33313231
Image Scale-Space from the Heat Kernel
In this paper, we show how the heat-kernel can be used to construct a scale-space for image smoothing and edge detection. We commence from an affinity weight matrix computed by exponentiating the difference in pixel grey-scale and distance. From the weight matrix, we compute the graph Laplacian. Information flow 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. Our scale-space is constructed by varying the time parameter of the heat-kernel. The larger the time the greater the the amount of information flow across the graph. The method has the effect of smoothing within regions, but does not blur region boundaries. Moreover, the boundaries do not move with time and this overcomes one of the problems with Gaussian scale-space. We illustrate the effectiveness of the method for image smoothing and edge detection.
195348993
A Riemannian Weighted Filter for Edge-sensitive Image Smoothing
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.
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.
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.
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.
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
2376990
Power-aware processor scheduling under average delay constraints
In this paper, voltage scaling strategies for scheduling aperiodic tasks under average delay constraints are studied. Dynamic voltage scaling in single processor systems is formulated as a constrained stochastic optimization problem for which the optimal solution can be obtained using a combination of Lagrange relaxation and the value iteration method. For multiprocessor systems, we present a two-phase approach. In the first phase, the speed settings and static workload distribution of the processors are optimized to minimize the total power dissipation. Dynamic voltage scaling techniques are then applied to each individual processor in the second phase. Both homogeneous and heterogeneous systems have been investigated. Based on queueing theory, the proposed algorithms guarantee conformity to the average delay constraint. Moreover, our simulation experiments have shown they are effective for minimizing power consumption.
13865930
Proxy-Assisted Scheduling for Energy-Efficient Multimedia Streaming over Wireless LAN
Energy is a critical resource for battery-driven mobile and wireless devices. The power-saving mode (PSM) provided by the 802.11 standard is not adequate for mobile clients running streaming media applications. We propose new power-aware scheduling strategies that enhance existing traffic shaping schemes for the purpose of minimizing the communication energy consumption of mobile clients. Scheduling decisions are made by the local proxy and executed at the access point. We consider two cases. In the first case, the proxy is unaware of the power characteristics of the clients. We present an optimal scheduling scheme that minimizes the time that mobile clients stay in high-power modes. This scheme achieves significant energy savings compared to using traffic shaping alone. In the second case, the power profiles and the residual battery capacities of the clients are taken into account in generating the schedule. Unlike most existing work, we believe these factors should be considered in the performance metric. We propose a dynamic programming approach that computes the optimal transmission schedule based on the new metric. We also present an efficient heuristic which exhibits near-optimal performance in the simulation experiments.
6097933
The Clar covering polynomial of hexagonal systems III
Abstract The Clar covering polynomial is a recently proposed concept of hexagonal systems by which some important topological indices such as perfect matching count, Clar number, first Herndon number, etc., can be easily obtained. In this paper we establish a relationship between the Clar covering polynomial and sextet polynomial. A lower bound of the Clar number and some properties of coefficients of the Clar covering polynomial are thus deduced. It is mentioned that the summation of coefficients of Clar covering polynomial can be used to calculate the number of perfect matchings of a certain kind of polyominoes relating to crystal physics.
6664703
The number of spanning trees of plane graphs with reflective symmetry
A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product the number of spanning trees of two smaller graphs. each of which has about half the number of vertices of G.