Fast Color Space Transformations Using Minimax Approximations

Color space transformations are frequently used in image processing, graphics, and visualization applications. In many cases, these transformations are complex nonlinear functions, which prohibits their use in time-critical applications. In this paper, we present a new approach called Minimax Approximations for Color-space Transformations (MACT).We demonstrate MACT on three commonly used color space transformations. Extensive experiments on a large and diverse image set and comparisons with well-known multidimensional lookup table interpolation methods show that MACT achieves an excellent balance among four criteria: ease of implementation, memory usage, accuracy, and computational speed

EIT-MESHER – Segmented FEM Mesh Generation and Refinement

EIT-MESHER (https://github.com/EIT-team/Mesher) is C++ software, based on the CGAL library, which generates high quality Finite Element Model tetrahedral meshes from binary masks of 3D volume segmentations. Originally developed for biomedical applications in Electrical Impedance Tomography (EIT) to address the need for custom, non-linear refinement in certain areas (e.g. around electrodes), EIT-MESHER can also be used in other fields where custom FEM refinement is required, such as Diffuse Optical Tomography (DOT)

Homeomorphic Tetrahedral Tessellation for Biomedical Images

We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes for biomedical images. The method uses an octree as the background grid from which to build the final graded conforming meshes. The algorithm is fast and robust. It produces meshes with high quality since it provides dihedral angle lower bound for the output tetrahedra. Moreover, the mesh boundary is a geometrically and topologically accurate approximation of the object surface in the sense that it allows for guaranteed bounds on the two-sided Hausdorff distance and the homeomorphism between the boundaries of the mesh and the boundaries of the materials. The theory and effectiveness of our method are illustrated with the experimental evaluation on synthetic and real medical data

Advancing Intra-operative Precision: Dynamic Data-Driven Non-Rigid Registration for Enhanced Brain Tumor Resection in Image-Guided Neurosurgery

During neurosurgery, medical images of the brain are used to locate tumors and critical structures, but brain tissue shifts make pre-operative images unreliable for accurate removal of tumors. Intra-operative imaging can track these deformations but is not a substitute for pre-operative data. To address this, we use Dynamic Data-Driven Non-Rigid Registration (NRR), a complex and time-consuming image processing operation that adjusts the pre-operative image data to account for intra-operative brain shift. Our review explores a specific NRR method for registering brain MRI during image-guided neurosurgery and examines various strategies for improving the accuracy and speed of the NRR method. We demonstrate that our implementation enables NRR results to be delivered within clinical time constraints while leveraging Distributed Computing and Machine Learning to enhance registration accuracy by identifying optimal parameters for the NRR method. Additionally, we highlight challenges associated with its use in the operating room

Tetrahedral Image-to-Mesh Conversion Software for Anatomic Modeling of Arteriovenous Malformations

We describe a new implementation of an adaptive multi-tissue tetrahedral mesh generator targeting anatomic modeling of Arteriovenous Malformation (AVM) for surgical simulations. Our method, initially constructs an adaptive Body-Centered Cubic (BCC) mesh of high quality elements. Then, it deforms the mesh surfaces to their corresponding physical image boundaries, hence, improving the mesh fidelity and smoothness. Our deformation scheme, which builds upon the ITK toolkit, is based on the concept of energy minimization, and relies on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of the extracted feature points needed for the registration, and thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. While many medical imaging applications require robust mesh generation, there are few codes available to the public. We compare our implementation with two similar open-source image-to-mesh conversion codes: (1) Cleaver from US, and (2) CGAL from EU. Our evaluation is based on five isotropic/anisotropic segmented images, and relies on metrics like geometric & topologic fidelity, mesh quality, gradation and smoothness. The implementation we describe is open- source and it will be available within: (i) the 3D Slicer package for visualization and image analysis from Harvard Medical School, and (ii) an interactive simulator for neurosurgical procedures involving vasculature using SOFA, a framework for real-time medical simulation developed by INRIA

Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body

An insight into the science of unstructured meshes in computer numerical simulation

Computer numerical simulation is a beneficial tool for studying various domains of knowledge. Among the steps in the whole process of numerical simulation is the generation of unstructured meshes. Since the unstructured meshes are usually generated using automatic software, the fundamental knowledge of the unstructured meshes is often neglected. This paper highlighted some useful insights into the unstructured meshes in numerical simulation for several application domains, such as the radiative heat transfer problem, ocean modelling and biomedical engineering. It also reviewed some fundamental concepts and frameworks for element generation in producing unstructured meshes, particularly the Delaunay triangulation and advancing front techniques

