Marcel Lüthi

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.

Face Reconstruction from Skull Shapes and Physical Attributes

Reconstructing a persons face from its skeletal remains is a task that has over many decades fascinated artist and scientist alike. In this paper we treat facial reconstruction as a machine learning problem. We use separate statistical shape models to represent the skull and face morphology. We learn the relationship between the parameters of the models by fitting them to a set of MR images of the head and using ridge regression on the resulting model parameters. Since the facial shape is not uniquely defined by the skull shape, we allow to specify target attributes, such as age or weight. Our experiments show that the reconstruction results are generally close to the original face, and that by specifying the right attributes the perceptual and measured difference between the original and the predicted face is reduced.

Probabilistic Modeling and Visualization of the Flexibility in Morphable Models

Statistical shape models, and in particular morphable models, have gained widespread use in computer vision, computer graphics and medical imaging. Researchers have started to build models of almost any anatomical structure in the human body. While these models provide a useful prior for many image analysis task, relatively little information about the shape represented by the morphable model is exploited. We propose a method for computing and visualizing the remaining flexibility, when a part of the shape is fixed. Our method, which is based on Probabilistic PCA, not only leads to an approach for reconstructing the full shape from partial information, but also allows us to investigate and visualize the uncertainty of a reconstruction. To show the feasibility of our approach we performed experiments on a statistical model of the human face and the femur bone. The visualization of the remaining flexibility allows for greater insight into the statistical properties of the shape.

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.

Using landmarks as a deformation prior for hybrid image registration

Hybrid registration schemes are a powerful alternative to fully automatic registration algorithms. Current methods for hybrid registration either include the landmark information as a hard constraint, which is too rigid and leads to difficult optimization problems, or as a soft-constraint, which introduces a difficult to tune parameter for the landmark accuracy. In this paper we model the deformations as a Gaussian process and regard the landmarks as additional information on the admissible deformations. Using Gaussian process regression, we integrate the landmarks directly into the deformation prior. This leads to a new, probabilistic regularization term that penalizes deformations that do not agree with the modeled landmark uncertainty. It thus provides a middle ground between the two aforementioned approaches, without sharing their disadvantages. Our approach works for a large class of different deformation priors and leads to a known optimization problem in a Reproducing Kernel Hilbert Space.

Curvature guided level set registration using adaptive finite elements

We consider the problem of non-rigid, point-to-point registration of two 3D surfaces. To avoid restrictions on the topology, we represent the surfaces as a level-set of their signed distance function. Correspondence is established by finding a displacement field that minimizes the sum of squared difference between the function values as well as their mean curvature.We use a variational formulation of the problem, which leads to a non-linear elliptic partial differential equation for the displacement field. The main contribution of this paper is the application of an adaptive finite element discretization for solving this non-linear PDE. Our code uses the software library DUNE, which in combination with pre- and post-processing through ITK leads to a powerful tool for solving this type of problem. This is confirmed by our experiments on various synthetic and medical examples. We show in this work that our numerical scheme yields accurate results using only a moderate number of elements even for complex problems.

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.

A Unified Approach to Shape Model Fitting and Non-rigid Registration

Non-rigid registration and shape model fitting are the central problems in any shape modeling pipeline. Even though the goal is in both problems to establishing point-to-point correspondence between two objects, their algorithmic treatment is usually very different. In this paper we present an approach that allows us to treat both problems in a unified algorithmic framework. We use the well known formulation of non-rigid registration as the problem of fitting a Gaussian process model, whose covariance function favors smooth deformations. We compute a low rank approximation of the Gaussian process using the Nystrom method, which allows us to formulate it as a parametric fitting problem of the same form as shape model fitting. Besides simplifying the modeling pipeline, our approach also lets us naturally combine shape model fitting and non-rigid registration, in order to reduce the bias in statistical model fitting, or to make registration more robust. As our experiments on 3D surfaces and 3D CT images show, the method leads to a registration accuracy that is comparable to standard registration methods.

Local regression based statistical model fitting

Fitting statistical models is a widely employed technique for the segmentation of medical images. While this approach gives impressive results for simple structures, shape models are often not flexible enough to accurately represent complex shapes. We present a fitting approach, which increases the model fitting accuracy without requiring a larger training data-set. Inspired by a local regression approach known from statistics, our method fits the full model to a neighborhood around each point of the domain. This increases the models flexibility considerably without the need to introduce an artificial segmentation of the structure. By adapting the size of the neighborhood from small to large, we can smoothly interpolate between localized fits, which accurately map the data but are more prone to noise, and global fits, which are less flexible but constrained to valid shapes only. We applied our method for the segmentation of teeth from 3D cone-beam ct-scans. Our experiments confirm that our method consistently increases the precision of the segmentation result compared to a standard global fitting approach.

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.