An O(mn) Gomory-Hu Tree Construction Algorithm for Unweighted Graphs

We present a fast algorithm for computing a Gomory-Hu tree or cut tree for an unweighted undirected graph G = (V,E). The expected running time of our algorithm is Õ(mc) where |E| = m and c is the maximum u-vedge connectivity, where u,v ∈ V. When the input graph is also simple (i.e., it has no parallel edges), then the u-v edge connectivity for each pair of vertices u and v is at most n-1; so the expected running time of our algorithm for simple unweighted graphs is Õ(mn).All the algorithms currently known for constructing a Gomory-Hu tree [8,9] use n-1 minimum s-t cut (i.e., max flow) subroutines. This in conjunction with the current fastest Õ(n20/9) max flow algorithm due to Karger and Levine [11] yields the current best running time of Õ(n20/9n) for Gomory-Hu tree construction on simpleunweighted graphs with m edges and n vertices. Thus we present the first Õ(mn) algorithm for constructing a Gomory-Hu tree for simple unweighted graphs.We do not use a max flow subroutine here; we present an efficient tree packing algorithm for computing Steiner edge connectivity and use this algorithm as our main subroutine. The advantage in using a tree packing algorithm for constructing a Gomory-Hu tree is that the work done in computing a minimum Steiner cut for a Steiner set S ⊆ V can be reused for computing a minimum Steiner cut for certain Steiner sets S' ⊆ S.

IMAGE DENOISING USING OPTIMALLY WEIGHTED BILATERAL FILTERS: A SURE AND FAST APPROACH

The bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive Gaussian noise. The denoising performance of the filter, however, is known to degrade quickly with the increase in noise level. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at a substantial computational overhead. In this paper, we report a simple pre-processing step that can substantially improve the denoising performance of the bilateral filter, at almost no additional cost. The modified filter is designed to be robust at large noise levels, and often tends to perform poorly below a certain noise threshold. To get the best of the original and the modified filter, we propose to combine them in a weighted fashion, where the weights are chosen to minimize (a surrogate of) the oracle mean-squared-error (MSE). The optimally-weighted filter is thus guaranteed to perform better than either of the component filters in terms of the MSE, at all noise levels. We also provide a fast algorithm for the weighted filtering. Visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of PSNR. Moreover, the denoising performance of the optimally-weighted bilateral filter is competitive with the computation-intensive non-local means filter.

Fast L0-based sparse signal recovery

This paper develops an algorithm for finding sparse signals from limited observations of a linear system. We assume an adaptive Gaussian model for sparse signals. This model results in a least square problem with an iteratively reweighted L2 penalty that approximates the L0-norm. We propose a fast algorithm to solve the problem within a continuation framework. In our examples, we show that the correct sparsity map and sparsity level are gradually learnt during the iterations even when the number of observations is reduced, or when observation noise is present. In addition, with the help of sophisticated interscale signal models, the algorithm is able to recover signals to a better accuracy and with reduced number of observations than typical L1-norm and reweighted L1 norm methods. ©2010 IEEE.

Fast Haar Transform Based Feature Extraction for Face Representation and Recognition

Subspace learning is the process of finding a proper feature subspace and then projecting high-dimensional data onto the learned low-dimensional subspace. The projection operation requires many floating-point multiplications and additions, which makes the projection process computationally expensive. To tackle this problem, this paper proposes two simple-but-effective fast subspace learning and image projection methods, fast Haar transform (FHT) based principal component analysis and FHT based spectral regression discriminant analysis. The advantages of these two methods result from employing both the FHT for subspace learning and the integral vector for feature extraction. Experimental results on three face databases demonstrated their effectiveness and efficiency.

Process monitoring approach using fast moving window PCA

This paper introduces a fast algorithm for moving window principal component analysis (MWPCA) which will adapt a principal component model. This incorporates the concept of recursive adaptation within a moving window to (i) adapt the mean and variance of the process variables, (ii) adapt the correlation matrix, and (iii) adjust the PCA model by recomputing the decomposition. This paper shows that the new algorithm is computationally faster than conventional moving window techniques, if the window size exceeds 3 times the number of variables, and is not affected by the window size. A further contribution is the introduction of an N-step-ahead horizon into the process monitoring. This implies that the PCA model, identified N-steps earlier, is used to analyze the current observation. For monitoring complex chemical systems, this work shows that the use of the horizon improves the ability to detect slowly developing drifts.

A fast method for fuzzy neural modeling and refinement

In the identification of complex dynamic systems using fuzzy neural networks, one of the main issues is the curse of dimensionality, which makes it difficult to retain a large number of system inputs or to consider a large number of fuzzy sets. Moreover, due to the correlations, not all possible network inputs or regression vectors in the network are necessary and adding them simply increases the model complexity and deteriorates the network generalisation performance. In this paper, the problem is solved by first proposing a fast algorithm for selection of network terms, and then introducing a refinement procedure to tackle the correlation issue. Simulation results show the efficacy of the method.

