15237049
Riemannian Graph Diffusion for DT-MRI Regularization
A new method for diffusion tensor MRI (DT-MRI) regularization is presented that relies on graph diffusion. We represent a DT image using a weighted graph, where the weights of edges are functions of the geodesic distances between tensors. Diffusion across this graph with time is captured by the heat-equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen-system with time. Tensor regularization is accomplished by computing the Riemannian weighted mean using the heat kernel as its weights. The method can efficiently remove noise, while preserving the fine details of images. Experiments on synthetic and real-world datasets illustrate the effectiveness of the method.
45771940
Smoothing Tensor-Valued Images Using Anisotropic Geodesic Diffusion
This paper considers the feature space of DT-MRI as a differential manifold with an affine-invariant metric. We generalise Di Zenzo’s structure tensor to tensor-valued images for edge detection. To improve the quality of the edges, we develop a generalised Perona-Malik method for smoothing tensor images. We demonstrate our algorithm on both synthetic and real DT-MRI data.
21190705
Evolving Spanning Trees Using the Heat Equation
This paper explores how to use the heat kernel to evolve the minimum spanning tree of a graph with time. We use the heat kernel to weight the edges of the graph, and these weights can be computed by exponentiating the Laplacian eigensystem of the graph with time. The resulting spanning trees exhibit an interesting behaviour as time increases. Initially, they are bushy and rooted near the centre of graph, but as time evolves they become string-like and hug the boundary of the graph. We characterise this behaviour using the distribution of terminal nodes with time, and use this distribution for the purposes of graph clustering and image segmentation.
14205748
Edge Detection and Anisotropic Diffusion for Tensor-Valued Images
This paper considers feature space of DT-MRI as a differential manifold with an affine-invariant metric, where we generalise Di Zenzo's structure tensor to tensor-valued images for edge detection. To improve the quality of the edges, we smooth out the noise by generalised Perona-Malik method for tensor images. We demonstrate our algorithm on both synthetic and real DT-MRI data.
15564869
Heat Kernel Smoothing of Scalar and Vector Image Data
This paper shows how the graph-spectral heat kernel can be used to smooth both gray-scale and color images. We represent images using weighted attributed graphs, and compute the associated Laplacian matrix. Diffusion across this weighted graph-structure with time is captured by the heat-equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen-system with time. Image smoothing is effected by convolving the heat kernel with the image. The method has the effect of smoothing within regions, but does not blur region boundaries. Experiments and comparisons on standard images illustrate the effectiveness of the method.
195348993
A Riemannian Weighted Filter for Edge-sensitive Image Smoothing
44874837
Z-transformation graphs of perfect matchings of plane bipartite graphs
Abstract Let G be a plane bipartite graph with at least two perfect matchings. The Z -transformation graph, Z F ( G ), of G with respect to a specific set F of faces is defined as a graph on the perfect matchings of G such that two perfect matchings M 1 and M 2 are adjacent provided M 1 and M 2 differ only in a cycle that is the boundary of a face in F . If F is the set of all interior faces, Z F ( G ) is the usual Z -transformation graph; If F contains all faces of G it is a novel graph and called the total Z -transformation graph. In this paper, we give some simple characterizations for the Z -transformation graphs to be connected by applying the above new idea. Furthermore, we show that the total Z -transformation graph of G is 2-connected if G is elementary; the total Z -transformation digraph of G is strongly connected if and only if G is elementary.
52810037
A Riemannian Weighted Filter for Edge-sensitive Image Smoothing
This paper describes a new method for image smoothing. We view the image features as residing on a differential manifold, and we work with a representation based on the exponential map for this manifold (i.e. the map from the manifold to a plane that preserves geodesic distances). On the exponential map we characterise the features using a Riemannian weighted mean. We show how both gradient descent and Newton's method can be used to find the mean. Based on this weighted mean, we develop an edge-preserving filter that combines Gaussian and median filters of gray-scale images. We demonstrate our algorithm both on direction fields from shape-from-shading and tensor-valued images
30156477
Examination of load-balancing methods to improve efficiency of a composite materials manufacturing process simulation under uncertainty using distributed computing
Process simulations play an important role in guiding process understanding and development, without requiring costly manufacturing trials. For process design under uncertainty, a large number of simulations is needed for an accurate convergence of the moments of the output distributions, which renders such stochastic analysis computationally intensive. This paper discusses the application of a basic distributed computing approach to reduce the computation time of a composite materials manufacturing process simulation under uncertainty. Specifically, several load-balancing methods are explored and analyzed to determine the best strategies given heterogeneous tasks and heterogeneous networks, especially when the individual task times cannot be predicted.
44967148
PVM Code Generator for the Fortran Parallel Transformer
5788058
Heredity of the index of convergence of the line digraph
Let D be a digraph, and let Ln(D) and k(D) denote the nth iterated line digraph of D and the index of convergence of D, respectively. We prove that if D contains neither sources nor sinks, then: (1) k(Ln(D))=k(D)=0 if every connected component of D is a directed cycle. (2) k(Ln(D))=k(D)+n if there exists at least one connected component of D that is not a directed cycle. Finally, we prove that if D has no sources or no sinks then k(D) ≤ k(L(D)) ≤ k(D)+1.