A Variational Approach to the Evolution of Radial Basis Functions for Image Segmentation

In this paper we derive differential equations for evolving radial basis functions (RBFs) to solve segmentation problems. The differential equations result from applying variational calculus to energy functionals designed for image segmentation. Our methodology supports evolution of all parameters of each RBF, including its position, weight, orientation, and anisotropy, if present. Our framework is general and can be applied to numerous RBF interpolants. The resulting approach retains some of the ideal features of implicit active contours, like topological adaptivity, while requiring low storage overhead due to the sparsity of our representation, which is an unstructured list of RBFs. We present the theory behind our technique and demonstrate its usefulness for image segmentation

Fully automatic cervical vertebrae segmentation framework for X-ray images

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The cervical spine is a highly flexible anatomy and therefore vulnerable to injuries. Unfortunately, a large number of injuries in lateral cervical X-ray images remain undiagnosed due to human errors. Computer-aided injury detection has the potential to reduce the risk of misdiagnosis. Towards building an automatic injury detection system, in this paper, we propose a deep learning-based fully automatic framework for segmentation of cervical vertebrae in X-ray images. The framework first localizes the spinal region in the image using a deep fully convolutional neural network. Then vertebra centers are localized using a novel deep probabilistic spatial regression network. Finally, a novel shape-aware deep segmentation network is used to segment the vertebrae in the image. The framework can take an X-ray image and produce a vertebrae segmentation result without any manual intervention. Each block of the fully automatic framework has been trained on a set of 124 X-ray images and tested on another 172 images, all collected from real-life hospital emergency rooms. A Dice similarity coefficient of 0.84 and a shape error of 1.69 mm have been achieved

Integrated Segmentation and Interpolation of Sparse Data

International audienceWe address the two inherently related problems of segmentation and interpolation of 3D and 4D sparse data and propose a new method to integrate these stages in a level set framework. The interpolation process uses segmentation information rather than pixel intensities for increased robustness and accuracy. The method supports any spatial configurations of sets of 2D slices having arbitrary positions and orientations. We achieve this by introducing a new level set scheme based on the interpolation of the level set function by radial basis functions. The proposed method is validated quantitatively and/or subjectively on artificial data and MRI and CT scans, and is compared against the traditional sequential approach which interpolates the images first, using a state-of-the-art image interpolation method, and then segments the interpolated volume in 3D or 4D. In our experiments, the proposed framework yielded similar segmentation results to the sequential approach, but provided a more robust and accurate interpolation. In particular, the interpolation was more satisfactory in cases of large gaps, due to the method taking into account the global shape of the object, and it recovered better topologies at the extremities of the shapes where the objects disappear from the image slices. As a result, the complete integrated framework provided more satisfactory shape reconstructions than the sequential approach

Interactive Segmentation of 3D Medical Images with Implicit Surfaces

To cope with a variety of clinical applications, research in medical image processing has led to a large spectrum of segmentation techniques that extract anatomical structures from volumetric data acquired with 3D imaging modalities. Despite continuing advances in mathematical models for automatic segmentation, many medical practitioners still rely on 2D manual delineation, due to the lack of intuitive semi-automatic tools in 3D. In this thesis, we propose a methodology and associated numerical schemes enabling the development of 3D image segmentation tools that are reliable, fast and interactive. These properties are key factors for clinical acceptance. Our approach derives from the framework of variational methods: segmentation is obtained by solving an optimization problem that translates the expected properties of target objects in mathematical terms. Such variational methods involve three essential components that constitute our main research axes: an objective criterion, a shape representation and an optional set of constraints. As objective criterion, we propose a unified formulation that extends existing homogeneity measures in order to model the spatial variations of statistical properties that are frequently encountered in medical images, without compromising efficiency. Within this formulation, we explore several shape representations based on implicit surfaces with the objective to cover a broad range of typical anatomical structures. Firstly, to model tubular shapes in vascular imaging, we introduce convolution surfaces in the variational context of image segmentation. Secondly, compact shapes such as lesions are described with a new representation that generalizes Radial Basis Functions with non-Euclidean distances, which enables the design of basis functions that naturally align with salient image features. Finally, we estimate geometric non-rigid deformations of prior templates to recover structures that have a predictable shape such as whole organs. Interactivity is ensured by restricting admissible solutions with additional constraints. Translating user input into constraints on the sign of the implicit representation at prescribed points in the image leads us to consider inequality-constrained optimization

Dense deformation field estimation for atlas registration using the active contour framework

