Linear Shape Deformation Models with Local Support Using Graph-based Structured Matrix Factorisation

Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determined. However, the resulting factors (the most dominant eigenvectors of the covariance matrix) have global support, i.e. changing the coefficient of a single factor deforms the entire shape. In this paper, a method to obtain deformation factors with local support is presented. The benefits of such models include better flexibility and interpretability as well as the possibility of interactively deforming shapes locally. For that, based on a well-grounded theoretical motivation, we formulate a matrix factorisation problem employing sparsity and graph-based regularisation terms. We demonstrate that for brain shapes our method outperforms the state of the art in local support models with respect to generalisation ability and sparse shape reconstruction, whereas for human body shapes our method gives more realistic deformations.Comment: Please cite CVPR 2016 versio

Shrinking VOD Traffic via Rényi-Entropic Optimal Transport

In response to the exponential surge in Internet Video on Demand (VOD) traffic, numerous research endeavors have concentrated on optimizing and enhancing infrastructure efficiency. In contrast, this paper explores whether users’ demand patterns can be shaped to reduce the pressure on infrastructure. Our main idea is to design a mechanism that alters the distribution of user requests to another distribution which is much more cache-efficient, but still remains ‘close enough’ (in the sense of cost) to fulfil each individual user’s preference. To quantify the cache footprint of VOD traffic, we propose a novel application of Rényi entropy as its proxy, capturing the ‘richness’ (the number of distinct videos or cache size) and the ‘evenness’ (the relative popularity of video accesses) of the on-demand video distribution. We then demonstrate how to decrease this metric by formulating a problem drawing on the mathematical theory of optimal transport (OT). Additionally, we establish a key equivalence theorem: minimizing Rényi entropy corresponds to maximizing soft cache hit ratio (SCHR) — a variant of cache hit ratio allowing similarity-based video substitutions. Evaluation on a real-world, city-scale video viewing dataset reveals a remarkable 83% reduction in cache size (associated with VOD caching traffic). Crucially, in alignment with the above-mentioned equivalence theorem, our approach yields a significant uplift to SCHR, achieving close to 100%

MR Shuffling: Accelerated Single-Scan Multi-Contrast Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is an attractive medical imaging modality as it is non-invasive and does not involve ionizing radiation. Routine clinical MRI exams obtain MR images corresponding to different soft tissue contrast by performing multiple scans. When two-dimensional (2D) imaging is used, these scans are often repeated in other scanning planes. As a result, the number of scans comprising an MRI exam leads to prohibitively long exam times as compared to other medical imaging modalities such as computed tomography. Many approaches have been designed to accelerate the MRI acquisition while maintaining diagnostic quality.One approach is to collect multiple measurements while the MRI signal is evolving due to relaxation. This enables a reduction in scan time, as fewer acquisition windows are needed to collect the same number of measurements. However, when the temporal aspect of the acquisition is left unmodeled, artifacts are likely to appear in the reconstruction. Most often, these artifacts manifest as image blurring. The effect depends on the acquisition parameters as well as the tissue relaxation itself, resulting in spatially varying blurring. The severity of the artifacts is directly related to the level of acceleration, and thus presents a tradeoff with scan time. The effect is amplified when imaging in three dimensions, severely limiting scan efficiency. Volumetric variants would be used if not for the blurring, as they are able to reconstruct images at isotropic resolution and support mutli-planar reformatting.Another established acceleration technique, called parallel imaging, takes advantage of spatially sensitive receive coil arrays to collect multiple MRI measurements in parallel. Thus, the acquisition is shortened, and the reconstruction uses the spatial sensitivity information to recover the image. More recently, methods have been developed that leverage image structure such as sparsity and low rank to reduce the required number of samples for a well-posed reconstruction. Compressed sensing and its low rank extensions use these concepts to acquire incoherent measurements below the Nyquist rate. These techniques are especially suited to MRI, as incoherent measurements can be easily achieved through pseudo-random under-sampling. As the mechanisms behind parallel imaging and compressed sensing are fundamentally different, they can be combined to achieve even higher acceleration.This dissertation proposes accelerated MRI acquisition and reconstruction techniques that account for the temporal dynamics of the MR signal. The methods build off of parallel imaging and compressed sensing to reduce scan time and flexibly model the temporal relaxation behavior. By randomly shuffling the sampling in the acquisition stage and imposing low rank constraints in the reconstruction stage, intrinsic physical parameters are modeled and their dynamics are recovered as multiple images of varying tissue contrast. Additionally, blurring artifacts are significantly reduced, as the temporal dynamics are accounted for in the reconstruction.This dissertation first introduces T2 Shuffling, a volumetric technique that reduces blurring and reconstructs multiple T2-weighted image contrasts from a single acquisition. The method is integrated into a clinical hospital environment and evaluated on patients. Next, this dissertation develops a fast and distributed reconstruction for T2 Shuffling that achieves clinically relevant processing time latency. Clinical validation results are shown comparing T2 Shuffling as a single-sequence alternative to conventional pediatric knee MRI. Based off the compelling results, a fast targeted knee MRI using T2 Shuffling is implemented, enabling same-day access to MRI at one-third the cost compared to the conventional exam. To date, over 2,400 T2 Shuffling patient scans have been performed.Continuing the theme of accelerated multi-contrast imaging, this dissertation extends the temporal signal model with T1-T2 Shuffling. Building off of T2 Shuffling, the new method additionally samples multiple points along the saturation recovery curve by varying the repetition time durations during the scan. Since the signal dynamics are governed by both T1 recovery and T2 relaxation, the reconstruction captures information about both intrinsic tissue parameters. As a result, multiple target synthetic contrast images are reconstructed, all from a single scan. Approaches for selecting the sequence parameters are provided, and the method is evaluated on in vivo brain imaging of a volunteer.Altogether, these methods comprise the theme of MR Shuffling, and may open new pathways toward fast clinical MRI