Finite Element Modeling Driven by Health Care and Aerospace Applications

This thesis concerns the development, analysis, and computer implementation of mesh generation algorithms encountered in finite element modeling in health care and aerospace. The finite element method can reduce a continuous system to a discrete idealization that can be solved in the same manner as a discrete system, provided the continuum is discretized into a finite number of simple geometric shapes (e.g., triangles in two dimensions or tetrahedrons in three dimensions). In health care, namely anatomic modeling, a discretization of the biological object is essential to compute tissue deformation for physics-based simulations. This thesis proposes an efficient procedure to convert 3-dimensional imaging data into adaptive lattice-based discretizations of well-shaped tetrahedra or mixed elements (i.e., tetrahedra, pentahedra and hexahedra). This method operates directly on segmented images, thus skipping a surface reconstruction that is required by traditional Computer-Aided Design (CAD)-based meshing techniques and is convoluted, especially in complex anatomic geometries. Our approach utilizes proper mesh gradation and tissue-specific multi-resolution, without sacrificing the fidelity and while maintaining a smooth surface to reflect a certain degree of visual reality. Image-to-mesh conversion can facilitate accurate computational modeling for biomechanical registration of Magnetic Resonance Imaging (MRI) in image-guided neurosurgery. Neuronavigation with deformable registration of preoperative MRI to intraoperative MRI allows the surgeon to view the location of surgical tools relative to the preoperative anatomical (MRI) or functional data (DT-MRI, fMRI), thereby avoiding damage to eloquent areas during tumor resection. This thesis presents a deformable registration framework that utilizes multi-tissue mesh adaptation to map preoperative MRI to intraoperative MRI of patients who have undergone a brain tumor resection. Our enhancements with mesh adaptation improve the accuracy of the registration by more than 5 times compared to rigid and traditional physics-based non-rigid registration, and by more than 4 times compared to publicly available B-Spline interpolation methods. The adaptive framework is parallelized for shared memory multiprocessor architectures. Performance analysis shows that this method could be applied, on average, in less than two minutes, achieving desirable speed for use in a clinical setting. The last part of this thesis focuses on finite element modeling of CAD data. This is an integral part of the design and optimization of components and assemblies in industry. We propose a new parallel mesh generator for efficient tetrahedralization of piecewise linear complex domains in aerospace. CAD-based meshing algorithms typically improve the shape of the elements in a post-processing step due to high complexity and cost of the operations involved. On the contrary, our method optimizes the shape of the elements throughout the generation process to obtain a maximum quality and utilizes high performance computing to reduce the overheads and improve end-user productivity. The proposed mesh generation technique is a combination of Advancing Front type point placement, direct point insertion, and parallel multi-threaded connectivity optimization schemes. The mesh optimization is based on a speculative (optimistic) approach that has been proven to perform well on hardware-shared memory. The experimental evaluation indicates that the high quality and performance attributes of this method see substantial improvement over existing state-of-the-art unstructured grid technology currently incorporated in several commercial systems. The proposed mesh generator will be part of an Extreme-Scale Anisotropic Mesh Generation Environment to meet industries expectations and NASA\u27s CFD visio

Enabling technology for non-rigid registration during image-guided neurosurgery

In the context of image processing, non-rigid registration is an operation that attempts to align two or more images using spatially varying transformations. Non-rigid registration finds application in medical image processing to account for the deformations in the soft tissues of the imaged organs. During image-guided neurosurgery, non-rigid registration has the potential to assist in locating critical brain structures and improve identification of the tumor boundary. Robust non-rigid registration methods combine estimation of tissue displacement based on image intensities with the spatial regularization using biomechanical models of brain deformation. In practice, the use of such registration methods during neurosurgery is complicated by a number of issues: construction of the biomechanical model used in the registration from the image data, high computational demands of the application, and difficulties in assessing the registration results. In this dissertation we develop methods and tools that address some of these challenges, and provide components essential for the intra-operative application of a previously validated physics-based non-rigid registration method.;First, we study the problem of image-to-mesh conversion, which is required for constructing biomechanical model of the brain used during registration. We develop and analyze a number of methods suitable for solving this problem, and evaluate them using application-specific quantitative metrics. Second, we develop a high-performance implementation of the non-rigid registration algorithm and study the use of geographically distributed Grid resources for speculative registration computations. Using the high-performance implementation running on the remote computing resources we are able to deliver the results of registration within the time constraints of the neurosurgery. Finally, we present a method that estimates local alignment error between the two images of the same subject. We assess the utility of this method using multiple sources of ground truth to evaluate its potential to support speculative computations of non-rigid registration

Multi-Material Mesh Representation of Anatomical Structures for Deep Brain Stimulation Planning

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. The proposed method decomposes an ambiguous grid cube into a set of tetrahedral cells and uses novel polygon generation rules that produce 2-manifold and watertight surface meshes with good-quality triangles. These meshes, being watertight and 2-manifold, are geometrically correct, and therefore can be used to initialize tetrahedral meshes. The 2-manifold DC method has been extended into the multi-material domain. Due to its multi-material nature, multi-material surface meshes will contain non-manifold elements along material interfaces or shared boundaries. The proposed multi-material DC algorithm can (1) generate multi-material surface meshes where each material sub-mesh is a 2-manifold and watertight mesh, (2) preserve the non-manifold elements along the material interfaces, and (3) ensure that the material interface or shared boundary between materials is consistent. The proposed method is used to generate multi-material surface meshes of deep brain anatomical structures from a digital atlas of the basal ganglia and thalamus. Although deep brain anatomical structures can be labeled as functionally separate, they are in fact continuous tracts of soft tissue in close proximity to each other. The multi-material meshes generated by the proposed DC algorithm can accurately represent the closely-packed deep brain structures as a single mesh consisting of multiple material sub-meshes. Each sub-mesh represents a distinct functional structure of the brain. Printed and/or digital atlases are important tools for medical research and surgical intervention. While these atlases can provide guidance in identifying anatomical structures, they do not take into account the wide variations in the shape and size of anatomical structures that occur from patient to patient. Accurate, patient-specific representations are especially important for surgical interventions like deep brain stimulation, where even small inaccuracies can result in dangerous complications. The last part of this research effort extends the discrete deformable 2-simplex mesh into the multi-material domain where geometry-based internal forces and image-based external forces are used in the deformation process. This multi-material deformable framework is used to segment anatomical structures of the deep brain region from Magnetic Resonance (MR) data