GPU-based Iterative Cone Beam CT Reconstruction Using Tight Frame Regularization

X-ray imaging dose from serial cone-beam CT (CBCT) scans raises a clinical concern in most image guided radiation therapy procedures. It is the goal of this paper to develop a fast GPU-based algorithm to reconstruct high quality CBCT images from undersampled and noisy projection data so as to lower the imaging dose. For this purpose, we have developed an iterative tight frame (TF) based CBCT reconstruction algorithm. A condition that a real CBCT image has a sparse representation under a TF basis is imposed in the iteration process as regularization to the solution. To speed up the computation, a multi-grid method is employed. Our GPU implementation has achieved high computational efficiency and a CBCT image of resolution 512\times512\times70 can be reconstructed in ~5 min. We have tested our algorithm on a digital NCAT phantom and a physical Catphan phantom. It is found that our TF-based algorithm is able to reconstrct CBCT in the context of undersampling and low mAs levels. We have also quantitatively analyzed the reconstructed CBCT image quality in terms of modulation-transfer-function and contrast-to-noise ratio under various scanning conditions. The results confirm the high CBCT image quality obtained from our TF algorithm. Moreover, our algorithm has also been validated in a real clinical context using a head-and-neck patient case. Comparisons of the developed TF algorithm and the current state-of-the-art TV algorithm have also been made in various cases studied in terms of reconstructed image quality and computation efficiency.Comment: 24 pages, 8 figures, accepted by Phys. Med. Bio

CNN for Very Fast Ground Segmentation in Velodyne LiDAR Data

This paper presents a novel method for ground segmentation in Velodyne point clouds. We propose an encoding of sparse 3D data from the Velodyne sensor suitable for training a convolutional neural network (CNN). This general purpose approach is used for segmentation of the sparse point cloud into ground and non-ground points. The LiDAR data are represented as a multi-channel 2D signal where the horizontal axis corresponds to the rotation angle and the vertical axis the indexes channels (i.e. laser beams). Multiple topologies of relatively shallow CNNs (i.e. 3-5 convolutional layers) are trained and evaluated using a manually annotated dataset we prepared. The results show significant improvement of performance over the state-of-the-art method by Zhang et al. in terms of speed and also minor improvements in terms of accuracy.Comment: ICRA 2018 submissio

Opt: A Domain Specific Language for Non-linear Least Squares Optimization in Graphics and Imaging

Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but their implementation in real code is tedious, especially when optimized for real-time performance on modern GPUs in interactive applications. In this work, we propose a new language, Opt (available under http://optlang.org), for writing these objective functions over image- or graph-structured unknowns concisely and at a high level. Our compiler automatically transforms these specifications into state-of-the-art GPU solvers based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate different variations of the solver, so users can easily explore tradeoffs in numerical precision, matrix-free methods, and solver approaches. In our results, we implement a variety of real-world graphics and vision applications. Their energy functions are expressible in tens of lines of code, and produce highly-optimized GPU solver implementations. These solver have performance competitive with the best published hand-tuned, application-specific GPU solvers, and orders of magnitude beyond a general-purpose auto-generated solver

Computational Physics on Graphics Processing Units

The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 201

VASP on a GPU: application to exact-exchange calculations of the stability of elemental boron

General purpose graphical processing units (GPU's) offer high processing speeds for certain classes of highly parallelizable computations, such as matrix operations and Fourier transforms, that lie at the heart of first-principles electronic structure calculations. Inclusion of exact-exchange increases the cost of density functional theory by orders of magnitude, motivating the use of GPU's. Porting the widely used electronic density functional code VASP to run on a GPU results in a 5-20 fold performance boost of exact-exchange compared with a traditional CPU. We analyze performance bottlenecks and discuss classes of problems that will benefit from the GPU. As an illustration of the capabilities of this implementation, we calculate the lattice stability {\alpha}- and {\beta}-rhombohedral boron structures utilizing exact-exchange. Our results confirm the energetic preference for symmetry-breaking partial occupation of the {\beta}-rhombohedral structure at low temperatures, but does not resolve the stability of {\alpha} relative to {\beta}

Real-time Visual Flow Algorithms for Robotic Applications

Vision offers important sensor cues to modern robotic platforms. Applications such as control of aerial vehicles, visual servoing, simultaneous localization and mapping, navigation and more recently, learning, are examples where visual information is fundamental to accomplish tasks. However, the use of computer vision algorithms carries the computational cost of extracting useful information from the stream of raw pixel data. The most sophisticated algorithms use complex mathematical formulations leading typically to computationally expensive, and consequently, slow implementations. Even with modern computing resources, high-speed and high-resolution video feed can only be used for basic image processing operations. For a vision algorithm to be integrated on a robotic system, the output of the algorithm should be provided in real time, that is, at least at the same frequency as the control logic of the robot. With robotic vehicles becoming more dynamic and ubiquitous, this places higher requirements to the vision processing pipeline. This thesis addresses the problem of estimating dense visual flow information in real time. The contributions of this work are threefold. First, it introduces a new filtering algorithm for the estimation of dense optical flow at frame rates as fast as 800 Hz for 640x480 image resolution. The algorithm follows a update-prediction architecture to estimate dense optical flow fields incrementally over time. A fundamental component of the algorithm is the modeling of the spatio-temporal evolution of the optical flow field by means of partial differential equations. Numerical predictors can implement such PDEs to propagate current estimation of flow forward in time. Experimental validation of the algorithm is provided using high-speed ground truth image dataset as well as real-life video data at 300 Hz. The second contribution is a new type of visual flow named structure flow. Mathematically, structure flow is the three-dimensional scene flow scaled by the inverse depth at each pixel in the image. Intuitively, it is the complete velocity field associated with image motion, including both optical flow and scale-change or apparent divergence of the image. Analogously to optic flow, structure flow provides a robotic vehicle with perception of the motion of the environment as seen by the camera. However, structure flow encodes the full 3D image motion of the scene whereas optic flow only encodes the component on the image plane. An algorithm to estimate structure flow from image and depth measurements is proposed based on the same filtering idea used to estimate optical flow. The final contribution is the spherepix data structure for processing spherical images. This data structure is the numerical back-end used for the real-time implementation of the structure flow filter. It consists of a set of overlapping patches covering the surface of the sphere. Each individual patch approximately holds properties such as orthogonality and equidistance of points, thus allowing efficient implementations of low-level classical 2D convolution based image processing routines such as Gaussian filters and numerical derivatives. These algorithms are implemented on GPU hardware and can be integrated to future Robotic Embedded Vision systems to provide fast visual information to robotic vehicles

Sparse matrix-vector multiplication on GPGPUs

The multiplication of a sparse matrix by a dense vector (SpMV) is a centerpiece of scientific computing applications: it is the essential kernel for the solution of sparse linear systems and sparse eigenvalue problems by iterative methods. The efficient implementation of the sparse matrix-vector multiplication is therefore crucial and has been the subject of an immense amount of research, with interest renewed with every major new trend in high performance computing architectures. The introduction of General Purpose Graphics Processing Units (GPGPUs) is no exception, and many articles have been devoted to this problem. With this paper we provide a review of the techniques for implementing the SpMV kernel on GPGPUs that have appeared in the literature of the last few years. We discuss the issues and trade-offs that have been encountered by the various researchers, and a list of solutions, organized in categories according to common features. We also provide a performance comparison across different GPGPU models and on a set of test matrices coming from various application domains