Cube-Cut: Vertebral Body Segmentation in MRI-Data through Cubic-Shaped Divergences

In this article, we present a graph-based method using a cubic template for volumetric segmentation of vertebrae in magnetic resonance imaging (MRI) acquisitions. The user can define the degree of deviation from a regular cube via a smoothness value Delta. The Cube-Cut algorithm generates a directed graph with two terminal nodes (s-t-network), where the nodes of the graph correspond to a cubic-shaped subset of the image's voxels. The weightings of the graph's terminal edges, which connect every node with a virtual source s or a virtual sink t, represent the affinity of a voxel to the vertebra (source) and to the background (sink). Furthermore, a set of infinite weighted and non-terminal edges implements the smoothness term. After graph construction, a minimal s-t-cut is calculated within polynomial computation time, which splits the nodes into two disjoint units. Subsequently, the segmentation result is determined out of the source-set. A quantitative evaluation of a C++ implementation of the algorithm resulted in an average Dice Similarity Coefficient (DSC) of 81.33% and a running time of less than a minute.Comment: 23 figures, 2 tables, 43 references, PLoS ONE 9(4): e9338

Probabilistic and geometric shape based segmentation methods.

Image segmentation is one of the most important problems in image processing, object recognition, computer vision, medical imaging, etc. In general, the objective of the segmentation is to partition the image into the meaningful areas using the existing (low level) information in the image and prior (high level) information which can be obtained using a number of features of an object. As stated in [1,2], the human vision system aims to extract and use as much information as possible in the image including but not limited to the intensity, possible motion of the object (in sequential images), spatial relations (interaction) as the existing information, and the shape of the object which is learnt from the experience as the prior information. The main objective of this dissertation is to couple the prior information with the existing information since the machine vision system cannot predict the prior information unless it is given. To label the image into meaningful areas, the chosen information is modelled to fit progressively in each of the regions by an optimization process. The intensity and spatial interaction (as the existing information) and shape (as the prior information) are modeled to obtain the optimum segmentation in this study. The intensity information is modelled using the Gaussian distribution. Spatial interaction that describes the relation between neighboring pixels/voxels is modelled by assuming that the pixel intensity depends on the intensities of the neighboring pixels. The shape model is obtained using occurrences of histogram of training shape pixels or voxels. The main objective is to capture the shape variation of the object of interest. Each pixel in the image will have three probabilities to be an object and a background class based on the intensity, spatial interaction, and shape models. These probabilistic values will guide the energy (cost) functionals in the optimization process. This dissertation proposes segmentation frameworks which has the following properties: i) original to solve some of the existing problems, ii) robust under various segmentation challenges, and iii) fast enough to be used in the real applications. In this dissertation, the models are integrated into different methods to obtain the optimum segmentation: 1) variational (can be considered as the spatially continuous), and 2) statistical (can be considered as the spatially discrete) methods. The proposed segmentation frameworks start with obtaining the initial segmentation using the intensity / spatial interaction models. The shape model, which is obtained using the training shapes, is registered to the image domain. Finally, the optimal segmentation is obtained using the optimization of the energy functionals. Experiments show that the use of the shape prior improves considerably the accuracy of the alternative methods which use only existing or both information in the image. The proposed methods are tested on the synthetic and clinical images/shapes and they are shown to be robust under various noise levels, occlusions, and missing object information. Vertebral bodies (VBs) in clinical computed tomography (CT) are segmented using the proposed methods to help the bone mineral density measurements and fracture analysis in bones. Experimental results show that the proposed solutions eliminate some of the existing problems in the VB segmentation. One of the most important contributions of this study is to offer a segmentation framework which can be suitable to the clinical works

CAD-Based Porous Scaffold Design of Intervertebral Discs in Tissue Engineering

With the development and maturity of three-dimensional (3D) printing technology over the past decade, 3D printing has been widely investigated and applied in the field of tissue engineering to repair damaged tissues or organs, such as muscles, skin, and bones, Although a number of automated fabrication methods have been developed to create superior bio-scaffolds with specific surface properties and porosity, the major challenges still focus on how to fabricate 3D natural biodegradable scaffolds that have tailor properties such as intricate architecture, porosity, and interconnectivity in order to provide the needed structural integrity, strength, transport, and ideal microenvironment for cell- and tissue-growth. In this dissertation, a robust pipeline of fabricating bio-functional porous scaffolds of intervertebral discs based on different innovative porous design methodologies is illustrated. Firstly, a triply periodic minimal surface (TPMS) based parameterization method, which has overcome the integrity problem of traditional TPMS method, is presented in Chapter 3. Then, an implicit surface modeling (ISM) approach using tetrahedral implicit surface (TIS) is demonstrated and compared with the TPMS method in Chapter 4. In Chapter 5, we present an advanced porous design method with higher flexibility using anisotropic radial basis function (ARBF) and volumetric meshes. Based on all these advanced porous design methods, the 3D model of a bio-functional porous intervertebral disc scaffold can be easily designed and its physical model can also be manufactured through 3D printing. However, due to the unique shape of each intervertebral disc and the intricate topological relationship between the intervertebral discs and the spine, the accurate localization and segmentation of dysfunctional discs are regarded as another obstacle to fabricating porous 3D disc models. To that end, we discuss in Chapter 6 a segmentation technique of intervertebral discs from CT-scanned medical images by using deep convolutional neural networks. Additionally, some examples of applying different porous designs on the segmented intervertebral disc models are demonstrated in Chapter 6

Automatic Localization and Identification of Vertebrae in Arbitrary Field-of-View CT Scans

Abstract. This paper presents a new method for automatic localiza-tion and identification of vertebrae in arbitrary field-of-view CT scans. No assumptions are made about which section of the spine is visible or to which extent. Thus, our approach is more general than previous work while being computationally efficient. Our algorithm is based on re-gression forests and probabilistic graphical models. The discriminative, regression part aims at roughly detecting the visible part of the spine. Ac-curate localization and identification of individual vertebrae is achieved through a generative model capturing spinal shape and appearance. The system is evaluated quantitatively on 200 CT scans, the largest dataset reported for this purpose. We obtain an overall median localization error of less than 6mm, with an identification rate of 81%.

Mixture Models for Image Analysis

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