Verifying volume rendering using discretization error analysis

pre-printWe propose an approach for verification of volume rendering correctness based on an analysis of the volume rendering integral, the basis of most DVR algorithms. With respect to the most common discretization of this continuous model (Riemann summation), we make assumptions about the impact of parameter changes on the rendered results and derive convergence curves describing the expected behavior. Specifically, we progressively refine the number of samples along the ray, the grid size, and the pixel size, and evaluate how the errors observed during refinement compare against the expected approximation errors. We derive the theoretical foundations of our verification approach, explain how to realize it in practice, and discuss its limitations. We also report the errors identified by our approach when applied to two publicly available volume rendering packages

Dynamic Volume Rendering of Functional Medical Data on Dissimilar Hardware Platforms

In the last 30 years, medical imaging has become one of the most used diagnostic tools in the medical profession. Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) technologies have become widely adopted because of their ability to capture the human body in a non-invasive manner. A volumetric dataset is a series of orthogonal 2D slices captured at a regular interval, typically along the axis of the body from the head to the feet. Volume rendering is a computer graphics technique that allows volumetric data to be visualized and manipulated as a single 3D object. Iso-surface rendering, image splatting, shear warp, texture slicing, and raycasting are volume rendering methods, each with associated advantages and disadvantages. Raycasting is widely regarded as the highest quality renderer of these methods. Originally, CT and MRI hardware was limited to providing a single 3D scan of the human body. The technology has improved to allow a set of scans capable of capturing anatomical movements like a beating heart. The capturing of anatomical data over time is referred to as functional imaging. Functional MRI (fMRI) is used to capture changes in the human body over time. While fMRI’s can be used to capture any anatomical data over time, one of the more common uses of fMRI is to capture brain activity. The fMRI scanning process is typically broken up into a time consuming high resolution anatomical scan and a series of quick low resolution scans capturing activity. The low resolution activity data is mapped onto the high resolution anatomical data to show changes over time. Academic research has advanced volume rendering and specifically fMRI volume rendering. Unfortunately, academic research is typically a one-off solution to a singular medical case or set of data, causing any advances to be problem specific as opposed to a general capability. Additionally, academic volume renderers are often designed to work on a specific device and operating system under controlled conditions. This prevents volume rendering from being used across the ever expanding number of different computing devices, such as desktops, laptops, immersive virtual reality systems, and mobile computers like phones or tablets. This research will investigate the feasibility of creating a generic software capability to perform real-time 4D volume rendering, via raycasting, on desktop, mobile, and immersive virtual reality platforms. Implementing a GPU-based 4D volume raycasting method for mobile devices will harness the power of the increasing number of mobile computational devices being used by medical professionals. Developing support for immersive virtual reality can enhance medical professionals’ interpretation of 3D physiology with the additional depth information provided by stereoscopic 3D. The results of this research will help expand the use of 4D volume rendering beyond the traditional desktop computer in the medical field. Developing the same 4D volume rendering capabilities across dissimilar platforms has many challenges. Each platform relies on their own coding languages, libraries, and hardware support. There are tradeoffs between using languages and libraries native to each platform and using a generic cross-platform system, such as a game engine. Native libraries will generally be more efficient during application run-time, but they require different coding implementations for each platform. The decision was made to use platform native languages and libraries in this research, whenever practical, in an attempt to achieve the best possible frame rates. 4D volume raycasting provides unique challenges independent of the platform. Specifically, fMRI data loading, volume animation, and multiple volume rendering. Additionally, real-time raycasting has never been successfully performed on a mobile device. Previous research relied on less computationally expensive methods, such as orthogonal texture slicing, to achieve real-time frame rates. These challenges will be addressed as the contributions of this research. The first contribution was exploring the feasibility of generic functional data input across desktop, mobile, and immersive virtual reality. To visualize 4D fMRI data it was necessary to build in the capability to read Neuroimaging Informatics Technology Initiative (NIfTI) files. The NIfTI format was designed to overcome limitations of 3D file formats like DICOM and store functional imagery with a single high-resolution anatomical scan and a set of low-resolution anatomical scans. Allowing input of the NIfTI binary data required creating custom C++ routines, as no object oriented APIs freely available for use existed. The NIfTI input code was built using C++ and the C++ Standard Library to be both light weight and cross-platform. Multi-volume rendering is another challenge of fMRI data visualization and a contribution of this work. fMRI data is typically broken into a single high-resolution anatomical volume and a series of low-resolution volumes that capture anatomical changes. Visualizing two volumes at the same time is known as multi-volume visualization. Therefore, the ability to correctly align and scale the volumes relative to each other was necessary. It was also necessary to develop a compositing method to combine data from both volumes into a single cohesive representation. Three prototype applications were built for the different platforms to test the feasibility of 4D volume raycasting. One each for desktop, mobile, and virtual reality. Although the backend implementations were required to be different between the three platforms, the raycasting functionality and features were identical. Therefore, the same fMRI dataset resulted in the same 3D visualization independent of the platform itself. Each platform uses the same NIfTI data loader and provides support for dataset coloring and windowing (tissue density manipulation). The fMRI data can be viewed changing over time by either animation through the time steps, like a movie, or using an interface slider to “scrub” through the different time steps of the data. The prototype applications data load times and frame rates were tested to determine if they achieved the real-time interaction goal. Real-time interaction was defined by achieving 10 frames per second (fps) or better, based on the work of Miller [1]. The desktop version was evaluated on a 2013 MacBook Pro running OS X 10.12 with a 2.6 GHz Intel Core i7 processor, 16 GB of RAM, and a NVIDIA GeForce GT 750M graphics card. The immersive application was tested in the C6 CAVE™, a 96 graphics node computer cluster comprised of NVIDIA Quadro 6000 graphics cards running Red Hat Enterprise Linux. The mobile application was evaluated on a 2016 9.7” iPad Pro running iOS 9.3.4. The iPad had a 64-bit Apple A9X dual core processor with 2 GB of built in memory. Two different fMRI brain activity datasets with different voxel resolutions were used as test datasets. Datasets were tested using both the 3D structural data, the 4D functional data, and a combination of the two. Frame rates for the desktop implementation were consistently above 10 fps, indicating that real-time 4D volume raycasting is possible on desktop hardware. The mobile and virtual reality platforms were able to perform real-time 3D volume raycasting consistently. This is a marked improvement for 3D mobile volume raycasting that was previously only able to achieve under one frame per second [2]. Both VR and mobile platforms were able to raycast the 4D only data at real-time frame rates, but did not consistently meet 10 fps when rendering both the 3D structural and 4D functional data simultaneously. However, 7 frames per second was the lowest frame rate recorded, indicating that hardware advances will allow consistent real-time raycasting of 4D fMRI data in the near future

