39543965
Maximum Red/Blue Interval Matching with Applications
In this paper, we consider the problem of computing a maximum cardinality matching among a set I of n intervals that are colored as either red or blue, such that a pair of intervals in I can be matched only if they overlap with each other and have different colors. This problem arises in some applications such as radiosurgery treatment planning. We present a greedy algorithm for this problem that runs in O(n log log n) time for sorted input.We also solve a useful generalization of this red/blue interval matching problem in the same time bound.
123098354
Globally optimal segmentation of interacting surfaces with geometric constraints
Efficient detection of globally optimal surfaces representing object boundaries in volumetric datasets is important and remains challenging in many medical image analysis applications. We have developed an optimal surface detection method that is capable of simultaneously detecting multiple interacting surfaces, in which the optimality is controlled by the cost functions designed for individual surfaces and several geometric constraints defining the surface smoothness and interrelations. The method solves the surface detection problems by transforming them into computing minimum s-t cuts in the derived edge-weighted directed graphs. The proposed algorithm has low-order polynomial complexity and is computationally efficient. The method has been validated on over 100 computer generated volumetric images and 96 CT-scanned datasets of different-sized plexiglas tubes, yielding highly accurate results (mean signed error of the measured inner- and outer-diameters of the plexiglas tubes was 0.21 /spl plusmn/ 3.20%). Our approach can be readily extended to higher dimensional image segmentation.
17909513
Determining an optimal penetration among weighted regions in two and three dimensions
We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n2(d−1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms.
27904596
Segmenting Doughnut-Shaped Objects in Medical Images
Image segmentation with specific constraints has found applications in several areas such as biomedical image analysis and data mining. In this paper, we study the problem of segmenting doughnut-shaped and smooth objects in 2-D medical images. Image objects of these shapes are often studied in medical applications. We present an O(IJU(U − L)logJlog(U − L)) time algorithm, where the size of the input 2-D image is I× J, M is the smoothness parameter with 1 ≤ M ≤ J, and L and U are the thickness parameters specifying the thickness between two border contours of a doughnut-shaped object. Previous approaches for solving this segmentation problem are computationally expensive and/or need a lot of user interference. Our algorithm improves the straightforward dynamic programming algorithm by a factor of \(O(\frac{J(U-L)M^2}{U{\rm log}J{\rm log}(U-L)})\). We explore some interesting observations, which make possible to apply the divide-and-conquer strategy combined with dynamic programming. Our algorithm is also based on computing optimal paths in an implicitly represented graph.
31548532
Efficient Algorithms and Implementations for Optimizing the Sum of Linear Fractional Functions, with Applications
This paper presents an improved algorithm for solving the sum of linear fractional functions (SOLF) problem in 1-D and 2-D. A key subproblem to our solution is the off-line ratio query (OLRQ) problem, which asks to find the optimal values of a sequence of m linear fractional functions (called ratios), each ratio subject to a feasible domain defined by O(n) linear constraints. Based on some geometric properties and the parametric linear programming technique, we develop an algorithm that solves the OLRQ problem in O((m+n)log (m+n)) time. The OLRQ algorithm can be used to speed up every iteration of a known iterative SOLF algorithm, from O(m(m+n)) time to O((m+n)log (m+n)), in 1-D and 2-D. Implementation results of our improved 1-D and 2-D SOLF algorithm have shown that in most cases it outperforms the commonly-used approaches for the SOLF problem. We also apply our techniques to some problems in computational geometry and other areas, improving the previous results.
39603817
Optimal Terrain Construction Problems and Applications in Intensity-Modulated Radiation Therapy
In this paper, we study several rectilinear terrain construction problems, which model leaf sequencing problems in intensity-modulated radiation therapy (IMRT). We present a novel unified approach based on geometric techniques for solving these terrain construction problems. Our approach leads to the first algorithms for several leaf sequencing problems in IMRT that are practically fast and guarantee the optimal quality of the output solutions. Our implementation results show that our terrain construction algorithms run very fast on real medical data.
