard PC), efficient, and accurate

A machine learning approach to statistical shape models with applications to medical image analysis

Statistical shape models have become an indispensable tool for image analysis. The use of shape models is especially popular in computer vision and medical image analysis, where they were incorporated as a prior into a wide range of different algorithms. In spite of their big success, the study of statistical shape models has not received much attention in recent years. Shape models are often seen as an isolated technique, which merely consists of applying Principal Component Analysis to a set of example data sets. In this thesis we revisit statistical shape models and discuss their construction and applications from the perspective of machine learning and kernel methods. The shapes that belong to an object class are modeled as a Gaussian Process whose parameters are estimated from example data. This formulation puts statistical shape models in a much wider context and makes the powerful inference tools from learning theory applicable to shape modeling. Furthermore, the formulation is continuous and thus helps to avoid discretization issues, which often arise with discrete models. An important step in building statistical shape models is to establish surface correspondence. We discuss an approach which is based on kernel methods. This formulation allows us to integrate the statistical shape model as an additional prior. It thus unifies the methods of registration and shape model fitting. Using Gaussian Process regression we can integrate shape constraints in our model. These constraints can be used to enforce landmark matching in the fitting or correspondence problem. The same technique also leads directly to a new solution for shape reconstruction from partial data. In addition to experiments on synthetic 2D data sets, we show the applicability of our methods on real 3D medical data of the human head. In particular, we build a 3D model of the human skull, and present its applications for the planning of cranio-facial surgeries

A Statistical Deformation Prior for Non-Rigid Image and Shape Registration

Non-rigid registration is central to many problems in computer vision and medical image analysis. We propose a registration algorithm which is regularized by prior knowledge in the form of a statistical deformation model. This model is obtained from previous registrations performed on a set of noise-free training examples given by images, or shapes represented by level set functions. Contrary to similar approaches, our method does not strictly constrain the result to lie in the span of the statistical model but rather uses the model for Tikhonov regularization. Therefore, our method can be used to reduce the influence of noise and artifacts even when the model contains only a few typical examples. This automatically gives rise to a bootstrapping strategy for building statistical models from noisy data sets requiring only a limited number of high quality examples. We demonstrate the effectiveness of the approach on synthetic and medical images. 1