A morphable model for the synthesis of 3D faces

PURPOSE\nTo measure macular choroidal thickness in normal eyes at different points using enhanced depth imaging (EDI) optical coherence tomography (OCT) and to evaluate the association of choroidal thickness and age.\n\n\nDESIGN\nRetrospective, observational case series.\n\n\nMETHODS\nEDI OCT images were obtained in patients without significant retinal or choroidal pathologic features. The images were obtained by positioning a spectral-domain OCT device close enough to the eye to acquire an inverted image. Seven sections were obtained within a 5 x 30-degree area centered at the fovea, with 100 scans averaged for each section. The choroid was measured from the outer border of the retinal pigment epithelium to the inner scleral border at 500-microm intervals of a horizontal section from 3 mm temporal to the fovea to 3 mm nasal to the fovea. Statistical analysis was performed to evaluate variations of choroidal thickness at each location and to correlate choroidal thickness and patient age.\n\n\nRESULTS\nThe mean age of the 30 patients (54 eyes) was 50.4 years (range, 19 to 85 years), and 14 patients (46.7%) were female. The choroid was thickest underneath the fovea (mean, 287 microm; standard deviation, +/- 76 microm). Choroidal thickness decreased rapidly in the nasal direction and averaged 145 microm (+/- 57 microm) at 3 mm nasal to the fovea. Increasing age was correlated significantly with decreasing choroidal thickness at all points measured. Regression analysis suggested that the subfoveal choroidal thickness decreased by 15.6 microm for each decade of life.\n\n\nCONCLUSIONS\nChoroidal thickness seems to vary topographically within the posterior pole. The thickness of the choroid showed a negative correlation with age. The decrease in the thickness of the choroid may play a role in the pathophysiologic features of various age-related ocular conditions.

Enhanced Depth Imaging Optical Coherence Tomography of the Choroid in Normal Eyes

https://journals.iucr.org/m/issues/2019/01/00/fq5003/fq5003.pdf

A Bayesian approach to beam-induced motion correction in cryo-EM single-particle analysis

The mathematical/statistical software platform R has seen an immense increase in popularity within the last decade. Its main advantages are its flexibility, a large repository of freely available extensions, its open-source nature and a thriving community. This tutorial gives an introduction into landmark/surface-mesh based statistical shape analysis in R – specifically using the packages Morpho and Rvcg. Beginning with examples based on sparse sets of anatomical landmarks, the tutorial will go on dealing with surface and curve landmarks and more challenging tasks such as mesh manipulations and surface registration. Apart from statistical analyses, emphasis will also be put on comprehensive visualization of the results. Extensive examples and code snippets are provided to allow the reader to easily replicate the analyses.

Morpho and Rvcg – Shape Analysis in R: R-Packages for Geometric Morphometrics, Shape Analysis and Surface Manipulations

Deep learning based 3D reconstruction techniques have recently achieved impressive results. However, while state-of-the-art methods are able to output complex 3D geometry, it is not clear how to extend these results to time-varying topologies. Approaches treating each time step individually lack continuity and exhibit slow inference, while traditional 4D reconstruction methods often utilize a template model or discretize the 4D space at fixed resolution. In this work, we present Occupancy Flow, a novel spatio-temporal representation of time-varying 3D geometry with implicit correspondences. Towards this goal, we learn a temporally and spatially continuous vector field which assigns a motion vector to every point in space and time. In order to perform dense 4D reconstruction from images or sparse point clouds, we combine our method with a continuous 3D representation. Implicitly, our model yields correspondences over time, thus enabling fast inference while providing a sound physical description of the temporal dynamics. We show that our method can be used for interpolation and reconstruction tasks, and demonstrate the accuracy of the learned correspondences. We believe that Occupancy Flow is a promising new 4D representation which will be useful for a variety of spatio-temporal reconstruction tasks.

/pdf/occupancy-flow-4d-reconstruction-by-learning-particle-y1y9vuacl3.pdf

Occupancy Flow: 4D Reconstruction by Learning Particle Dynamics

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-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 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.

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.

Medical image registration is an active research topic and forms a basis for many medical image analysis tasks. Although image registration is a rather general concept specialized methods are usually required to target a specific registration problem. The development and implementation of such methods has been tough so far as the gradient of the objective has to be computed. Also, its evaluation has to be performed preferably on a GPU for larger images and for more complex transformation models and regularization terms. This hinders researchers from rapid prototyping and poses hurdles to reproduce research results. There is a clear need for an environment which hides this complexity to put the modeling and the experimental exploration of registration methods into the foreground. With the "Autograd Image Registration Laboratory" (AIRLab), we introduce an open laboratory for image registration tasks, where the analytic gradients of the objective function are computed automatically and the device where the computations are performed, on a CPU or a GPU, is transparent. It is meant as a laboratory for researchers and developers enabling them to rapidly try out new ideas for registering images and to reproduce registration results which have already been published. AIRLab is implemented in Python using PyTorch as tensor and optimization library and SimpleITK for basic image IO. Therefore, it profits from recent advances made by the machine learning community concerning optimization and deep neural network models. The presented draft of this paper outlines AIRLab with first code snippets and performance analyses. A more exhaustive introduction will follow as a final version soon.

AirLab: Autograd Image Registration Laboratory.

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.

Using landmarks as a deformation prior for hybrid image 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.

/pdf/a-unified-approach-to-shape-model-fitting-and-non-rigid-20wuqfcu85.pdf

Christoph Jud

Papers

Gaussian Process Morphable Models

Gaussian Process Morphable Models

AirLab: Autograd Image Registration Laboratory.

Using landmarks as a deformation prior for hybrid image registration

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