6,571 research outputs found
Radial Basis Functions: Biomedical Applications and Parallelization
Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc.
The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method.
Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work
Broadcasting Convolutional Network for Visual Relational Reasoning
In this paper, we propose the Broadcasting Convolutional Network (BCN) that
extracts key object features from the global field of an entire input image and
recognizes their relationship with local features. BCN is a simple network
module that collects effective spatial features, embeds location information
and broadcasts them to the entire feature maps. We further introduce the
Multi-Relational Network (multiRN) that improves the existing Relation Network
(RN) by utilizing the BCN module. In pixel-based relation reasoning problems,
with the help of BCN, multiRN extends the concept of `pairwise relations' in
conventional RNs to `multiwise relations' by relating each object with multiple
objects at once. This yields in O(n) complexity for n objects, which is a vast
computational gain from RNs that take O(n^2). Through experiments, multiRN has
achieved a state-of-the-art performance on CLEVR dataset, which proves the
usability of BCN on relation reasoning problems.Comment: Accepted paper at ECCV 2018. 24 page
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