8713870
Optimal Terrain Construction Problems and Applications
in Intensity-Modulated Radiation Therapy
AbstractIn this paper we study several rectilinear terrain construction
problems, which model the 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 ideas include formulating the terrain
construction problems as computing shortest paths in a weighted directed
graph and building the graph by computing optimal bipartite matchings on various geometric objects
subject to specific constraints of each of the problems. Further,
since we need to compute optimal bipartite matchings on many sets
of geometric objects, we use techniques for computing such
matchings in a batch fashion to speed up these matching
computations. Our approach leads to the first algorithms for several leaf
sequencing problems in IMRT that are practically fast and guarantee
 an output which is optimal for a large sub-class of solutions. The previously known leaf
sequencing algorithms which are currently used in radiation therapy practice
are all heuristics that do not guarantee any good
quality of the output solutions and may run in a long time.
Our implementation
results show that our terrain construction algorithms run very
fast on real medical data (all under few seconds).
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.
47381475
Geometric algorithms for static leaf sequencing problems in radiation therapy
The static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to accomplish the delivery of a radiation prescription to a target tumor in the minimum amount of delivery time. Geometrically, the SLS problem can be formulated as a 3-D partition problem for which the 2-D problem of partitioning a polygonal domain (possibly with holes) into a minimum set of monotone polygons is a special case. In this paper, we present new geometric algorithms for a basic case of the 3-D SLS problem (which is also of clinical value) and for the general 3-D SLS problem. Our basic 3-D SLS algorithm, based on new geometric observations, produces guaranteed optimal quality solutions using O(1) Steiner points in polynomial time; the previously best known basic 3-D SLS algorithm gives optimal outputs only for the case without considering any Steiner points, and its time bound involves a multiplicative factor of a factorial function of the input. Our general 3-D SLS algorithm is based on our basic 3-D SLS algorithm and a polynomial time algorithm for partitioning a polygonal domain (possibly with holes) into a minimum set of x-monotone polygons, and has a fast running time. Experiments of our SLS algorithms and software in clinical settings have shown substantial improvements over the current most popular commercial treatment planning system and the most well-known SLS algorithm in medical literature. The radiotherapy plans produced by our software not only take significantly shorter delivery times, but also have a much better treatment quality. This proves the feasibility of our software and has led to its clinical applications at the Department of Radiation Oncology at the University of Maryland Medical Center. Some of our techniques and geometric procedures (e.g., for partitioning a polygonal domain into a minimum set of x-monotone polygons) are interesting in their own right.
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.
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.
11091243
Efficient Algorithms for Intensity Map Splitting Problems in Radiation Therapy
In this paper, we study several interesting intensity map splitting (IMSp) problems that arise in Intensity-Modulated Radiation Therapy (IMRT), a state-of-the-art radiation therapy technique for cancer treatments. In current clinical practice, a multi-leaf collimator (MLC) with a maximum leaf spread is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of an MLC may require to split a large intensity map into several abutting sub-IMs each being delivered separately, which results in prolonged treatment time. Few IM splitting techniques reported in the literature has addressed the issue of treatment delivery efficiency for large IMs. We develop a unified approach for solving the IMSp problems while minimizing the total beam-on time in various settings. Our basic idea is to formulate the IMSp problem as computing a k-link shortest path in a directed acyclic graph. We carefully characterize the intrinsic structures of the graph, yielding efficient algorithms for the IMSp problems.
14606443
Database classification for multi-database mining
Many large organizations have multiple databases distributed in different branches, and therefore multidatabase mining is an important task for data mining. To reduce the search cost in the data from all databases, we need to identify which databases are most likely relevant to a data mining application. This is referred to as database selection. For real-world applications, database selection has to be carried out multiple times to identify relevant databases that meet different applications. In particular, a mining task may be without reference to any specific application. In this paper, we present an efficient approach for classifying multiple databases based on their similarity between each other. Our approach is application-independent.
29396765
Detection of LSB Steganography via Sample Pair Analysis
This paper introduces a new, principled approach to detecting LSB steganography in digital signals such as images and audio. It is shown that the length of hidden message embedded in the least significant bits of signal samples can be estimated with relatively high precision. The new steganalytic approach is based on some statistical measures of sample pairs that are highly sensitive to LSB embedding operations. The resulting detection algorithm is simple and fast. To evaluate the robustness of the proposed steganalytic approach, bounds on estimation errors are developed. Furthermore, the vulnerability of the new approach to possible attacks is also assessed, and counter measures are suggested.
18740255
Selected String Representation for Whole Genomes
The increase in the amount of available genomic data has made phylogenetic analysis possible at the whole genome scale. However, such a huge amount of data imposes computational challenges in both memory consumption and CPU usage. One novel proposal in this paper is to extract sequence patterns that are biologically meaningful. Using these patterns, whole genomes can be mapped into a significantly lower dimensional space and subsequent studies using these representations become computationally feasible. Experiments on two datasets of 64 vertebrate mitochondrial genomes and 99 prokaryote whole genomes demonstrate that the selected sequence patterns result in good quality evolutionary distances in terms of the final phylogeny.
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.
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.