Intervertebral discs (IVDs), as small joints lying between adjacent vertebrae, have played an important role in pressure buffering and tissue protection. The fully-automatic localization and segmentation of IVDs have been discussed in the literature for many years since they are crucial to spine disease diagnosis and provide quantitative parameters in the treatment. Traditionally hand-crafted features are derived based on image intensities and shape priors to localize and segment IVDs. With the advance of deep learning, various neural network models have gained great success in image analysis including the recognition of intervertebral discs. Particularly, U-Net stands out among other approaches due to its outstanding performance on biomedical images with a relatively small set of training data. This paper proposes a novel convolutional framework based on 3D U-Net to segment IVDs from multi-modality MRI images. We first localize the centers of intervertebral discs in each spine sample and then train the network based on the cropped small volumes centered at the localized intervertebral discs. A detailed comprehensive analysis of the results using various combinations of multi-modalities is presented. Furthermore, experiments conducted on 2D and 3D U-Nets with augmented and non-augmented datasets are demonstrated and compared in terms of Dice coefficient and Hausdorff distance. Our method has proved to be effective with a mean segmentation Dice coefficient of 89.0% and a standard deviation of 1.4%.

Abstract Recent advances in scanning device technologies and improvements in techniques that generate and synthesize 3D shapes have made 3D models widespread in various fields including medical research, biology, engineering, etc. 3D shape descriptors play a fundamental role in many 3D shape analysis tasks such as point matching, establishing point‐to‐point correspondence, shape segmentation and labelling, and shape retrieval to name a few. Various methods have been proposed to calculate succinct and informative descriptors for 3D models. Emerging data‐driven techniques use machine learning algorithms to construct accurate and reliable shape descriptors. This survey provides a thorough review of the data‐driven 3D shape descriptors from the machine learning point of view and compares them in different criteria. Also, a comprehensive taxonomy of the existing descriptors is proposed based on the exploited machine learning algorithms. Advantages and disadvantages of each category have been discussed in detail. Besides, two alternative categorizations from the data type and the application perspectives are presented. Finally, some directions for possible future research are also suggested.

Porous structures had traditionally been generated using triply periodic minimal surfaces (TPMS), which however often encounter problems with the continuity and integrality of the generated curved surfaces when applying to irregular models. The present work describes a new porous-structure designing method using a combination of parameterized hexahedral mesh and traditional TPMS surfaces. The primary steps of the proposed method include: 1) re-meshing an input model into a hexahedral mesh; 2) solving parametric expressions of 12 geodesic lines using heat conduction models; 3) constructing quadrilateral surface meshes, and hexahedral volume meshes with harmonic-map; 4) generating standard TPMS surfaces within a regular hexahedron using the Marching Cube (MC) algorithm and then mapping the generated surface onto the parameterized hexahedral mesh using tri-linear interpolation. The experimental results have shown that the present method can solve the problem of discontinuity when the constraint hexahedron is deformed.

In this paper, a tetrahedral mesh-based approach is investigated for 3D image segmentation on a given image volume. We present a series of algorithms to generate high quality, feature-sensitive, and adaptive meshes to partition a 3D volume, where the 3D Canny edge detector is utilized to preserve important feature boundaries in the generated tetrahedral mesh. Each cluster of voxels within a tetrahedron is called a supervoxel, which is treated as a node in a graph and weighted edges are formed between adjacent tetrahedra (or supervoxels). A graph cut method is then applied on the weighted graph to partition the tetrahedral mesh, resulting in a segmentation of the original image volume. Thanks to the significantly reduced number of elements (supervoxels) as compared to that of voxels in a 3D image volume, the supervoxel-based segmentation method has tremendously improved the segmentation speed. In addition, the segmented image feature is naturally composed of high-quality, adaptive tetrahedral mesh that can be readily used for finite element analysis without further post-generation of tetrahedral mesh.

Abstract The emergence of laser/LiDAR sensors, reliable multi‐view stereo techniques and more recently consumer depth cameras have brought point clouds to the forefront as a data format useful for a number of applications. Unfortunately, the point data from those channels often incur imperfection, frequently contaminated with severe outliers and noise. This paper presents a robust consolidation algorithm for low‐quality point data from outdoor scenes, which essentially consists of two steps: 1) outliers filtering and 2) noise smoothing. We first design a connectivity‐based scheme to evaluate outlierness and thereby detect sparse outliers. Meanwhile, a clustering method is used to further remove small dense outliers. Both outlier removal methods are insensitive to the choice of the neighborhood size and the levels of outliers. Subsequently, we propose a novel approach to estimate normals for noisy points based on robust partial rankings, which is the basis of noise smoothing. Accordingly, a fast approach is exploited to smooth noise, while preserving sharp features. We evaluate the effectiveness of the proposed method on the point clouds from a variety of outdoor scenes.

