Robust semi-automated path extraction for visualising stenosis of the coronary arteries

Computed tomography angiography (CTA) is useful for diagnosing and planning treatment of heart disease. However, contrast agent in surrounding structures (such as the aorta and left ventricle) makes 3-D visualisation of the coronary arteries difficult. This paper presents a composite method employing segmentation and volume rendering to overcome this issue. A key contribution is a novel Fast Marching minimal path cost function for vessel centreline extraction. The resultant centreline is used to compute a measure of vessel lumen, which indicates the degree of stenosis (narrowing of a vessel). Two volume visualisation techniques are presented which utilise the segmented arteries and lumen measure. The system is evaluated and demonstrated using synthetic and clinically obtained datasets

K2-ABC: Approximate Bayesian Computation with Kernel Embeddings

Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will "leak" information, which leads to ABC algorithms yielding samples from an incorrect (partial) posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) as a dissimilarity measure between the distributions over observed and simulated data. MMD is easily estimated as the squared difference between their empirical kernel embeddings. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm

Fast Contour Matching Using Approximate Earth Mover's Distance

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits

Computing Double Precision Euclidean Distances using GPU Tensor Cores

Tensor cores (TCs) are a type of Application-Specific Integrated Circuit (ASIC) and are a recent addition to Graphics Processing Unit (GPU) architectures. As such, TCs are purposefully designed to greatly improve the performance of Matrix Multiply-Accumulate (MMA) operations. While TCs are heavily studied for machine learning and closely related fields, where their high efficiency is undeniable, MMA operations are not unique to these fields. More generally, any computation that can be expressed as MMA operations can leverage TCs, and potentially benefit from their higher computational throughput compared to other general-purpose cores, such as CUDA cores on Nvidia GPUs. In this paper, we propose the first double precision (FP64) Euclidean distance calculation algorithm, which is expressed as MMA operations to leverage TCs on Nvidia GPUs, rather than the more commonly used CUDA cores. To show that the Euclidean distance can be accelerated in a real-world application, we evaluate our proposed TC algorithm on the distance similarity self-join problem, as the most computationally intensive part of the algorithm consists of computing distances in a multi-dimensional space. We find that the performance gain from using the tensor core algorithm over the CUDA core algorithm depends weakly on the dataset size and distribution, but is strongly dependent on data dimensionality. Overall, TCs are a compelling alternative to CUDA cores, particularly when the data dimensionality is low ($\leq{4}$), as we achieve an average speedup of $1.28\times$ and up to $2.23\times$ against a state-of-the-art GPU distance similarity self-join algorithm. Furthermore, because this paper is among the first to explore the use of TCs for FP64 general-purpose computation, future research is promising.Comment: Accepted for publicatio

Nonparametric Transient Classification using Adaptive Wavelets

Classifying transients based on multi band light curves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. Here we present a nonparametric classifier that uses the transient's light curve measurements to predict its class given training data. It implements two novel components: the first is the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients. The second novelty is the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The ranked classifier is simple and quick to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant, hence they do not need the light curves to be aligned to extract features. Further, BAGIDIS is nonparametric so it can be used for blind searches for new objects. We demonstrate the effectiveness of our ranked wavelet classifier against the well-tested Supernova Photometric Classification Challenge dataset in which the challenge is to correctly classify light curves as Type Ia or non-Ia supernovae. We train our ranked probability classifier on the spectroscopically-confirmed subsample (which is not representative) and show that it gives good results for all supernova with observed light curve timespans greater than 100 days (roughly 55% of the dataset). For such data, we obtain a Ia efficiency of 80.5% and a purity of 82.4% yielding a highly competitive score of 0.49 whilst implementing a truly "model-blind" approach to supernova classification. Consequently this approach may be particularly suitable for the classification of astronomical transients in the era of large synoptic sky surveys.Comment: 14 pages, 8 figures. Published in MNRA