François Lauze

Deep Feature Learning for Knee Cartilage Segmentation Using a Triplanar Convolutional Neural Network

Segmentation of anatomical structures in medical images is often based on a voxel/pixel classification approach. Deep learning systems, such as convolutional neural networks (CNNs), can infer a hierarchical representation of images that fosters categorization. We propose a novel system for voxel classification integrating three 2D CNNs, which have a one-to-one association with the xy, yz and zx planes of 3D image, respectively. We applied our method to the segmentation of tibial cartilage in low field knee MRI scans and tested it on 114 unseen scans. Although our method uses only 2D features at a single scale, it performs better than a state-of-the-art method using 3D multi-scale features. In the latter approach, the features and the classifier have been carefully adapted to the problem at hand. That we were able to get better results by a deep learning architecture that autonomously learns the features from the images is the main insight of this study.

Adaptive Structure Tensors and their Applications

The structure tensor, also known as second moment matrix or Forstner interest operator, is a very popular tool in image processing. Its purpose is the estimation of orientation and the local analysis of structure in general. It is based on the integration of data from a local neighborhood. Normally, this neighborhood is defined by a Gaussian window function and the structure tensor is computed by the weighted sum within this window. Some recently proposed methods, however, adapt the computation of the structure tensor to the image data. There are several ways how to do that. This chapter wants to give an overview of the different approaches, whereas the focus lies on the methods based on robust statistics and nonlinear diffusion. Furthermore, the data-adaptive structure tensors are evaluated in some applications. Here the main focus lies on optic flow estimation, but also texture analysis and corner detection are considered.

Manifold valued statistics, exact principal, geodesic analysis and the effect of linear, approximations

Manifolds are widely used to model non-linearity arising in a range of computer vision applications. This paper treats statistics on manifolds and the loss of accuracy occurring when linearizing the manifold prior to performing statistical operations. Using recent advances in manifold computations, we present a comparison between the non-linear analog of Principal Component Analysis, Principal Geodesic Analysis, in its linearized form and its exact counterpart that uses true intrinsic distances. We give examples of datasets for which the linearized version provides good approximations and for which it does not. Indicators for the differences between the two versions are then developed and applied to two examples of manifold valued data: outlines of vertebrae from a study of vertebral fractures and spacial coordinates of human skeleton end-effectors acquired using a stereo camera and tracking software.

Unscented Kalman Filtering on Riemannian Manifolds

In recent years there has been a growing interest in problems, where either the observed data or hidden state variables are confined to a known Riemannian manifold. In sequential data analysis this interest has also been growing, but rather crude algorithms have been applied: either Monte Carlo filters or brute-force discretisations. These approaches scale poorly and clearly show a missing gap: no generic analogues to Kalman filters are currently available in non-Euclidean domains. In this paper, we remedy this issue by first generalising the unscented transform and then the unscented Kalman filter to Riemannian manifolds. As the Kalman filter can be viewed as an optimisation algorithm akin to the Gauss-Newton method, our algorithm also provides a general-purpose optimisation framework on manifolds. We illustrate the suggested method on synthetic data to study robustness and convergence, on a region tracking problem using covariance features, an articulated tracking problem, a mean value optimisation and a pose optimisation problem.

Toward a Theory of Statistical Tree-Shape Analysis

To develop statistical methods for shapes with a tree-structure, we construct a shape space framework for tree-shapes and study metrics on the shape space. This shape space has singularities which correspond to topological transitions in the represented trees. We study two closely related metrics on the shape space, TED and QED. QED is a quotient euclidean distance arising naturally from the shape space formulation, while TED is the classical tree edit distance. Using Gromovs metric geometry, we gain new insight into the geometries defined by TED and QED. We show that the new metric QED has nice geometric properties that are needed for statistical analysis: Geodesics always exist and are generically locally unique. Following this, we can also show the existence and generic local uniqueness of average trees for QED. TED, while having some algorithmic advantages, does not share these advantages. Along with the theoretical framework we provide experimental proof-of-concept results on synthetic data trees as well as small airway trees from pulmonary CT scans. This way, we illustrate that our framework has promising theoretical and qualitative properties necessary to build a theory of statistical tree-shape analysis.

