15599036
Simultaneous Segmentation of Multiple Closed Surfaces Using Optimal Graph Searching
This paper presents a general graph-theoretic technique for simultaneously segmenting multiple closed surfaces in volumetric images, which employs a novel graph-construction scheme based on triangulated surface meshes obtained from a topological presegmentation. The method utilizes an efficient graph-cut algorithm that guarantees global optimality of the solution under given cost functions and geometric constraints. The method's applicability to difficult biomedical image analysis problems was demonstrated in a case study of co-segmenting the bone and cartilage surfaces in 3-D magnetic resonance (MR) images of human ankles. The results of our automated segmentation were validated against manual tracings in 55 randomly selected image slices. Highly accurate segmentation results were obtained, with signed surface positioning errors for the bone and cartilage surfaces being 0.02 +/- 0.11mm and 0.17 +/- 0.12mm, respectively.
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.
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.
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.
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.
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.
35689582
A fast recurring two-dimensional entropic thresholding algorithm
Thresholding is an important form of image segmentation and is used in the processing of images for many applications. One of the criteria to select a suitable threshold is the maximization of the two-dimensional (2-D) entropies based on the 2-D (gray-level/local average gray-level) histogram. The rationale of this approach is introduced. In order to reduce the computation time of entropy function, a fast recurring algorithm for 2-D entropic thresholding method is presented. The experimental results show that the processing time to obtain the threshold vector from 2-D histogram is reduced from 30 to 0.15 s.
26409739
Guest Editors' Introduction
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.
16426940
An accurate error measure for adaptive subdivision surfaces
A tight estimate on the maximum distance between a subdivision surface and its linear approximation is introduced to guide adaptive subdivision with guaranteed accuracy.
33348508
Knowledge Discovery in Multiple Databases