Doctor of Philosophy

dissertationIn this dissertation, we advance the theory and practice of verifying visualization algorithms. We present techniques to assess visualization correctness through testing of important mathematical properties. Where applicable, these techniques allow us to distinguish whether anomalies in visualization features can be attributed to the underlying physical process or to artifacts from the implementation under verification. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. The contributions of this dissertation are manifold. We derive the mathematical framework for the expected behavior of several visualization algorithms, and compare them to experimentally observed results in the selected codes. In the Computational Science & Engineering community CS&E, this technique is know as the Method of Manufactured Solution (MMS). We apply MMS to the verification of geometrical and topological properties of isosurface extraction algorithms, and direct volume rendering. We derive the convergence of geometrical properties of isosurface extraction techniques, such as function value and normals. For the verification of topological properties, we use stratified Morse theory and digital topology to design algorithms that verify topological invariants. In the case of volume rendering algorithms, we provide the expected discretization errors for three different error sources. The results of applying the MMS is another important contribution of this dissertation. We report unexpected behavior for almost all implementations tested. In some cases, we were able to find and fix bugs that prevented the correctness of the visualization algorithm. In particular, we address an almost 2 0 -year-old bug with the core disambiguation procedure of Marching Cubes 33, one of the first algorithms intended to preserve the topology of the trilinear interpolant. Finally, an important by-product of this work is a range of responses practitioners can expect to encounter with the visualization technique under verification