Low power field programmable gate array implementation of fast digital signal processing algorithms: characterisation and manipulation of data locality

Dynamic power consumption is very dependent on interconnect, so clever mapping of digital signal processing algorithms to parallelised realisations with data locality is vital. This is a particular problem for fast algorithm implementations where typically, designers will have sacrificed circuit structure for efficiency in software implementation. This study outlines an approach for reducing the dynamic power consumption of a class of fast algorithms by minimising the index space separation; this allows the generation of field programmable gate array (FPGA) implementations with reduced power consumption. It is shown how a 50% reduction in relative index space separation results in a measured power gain of 36 and 37% over a Cooley-Tukey Fast Fourier Transform (FFT)-based solution for both actual power measurements for a Xilinx Virtex-II FPGA implementation and circuit measurements for a Xilinx Virtex-5 implementation. The authors show the generality of the approach by applying it to a number of other fast algorithms namely the discrete cosine, the discrete Hartley and the Walsh-Hadamard transforms.

A sparse representation based fast detection method for surface defect detection of bottle caps

A practical machine-vision-based system is developed for fast detection of defects occurring on the surface of bottle caps. This system can be used to extract the circular region as the region of interests (ROI) from the surface of a bottle cap, and then use the circular region projection histogram (CRPH) as the matching features. We establish two dictionaries for the template and possible defect, respectively. Due to the requirements of high-speed production as well as detecting quality, a fast algorithm based on a sparse representation is proposed to speed up the searching. In the sparse representation, non-zero elements in the sparse factors indicate the defect's size and position. Experimental results in industrial trials show that the proposed method outperforms the orientation code method (OCM) and is able to produce promising results for detecting defects on the surface of bottle caps.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Does the Swedish Interactive Threshold Algorithm (SITA) accurately map visual field loss attributed to vigabatrin?

Background: Vigabatrin (VGB) is an anti-epileptic medication which has been linked to peripheral constriction of the visual field. Documenting the natural history associated with continued VGB exposure is important when making decisions about the risk and benefits associated with the treatment. Due to its speed the Swedish Interactive Threshold Algorithm (SITA) has become the algorithm of choice when carrying out Full Threshold automated static perimetry. SITA uses prior distributions of normal and glaucomatous visual field behaviour to estimate threshold sensitivity. As the abnormal model is based on glaucomatous behaviour this algorithm has not been validated for VGB recipients. We aim to assess the clinical utility of the SITA algorithm for accurately mapping VGB attributed field loss. Methods: The sample comprised one randomly selected eye of 16 patients diagnosed with epilepsy, exposed to VGB therapy. A clinical diagnosis of VGB attributed visual field loss was documented in 44% of the group. The mean age was 39.3 years∈±∈14.5 years and the mean deviation was -4.76 dB ±4.34 dB. Each patient was examined with the Full Threshold, SITA Standard and SITA Fast algorithm. Results: SITA Standard was on average approximately twice as fast (7.6 minutes) and SITA Fast approximately 3 times as fast (4.7 minutes) as examinations completed using the Full Threshold algorithm (15.8 minutes). In the clinical environment, the visual field outcome with both SITA algorithms was equivalent to visual field examination using the Full Threshold algorithm in terms of visual inspection of the grey scale plots, defect area and defect severity. Conclusions: Our research shows that both SITA algorithms are able to accurately map visual field loss attributed to VGB. As patients diagnosed with epilepsy are often vulnerable to fatigue, the time saving offered by SITA Fast means that this algorithm has a significant advantage for use with VGB recipients.

Information-theoretic analysis of brain white matter fiber orientation distribution functions

We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multisubject statistical analysis of HARDI data.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

Maximum compatible classes from compatibility matrices

A fast algorithm for the computation of maximum compatible classes (mcc) among the internal states of an incompletely specified sequential machine is presented in this paper. All the maximum compatible classes are determined by processing compatibility matrices of progressingly diminishing order, whose total number does not exceed (p + m), where p is the largest cardinality among these classes, and m is the number of such classes. Consequently the algorithm is specially suitable for the state minimization of very large sequential machines as encountered in vlsi circuits and systems.

Focussed Crawling with large scale Ordinal Regression Solvers

In this paper we propose a novel, scalable, clustering based Ordinal Regression formulation, which is an instance of a Second Order Cone Program (SOCP) with one Second Order Cone (SOC) constraint. The main contribution of the paper is a fast algorithm, CB-OR, which solves the proposed formulation more eficiently than general purpose solvers. Another main contribution of the paper is to pose the problem of focused crawling as a large scale Ordinal Regression problem and solve using the proposed CB-OR. Focused crawling is an efficient mechanism for discovering resources of interest on the web. Posing the problem of focused crawling as an Ordinal Regression problem avoids the need for a negative class and topic hierarchy, which are the main drawbacks of the existing focused crawling methods. Experiments on large synthetic and benchmark datasets show the scalability of CB-OR. Experiments also show that the proposed focused crawler outperforms the state-of-the-art.

Computing Reeb Graphs as a Union of Contour Trees

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.