A key research area in computer vision is image segmentation. Image segmentation aims at extracting objects of interest in images or video sequences. These objects contain relevant information for a given application. For example, a video surveillance application generally requires to extract moving objects (vehicles, persons or animals) from a sequence of images in order to check that their path stays conformed to the regulation rules set for the observed scene. Image segmentation is not an easy task. In many applications, the contours of the objects of interest are difficult to delineate, even manually. The problems linked to segmentation are often due to low contrast, fuzzy contours or too similar intensities with adjacent objects. In some cases, the objects to be extracted have no real contours in the image. This kind of objects is called virtual objects. Virtual objects appear especially in medical applications. To draw them, medical experts usually estimate their position from surrounding objects. The problems related to image segmentation can be greatly simplified with information known in advance on the objects to be extracted (the prior knowledge). A widely used method consists to extract the needed prior knowledge from a reference image often called atlas. The goal of the atlas is to describe the image to be segmented like a map would describe the components of a geographical area. An atlas can contain three types of information on each object being part of the image: an estimation of its position in the image, a description of its shape and texture, and the features of its adjacent objects. The atlas-based segmentation method is rather used when the atlas can characterize a range of images. This method is thus especially adapted to medical images due to the existing consistency between anatomical structures of same type. There exist two types of atlas: the determinist atlas and the statistical atlas. The determinist atlas is an image which has been selected or computed, to be the most representative of an image category to be segmented. This image is called intensity atlas. The contours of the objects of interest (the objects to be extracted in images of the same type) have been traced manually on the intensity atlas, or by using a semi-automatic method. A label is often attributed to each one of these objects in order to differentiate them. In this way, we obtain a labeled version of the atlas called labeled atlas. The statistical atlas is an atlas created from a database of images in order to be the most representative of a certain type of images to be segmented. In this atlas, the position and the features of the objects of interest depend on statistical measures. In this thesis, we are focused on the use of determinist atlases for image segmentation. The segmentation process with a determinist atlas consists to deform the objects delineated in the atlas in order to better align them with their corresponding objects in the image to be segmented. To perform this task, we have distinguished two types of approaches in the literature. The first approach consists to reduce the segmentation problem in an image registration problem. First of all, a dense deformation field that registers (i.e. puts in point-to-point spatial correspondence) the atlas to the image to be segmented, is explicitly computed. Then, this transformation is used to project the assigned labels onto each atlas structure on the image to be segmented. The advantage of this approach is that the deformation field computed from the registration of visible contours allows to easily estimate the position of virtual objects or objects with fuzzy contours. However, the methods currently used for the atlas registration are often only based on the intensity atlas. That means that they do not exploit the object-based information that can be obtained by combining the intensity atlas with its labeled version. In the second approach, the atlas contours selected by the labeled atlas are directly deformed without using a geometrical deformation. For that, this approach is based on matching contour techniques, generally called deformable models. In this thesis, we are interested to a particular type of deformable models, which are the active contour segmentation models. The advantage of the active contour method is that this segmentation technique has been designed to exploit the image information directly linked to the object to be delineated. By using object-based information, active contour models are frequently able to extract regions where the atlas-based segmentation method by registration fails. On the other hand, the result of this local segmentation method is very sensitive to the initial atlas contour position regarding to the target contours. On the other hand, this local segmentation method is very sensitive to the initial position of the atlas contours: the closer they are to the contours to be detected, the more robust the active contour-based segmentation will be. Besides, this segmentation technique needs prior shape models to be able to estimate the position of virtual objects. The main objective of this thesis is to design an algorithm for atlas-based segmentation which combines the advantages of the dense deformation field computed by the registration algorithms, with local segmentation constraints coming from the active contour framework. This implies to design a model where the registration and segmentation by active contours are jointly performed. The atlas registration algorithm that we propose is based on a formulation allowing the integration of any segmentation or contour regularization forces derived from the theory of the active contours in a non parametric registration process. Our algorithm led us to introduce the concept of hierarchical atlas registration. Its principle is that the registration of the main image objects helps the registration of depending objects. This allows to bring progressively the atlas contours closer to their target and thus, to limit the risk to be stuck in a local minimum. Our model had been designed to be easily adaptable to various types of segmentation problems. At the end of the thesis, we present several examples of atlas registration applications in medical imaging. These applications highlight the integration of manual constraints in an atlas registration process, the modeling of a tumor growth in the atlas, the labelization of the thalamus for a statistical study on neuronal connections, the localization of the subthalamic nucleus (STN) for deep brain stimulation (DBS) and the compensation of intra-operative brain shift for neuronavigation systems