A multi-scale kernel bundle for LDDMM: towards sparse deformation description across space and scales

The Large Deformation Diffeomorphic Metric Mapping framework constitutes a widely used and mathematically well-founded setup for registration in medical imaging. At its heart lies the notion of the regularization kernel, and the choice of kernel greatly affects the results of registrations. This paper presents an extension of the LDDMM framework allowing multiple kernels at multiple scales to be incorporated in each registration while preserving many of the mathematical properties of standard LDDMM. On a dataset of landmarks from lung CT images, we show by example the influence of the kernel size in standard LDDMM, and we demonstrate how our framework, LDDKBM, automatically incorporates the advantages of each scale to reach the same accuracy as the standard method optimally tuned with respect to scale. The framework, which is not limited to landmark data, thus removes the need for classical scale selection. Moreover, by decoupling the momentum across scales, it promises to provide better interpolation properties, to allow sparse descriptions of the total deformation, to remove the tradeoff between match quality and regularity, and to allow for momentum based statistics using scale information.

The Improbability of Harris Interest Points

An elementary characterization of the map underlying Harris corners, also known as Harris interest points or key points, is provided. Two principal and basic assumptions made are: (1) Local image structure is captured in an uncommitted way, simply using weighted raw image values around every image location to describe the local image information, and (2) the lower the probability of observing the image structure present in a particular point, the more salient, or interesting, this position is, i.e., saliency is related to how uncommon it is to see a certain image structure, how surprising it is. Through the latter assumption, the axiomatization proposed makes a sound link between image saliency in computer vision on the one hand and, on the other, computational models of preattentive human visual perception, where exactly the same definition of saliency has been proposed. Because of this link, the characterization provides a compelling case in favor of Harris interest points over other approaches.

Geometries on spaces of treelike shapes

In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for treelike shapes and study metrics on the shape space. The shape space has singularities, which correspond to topological transitions in the represented trees. We study two closely related metrics, TED and QED. The QED is a quotient euclidean distance arising from the new shape space formulation, while TED is essentially the classical tree edit distance. Using Gromovs metric geometry we gain new insight into the geometries defined by TED and QED. In particular, we show that the new metric QED has nice geometric properties which facilitate statistical analysis, such as existence and local uniqueness of geodesics and averages. TED, on the other hand, has algorithmic advantages, while it does not share the geometric strongpoints of QED. We provide a theoretical framework as well as computational results such as matching of airway trees from pulmonary CT scans and geodesics between synthetic data trees illustrating the dynamic and geometric properties of the QED metric.

Automatic Hair Detection in the Wild

This paper presents an algorithm for segmenting the hair region in uncontrolled, real life conditions images. Our method is based on a simple statistical hair shape model representing the upper hair part. We detect this region by minimizing an energy which uses active shape and active contour. The upper hair region then allows us to learn the hair appearance parameters (color and texture) for the image considered. Finally, those parameters drive a pixel-wise segmentation technique that yields the desired (complete) hair region. We demonstrate the applicability of our method on several real images.

Deinterlacing Using Variational Methods

We present a variational framework for deinterlacing that was originally used for inpainting and subsequently redeveloped for deinterlacing. From the framework, we derive a motion adaptive (MA) deinterlacer and a motion compensated (MC) deinterlacer and test them together with a selection of known deinterlacers. To illustrate the need for MC deinterlacing, the problem of details in motion (DIM) is introduced. It cannot be solved by MA deinterlacers or any simpler deinterlacers but only by MC deinterlacers. The major problem in MC deinterlacing is computing reliable optical flow [motion estimation (ME)] in interlaced video. We discuss a number of strategies for computing optical flows on interlaced video hoping to shed some light on this problem. We produce results on challenging real world video data with our variational MC deinterlacer that in most cases are indistinguishable from the ground truth.