19420160
Multiscale LMMSE-based image denoising with optimal wavelet selection
In this paper, a wavelet-based multiscale linear minimum mean square-error estimation (LMMSE) scheme for image denoising is proposed, and the determination of the optimal wavelet basis with respect to the proposed scheme is also discussed. The overcomplete wavelet expansion (OWE), which is more effective than the orthogonal wavelet transform (OWT) in noise reduction, is used. To explore the strong interscale dependencies of OWE, we combine the pixels at the same spatial location across scales as a vector and apply LMMSE to the vector. Compared with the LMMSE within each scale, the interscale model exploits the dependency information distributed at adjacent scales. The performance of the proposed scheme is dependent on the selection of the wavelet bases. Two criteria, the signal information extraction criterion and the distribution error criterion, are proposed to measure the denoising performance. The optimal wavelet that achieves the best tradeoff between the two criteria can be determined from a library of wavelet bases. To estimate the wavelet coefficient statistics precisely and adaptively, we classify the wavelet coefficients into different clusters by context modeling, which exploits the wavelet intrascale dependency and yields a local discrimination of images. Experiments show that the proposed scheme outperforms some existing denoising methods.
18130193
Preemptive maximum stretch optimization scheduling for wireless on-demand data broadcast
On-demand broadcast is an attractive data dissemination method for mobile and wireless computing. We need an on-demand broadcast scheduling algorithm which can balance individual and overall performance, at the same time avoid the starvation of data items, and scale in terms of client population, database size, and data size in heterogeneous settings. As stretch is regarded as a fair performance metric for variable-sized data requests, in this paper, we propose a new preemptive, heuristic online scheduling algorithm, called PRS for on-demand broadcast system to optimize the worst case stretch across all criteria. We have done a series of simulation experiments to evaluate the performance of our algorithm as compared with other recently proposed methods under a range of scenarios. The experimental results show that our algorithm can substantially reduce the maximum stretch without jeopardizing the overall system performance.
13903489
Whole genome phylogeny based on clustered signature string composition
Peptide compositions constructed out of whole sets of protein sequences can be used as species signatures for phylogenetic analysis. To account for point mutations, an amino acid substitution model is integrated into the complete composition vectors through a novel peptide clustering algorithm. Such a refined signature is expected to highlight deeper evolutionary relationships among the species and employed into the whole genome phylogenetic analysis to define a new evolutionary distance measure. Computational experiments have been set up to validate the effectiveness of this new measure and a vertebrate evolutionary tree using a dataset of 832 proteins for 64 vertebrates is reported.
2809067
Support vector machines based on K-means clustering for real-time business intelligence systems
Support vector machines (SVM) have been applied to build classifiers, which can help users make well-informed business decisions. Despite their high generalisation accuracy, the response time of SVM classifiers is still a concern when applied into real-time business intelligence systems, such as stock market surveillance and network intrusion detection. This paper speeds up the response of SVM classifiers by reducing the number of support vectors. This is done by the K-means SVM (KMSVM) algorithm proposed in this paper. The KMSVM algorithm combines the K-means clustering technique with SVM and requires one more input parameter to be determined: the number of clusters. The criterion and strategy to determine the input parameters in the KMSVM algorithm are given in this paper. Experiments compare the KMSVM algorithm with SVM on real-world databases, and the results show that the KMSVM algorithm can speed up the response time of classifiers by both reducing support vectors and maintaining a similar testing accuracy to SVM.
11758071
Algorithms for optimal multi-resolution quantization
Multi-resolution quantization is a way of constructing a progressively refinable description of a discrete random variable. The underlying discrete optimization problem is to minimize an expected distortion over all refinement levels weighted by the probability or importance of the descriptions of different resolutions. This research is motivated by the application of multimedia communications via variable-rate channels. We propose an O(rN2) time and O(N2 log N) space algorithm to design a minimum-distortion quantizer of r levels for a random variable drawn from an alphabet of size N. It is shown that for a very large class of distortion measures the objective function of optimal multi-resolution quantization satisfies the convex Monge property. The efficiency of the proposed algorithm hinges on the convex Monge property. But our algorithm is simpler (even though of the same asymptotic complexity) than the well-known SMAWK fast matrix search technique, which is the best existing solution to the quantization problem. For exponential random variables our approach leads to a solution of even lower complexity: O(rN) time and O(N log N) space, which outperforms all the known algorithms for optimal quantization in both multi- and single-resolution cases. We also generalize the multi-resolution quantization problem to a graph problem, for which our algorithm offers an efficient solution.