High performance kernel smoothing library for biomedical imaging

Abstract

The estimation of probability density and probability density derivatives has full potential for applications. In biomedical imaging, the estimation of the first and second derivatives of the density is crucial to extract tubular structures, such as blood vessels and neuron traces. Probability density and probability density derivatives are often estimated using nonparametric data-driven methods. One of the most popular nonparametric methods is the Kernel Density Estimation (KDE) and Kernel Density Derivative Estimation (KDDE). However, a very serious drawback of using KDE and KDDE is the intensive computational requirements, especially for large data sets. In this thesis, we develop a high performance kernel smoothing library to accelerate KDE and KDDE methods. A series of hardware optimizations are used to deliver a high performance code. On the host side, multi-core platforms and parallel programming frameworks are used to accelerate the execution of the library. For 2 or 3-dimensional data points, the Graphic Processing Unit (GPU) platform is used to provide high levels of performance to the kernel density estimators, kernel gradient estimators as well as the kernel curvature estimators. Several Compute Unified Device Architecture (CUDA) based techniques are used to optimize their performances. What's more, a graph-based algorithm is designed to calculate the derivatives efficiently and a fast k-nearest neighbor bandwidth selector is designed to speed up the variable bandwidth selection for image data on GPU.