9160894
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 Steiner points in polynomial time; the previously best known basic 3-D SLS algorithm gives optimal outputs only for the case without 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 and comparisons using real medical data and on a real radiotherapy machine have shown that our 3-D SLS algorithms and software produce treatment plans that use significantly shorter delivery time and give better treatment quality than the current most popular commercial treatment planning system and the most well-known SLS algorithm. Some of our techniques and geometric procedures (e.g., for the problem of 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.
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.
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.
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.
17164296
Optimal context quantization in lossless compression of image data sequences
In image compression context-based entropy coding is commonly used. A critical issue to the performance of context-based image coding is how to resolve the conflict of a desire for large templates to model high-order statistic dependency of the pixels and the problem of context dilution due to insufficient sample statistics of a given input image. We consider the problem of finding the optimal quantizer Q that quantizes the K-dimensional causal context C/sub t/=(X/sub t-t1/,X/sub t-t2/,...,X/sub t-tK/) of a source symbol X/sub t/ into one of a set of conditioning states. The optimality of context quantization is defined to be the minimum static or minimum adaptive code length of given a data set. For a binary source alphabet an optimal context quantizer can be computed exactly by a fast dynamic programming algorithm. Faster approximation solutions are also proposed. In case of m-ary source alphabet a random variable can be decomposed into a sequence of binary decisions, each of which is coded using optimal context quantization designed for the corresponding binary random variable. This optimized coding scheme is applied to digital maps and /spl alpha/-plane sequences. The proposed optimal context quantization technique can also be used to establish a lower bound on the achievable code length, and hence is a useful tool to evaluate the performance of existing heuristic context quantizers.
16765511
A preemptive scheduling algorithm for wireless real-time on-demand data broadcast
On-demand broadcast is an attractive data dissemination method for mobile and wireless computing. In this paper, we propose a new online preemptive scheduling algorithm, called PRDS that incorporates the urgency, the data size and the number of pending requests for real-time on-demand broadcast system. Furthermore, we use pyramid preemption to optimize performance and reduce overhead. We have done a series of simulation experiments to evaluate the performance of our algorithm as compared with other previously proposed methods under a range of scenarios. The experimental results show that our algorithm can substantially outperform other algorithms without jeopardizing other performance metrics, such as response time and stretch.
16021441
Hybrid inter- and intra-wavelet scale image restoration
This paper exploits both the inter- and intra-scale interdependencies that exist in wavelet coefficients to improve image restoration from noise-corrupted data. Using an over-complete wavelet expansion, we group the wavelet coefficients with the same spatial orientation at several scales. We then apply the linear minimum mean squared-error estimation to smooth noise. This scheme exploits the inter-scale correlation information of wavelet coefficients. To exploit the intra-scale dependencies, we calculate the co-variance matrix of each vector locally using a centered square-shaped window. Experiments show that the proposed hybrid scheme significantly outperforms methods exploiting only the intra- or inter-scale dependencies. The performance of noise removal also depends on wavelet filters. In our experiments a biorthogonal wavelet, which best characterizes the image inter-scale dependencies, achieves the best results.
11584790
SLEVEs for planar spline curves
Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances. This is the simplest instance of a subdividable linear efficient variety enclosure, short sleve.We develop general criteria, that certify correctness of a global, polygonal enclosure built from a sequence of individual bounding boxes by extending and intersecting their edges. These criteria prove correctness of the sleve construction.
19709239
Scheduling real-time requests in on-demand data broadcast environments
On-demand broadcast is an attractive data dissemination method for mobile and wireless computing. In this paper, we propose a new online preemptive scheduling algorithm, called PRDS that incorporates urgency, data size and number of pending requests for real-time on-demand broadcast system. Furthermore, we use pyramid preemption to optimize performance and reduce overhead. A series of simulation experiments have been performed to evaluate the real-time performance of our algorithm as compared with other previously proposed methods. The experimental results show that our algorithm substantially outperforms other algorithms over a wide range of workloads and parameter settings.