14088697
Approximate shortest paths in anisotropic regions
Our goal is to find an approximate shortest path for a point robot moving in a planar subdivision with <i>n</i> vertices. Let ρ ≥ 1 be a real number. Distances in each face of this subdivision are measured by a convex distance function whose unit disk is contained in a concentric unit Euclidean disk, and contains a concentric Euclidean disk with radius 1/ρ. Different convex distance functions may be used for different faces, and obstacles are allowed. These convex distance functions may be asymmetric. For all ε ∈ (0, 1), and for any two points <i>v<inf>s</inf></i> and <i>v<inf>d</inf></i>, we give an algorithm that finds a path from <i>v<inf>s</inf></i> to <i>v<inf>d</inf></i> whose cost is at most (1 + ε) times the minimum cost. Our algorithm runs in <i>O</i> (ρ<sub>2</sub>logρ/ε<sup>2</sup>n<sup>3</sup> log (ρn/ε)) time. This bound does not depend on any other parameters; in particular, it does not depend on the minimum angle in the subdivision. We give applications to two special cases that have been considered before: the weighted region problem and motion planning in the presence of uniform flows. For the weighted region problem with weights in [1, ρ] ∪ {∞}, the time bound of our algorithm improves to <i>O</i> (ρ<sub>2</sub>logρ/εn<sup>3</sup> log (ρn/ε)).
38202538
Infix-free Regular Expressions and Languages
We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of ...
21531236
Towards Unsupervised Segmentation of Semi-rigid Low-Resolution Molecular Surfaces
In this paper, we study a particular type of surface segmentation problem motivated by molecular biology applications. In particular, two input surfaces are given, coarsely modeling two different conformations of a molecule undergoing a semi-rigid deformation. The molecule consists of two subunits that move in a roughly rigid manner. The goal is to segment the input surfaces into these semi-rigid subcomponents. The problem is closely related to non-rigid surface registration problems, although considering only a special type of deformation that exists commonly in macromolecular movements (such as the popular hinge motion). We present and implement an efficient paradigm for this problem, which combines several existing and new ideas. We demonstrate the performance of our new algorithm by some preliminary experimental results in segmenting low-resolution molecular surfaces.
2617111
Efficient Algorithms for Traffic Grooming in SONET/WDM Networks
In SONET/WDM optical networks, a wavelength channel is shared by multiple low-rate traffic demands. The multiplexing is known as traffic grooming and carried out by SONET add-drop multiplexers (SADM). A key optimization problem in traffic grooming is to minimize the number of SADMs. This optimization problem is challenging and NP-hard even for unidirectional SONET/WDM rings (UPSR) with symmetric unitary traffic demands. In this paper, we give a linear time heuristic algorithm for this NP-hard problem. Empirical results show that the algorithm outperforms previous algorithms. The algorithm uses the minimum number of wavelengths, which are also precious resources in optical networks. An important subclass of the symmetric unitary traffic pattern is the regular traffic pattern, where each network node appears in exactly r symmetric demands. The regular traffic pattern is a generalization of the well known all-to-all traffic pattern, in which r = n - 1 for a network of n nodes. We prove that the optimization problem remains NP-hard for the regular traffic pattern on the UPSR. We also propose an algorithm for this problem with a better upper bound on the number of used SADMs than previous algorithms. This algorithm always uses the minimum number of wavelengths as well
3063945
Statistical-based approach to word segmentation
This paper presents a text word extraction algorithm that takes a set of bounding boxes of glyphs and their associated text lines of a given document and partitions the glyphs into a set of text words, using only the geometric information of the input glyphs. The algorithm is probability based. An iterative, relaxation-like method is used to find the partitioning solution that maximizes the joint probability. To evaluate the performance of our test word extraction algorithm, we used a 3-fold validation method and developed a quantitative performance measure. The algorithm was evaluated on the UW-III database of some 1600 scanned document image pages. An area-overlap measure was used to find the correspondence between the detected entities and the ground-truth. For a total of 827, 433 ground truth words, the algorithm identified and segmented 800, 149 words correctly, an accuracy of 97.43%.
7477567
Design formalism for collaborative assembly design
Abstract Joints in product design are common because of the limitations of component geometric configurations and material properties, and the requirements of inspection, accessibility, repair, and portability. Collaborative product design is emerging as a viable alternative to the traditional design process. The collaborative assembly design (AsD) methodologies are needed for distributed product development. Existing AsD methodologies have limitations in capturing the non-geometric aspects of designer's intent on joining and are not efficient for a collaborative design environment. This paper introduces an AsD formalism and associated AsD tools to capture joining relations and spatial relationship implications. This AsD formalism allows the joining relations to be modeled symbolically for computer interpretation, and the model can be used for inferring mathematical and physical implications. An AsD model generated from the AsD formalism is used to exchange AsD information transparently in a collaborative AsD environment. An assembly relation model and a generic assembly relationship diagram are to capture assembly and joining information concisely and persistently. As a demonstration, the developed AsD formalism and AsD tools are applied on a connector assembly with arc weld and rivet joints.
21757365
Estimating coronary artery lumen area with optimization-based contour detection
A modified optimization-based contour detection method was presented to compute the lumen area of the coronary artery from intravascular ultrasound (IVUS) video images. First, the search range for the artery inner wall was determined based on the continuity of IVUS video frames. Next, the internal and external energy were calculated to describe the smoothness of the arterial wall and the grayscale variation of ultrasound images, respectively. Here, a novel form of the external energy which combines the gradient and variance of the intensity of image in the radial direction was used. Finally, the minimal energy path based on the optimum contour of the artery wall was obtained using circular dynamic programming (DP). By the comparison with the typical DP procedure using the traditional external energy form, based only on the image gradient, the reliability of this modified method is considerably improved in the measurement of coronary artery lumen area.