In this paper we present a novel point set registration algorithm based on the robust Gaussian Mixture Model(GMM). We take advantage of a robust estimation to weigh the noise component in GMM. Moreover, a bidirectional EM process is introduced to model outliers in both point sets in contrast to traditional methods. The performance of the method is demonstrated and validated in carefully designed synthetic data and point sets extracted from medical images. Results show that the proposed method can improve the robustness and accuracy as compared to the traditional registration techniques.

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca(2+)). To investigate how the t-tubule microanatomy and the distribution of membrane Ca(2+) flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca(2+) signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca(2+) signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca(2+) flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca(2+) buffers, including the Ca(2+) indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca(2+) transients was found when the Ca(2+) flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca(2+) signals are predicted. Even at modest elevation of Ca(2+), reached during Ca(2+) influx, large and steep Ca(2+) gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca(2+) flux density along the cell membrane support initiation and propagation of Ca(2+) waves in rat myocytes.

We present computational solutions to two problems of macromolecular structure interpretation from reconstructed three-dimensional electron microscopy (3D-EM) maps of large bio-molecular complexes at intermediate resolution (5A-15 A). The two problems addressed are: 1) 3D structural alignment (matching) between identified and segmented 3D maps of structure units (e.g. trimeric configuration of proteins), and 2) the secondary structure identification of a segmented protein 3D map (i.e.locations of alpha-helices, beta-sheets). For problem 1, we present an efficient algorithm to correlate spatially (and structurally) two 3D maps of structure units. Besides providing a similarity score between structure units, the algorithm yields an effective technique for resolution refinement of repeated structure units, by 3D alignment and averaging. For problem 2, we present an efficient algorithm to compute eigenvalues and link eigenvectors of a Gaussian convoluted structure tensor derived from the protein 3D Map, thereby identifying and locating secondary structural motifs of proteins. The efficiency and performance of our approach is demonstrated on several experimentally reconstructed 3D maps of virus capsid shells from single-particle cryo-electron microscopy (cryo-EM), as well as computationally simulated protein structure density 3D maps generated from protein model entries in the Protein Data Bank.

We present an approach for three-dimensional (3D) image skeletonization, based on the local structure tensor idea. Two major types of features are addressed: helical and planar. Accordingly, we also discussed how the skeletonization approach is successfully applied to the protein secondary structure analysis, including the alpha-helix (helical type) and beta-sheet (planar type) identifications.

We present an automatic algorithm to segment all the local and global asymmetric units of a three-dimensional density map of icosahedral viruses. This approach is readily applicable to the structural analysis of a broad range of virus structures that are reconstructed using cryo-electron microscopy (cryo-EM) technique. Our algorithm includes three major steps operating on the three dimensional density map: the detection of critical points of the volumetric density function, the detection of global and local symmetry axes, and, finally, the boundary segmentation of all the asymmetric units. We demonstrate the efficacy of our algorithm and report our results on several experimental volumetric datasets, consisting of both reconstructed cryo-EM molecular density maps taken from the European Bioinformatics Institute archive, as well our own synthetically generated (blurred) maps calculated from X-ray resolution molecular structural data taken from the Protein Data Bank.

In this paper we describe a fast approach for image contrast enhancement, based on localized contrast manipulation. Our approach is not only last and easy to implement, but also has several other promising properties (adaptive, multiscale, weighted localization, etc.). We will also discuss in this paper an anisotropic version of our approach. Several examples of medical images, including brain MR images, chest CT images and mammography images, will be provided to demonstrate the performance of our approach.

Anisotropic diffusion has been widely used in image processing for its efficiency of smoothing the noisy images while preserving the sharp edges. In this paper we explore a general version of anisotropic diffusion schemes for vector-valued images, based on the polar-coordinate representation of the vectors. As an example, we apply our method to color images and show its ability of edge-preserving smoothing on vector-valued images.