Hardware acceleration of photon mapping

PhD ThesisThe quest for realism in computer-generated graphics has yielded a range of algorithmic techniques, the most advanced of which are capable of rendering images at close to photorealistic quality. Due to the realism available, it is now commonplace that computer graphics are used in the creation of movie sequences, architectural renderings, medical imagery and product visualisations. This work concentrates on the photon mapping algorithm [1, 2], a physically based global illumination rendering algorithm. Photon mapping excels in producing highly realistic, physically accurate images. A drawback to photon mapping however is its rendering times, which can be significantly longer than other, albeit less realistic, algorithms. Not surprisingly, this increase in execution time is associated with a high computational cost. This computation is usually performed using the general purpose central processing unit (CPU) of a personal computer (PC), with the algorithm implemented as a software routine. Other options available for processing these algorithms include desktop PC graphics processing units (GPUs) and custom designed acceleration hardware devices. GPUs tend to be efficient when dealing with less realistic rendering solutions such as rasterisation, however with their recent drive towards increased programmability they can also be used to process more realistic algorithms. A drawback to the use of GPUs is that these algorithms often have to be reworked to make optimal use of the limited resources available. There are very few custom hardware devices available for acceleration of the photon mapping algorithm. Ray-tracing is the predecessor to photon mapping, and although not capable of producing the same physical accuracy and therefore realism, there are similarities between the algorithms. There have been several hardware prototypes, and at least one commercial offering, created with the goal of accelerating ray-trace rendering [3]. However, properties making many of these proposals suitable for the acceleration of ray-tracing are not shared by photon mapping. There are even fewer proposals for acceleration of the additional functions found only in photon mapping. All of these approaches to algorithm acceleration offer limited scalability. GPUs are inherently difficult to scale, while many of the custom hardware devices available thus far make use of large processing elements and complex acceleration data structures. In this work we make use of three novel approaches in the design of highly scalable specialised hardware structures for the acceleration of the photon mapping algorithm. Increased scalability is gained through: • The use of a brute-force approach in place of the commonly used smart approach, thus eliminating much data pre-processing, complex data structures and large processing units often required. • The use of Logarithmic Number System (LNS) arithmetic computation, which facilitates a reduction in processing area requirement. • A novel redesign of the photon inclusion test, used within the photon search method of the photon mapping algorithm. This allows an intelligent memory structure to be used for the search. The design uses two hardware structures, both of which accelerate one core rendering function. Renderings produced using field programmable gate array (FPGA) based prototypes are presented, along with details of 90nm synthesised versions of the designs which show that close to an orderof- magnitude speedup over a software implementation is possible. Due to the scalable nature of the design, it is likely that any advantage can be maintained in the face of improving processor speeds. Significantly, due to the brute-force approach adopted, it is possible to eliminate an often-used software acceleration method. This means that the device can interface almost directly to a frontend modelling package, minimising much of the pre-processing required by most other proposals

Generalized Low Rank Models

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, $k$-means, $k$-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.Comment: 84 pages, 19 figure