Arbitrary Line Segments Research Articles

Learning-based collision-free planning on arbitrary optimization criteria in the latent space through cGANs

We propose a new method for collision-free planning using Conditional Generative Adversarial Networks (cGANs) to transform between the robot's joint space and a latent space that captures only collision-free areas of the joint space, conditioned by an obstacle map. Generating multiple plausible trajectories is convenient in applications such as the manipulation of a robot arm by enabling the selection of trajectories that avoids collision with the robot or surrounding environment. In the proposed method, various trajectories that avoid obstacles can be generated by connecting the start and goal state with arbitrary line segments in this generated latent space. Our method provides this collision-free latent space, after which any planner, using any optimization conditions, can be used to generate the most suitable paths on the fly. We successfully verified this method with a simulated and actual UR5e 6-DoF robotic arm. We confirmed that different trajectories could be generated depending on optimization conditions.

Equipment complex and method for aiming laser beams at specified target points

We describe a technique for automatic alignment and targeting of laser beams on a specific point in space using the simulated cubical targets typically used for focusing and targeting of laser light in a multiple beamline laser facility where the target is illuminated in cubical symmetry for high-temperature plasma physics research. We describe the targeting system and the steps for targeting and focusing laser beams at specific points in the target chamber, as well as a method for measuring the length of an arbitrary line segment on a distant object from an image on a display, and an experimental estimate of the accuracy of such measurements on a test object—the edge of the simulated cubical target.

Eliminating Lining Seams in Tunnel Concrete Crack Images via Line Segments’ Translation and Expansion

Cracks are the main form of tunnel complications and have drawn much attention in current tunnel safety monitoring. However, automatic crack detection cannot accurately extract cracks from tunnel concrete lining surfaces because of the inference of noises like lining seams, which have similar gray values and textures to cracks, and increase the topological complexity of cracks. In this paper, we proposed a novel method for eliminating lining seams in tunnel concrete crack images, to address the above-mentioned issues. Our contributions are shown as follows: 1) classified arbitrary line segments to better distinguish the edges on the cracks and the seams, and proposed uniform k-divided angle model to get accurate classification and 2) introduced two new principles to help effectively eliminate lining seams through the information of translation direction and expansion width of all line segments. The experimental results proved the superior precision and efficiency of our method compared with the existing methods.

Imaging with extended depth of field by means of the peacock eye optical element

The paper presents imaging properties of the peacock eye optical element. Its abilities for imaging with extended depth of field is illustrated experimentally in monochromatic as well as polychromatic light. According to the obtained results the element makes possible to maintain the acceptable resolution, contrast and brightness of the output images for a wide range of defocusing. Full Text: PDF ReferencesJ. Ares, R. Flores, S. Bara, and Z. Jaroszewicz, "Presbyopia Compensation with a Quartic Axicon", Optom. Vis. Sci. 82, 107 (2005). CrossRef G.-m. Dai, "Optical surface optimization for the correction of presbyopia", Appl. Opt. 45, 4184 (2006). CrossRef Z. Liu, A. Flores, M. R. Wang, and J. J. Yang, "Diffractive infrared lens with extended depth of focus", Opt. Eng. 46, 018002 (1-9) (2007). CrossRef E. E. Garcia-Guerrero, E. R. Mendez, H. M. Escamilla, T. A. Leskova, and A. A. Maradudin, "Design and fabrication of random phase diffusers for extending the depth of focus", Opt. Express 15, 910 (2007). CrossRef J. Lin, J. Liu, J. Ye, and S. Liu, "Design of microlenses with long focal depth based on the general focal length function", J. Opt. Soc. Am. A 24, 1747 (2007). CrossRef N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth", Opt. Lett. 16, 523 (1991). CrossRef A. Kołodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The Light Sword Optical Element?a New Diffraction Structure with Extended Depth of Focus", J. Mod. Opt. 37, 1283 (1990). CrossRef K. Petelczyc, S. Bará, A. Ciro Lopez, Z. Jaroszewicz, K. Kakarenko, A. Kolodziejczyk, and M. Sypek, "Imaging properties of the light sword optical element used as a contact lens in a presbyopic eye model", Opt. Express 19, 25602 (2011). CrossRef K. Kakarenko, I. Ducin, K. Grabowiecki, Z. Jaroszewicz, A. Kolodziejczyk, A. Mira-Agudelo, K. Petelczyc, A. Składowska, M. Sypek, "Assessment of imaging with extended depth-of-field by means of the light sword lens in terms of visual acuity scale", Biomed Opt Express 6, 1738 (2015). CrossRef Z. Jaroszewicz, A. Kołodziejczyk, D. Mouriz, and J. Sochacki, "Generalized Zone Plates Focusing Light into Arbitrary Line Segments", J. Mod. Opt. 40, 601 (1993). CrossRef L. A. Romero, M. S. Millían, Z. Jaroszewicz, A. Kolodziejczyk, "Double peacock eye optical element for extended focal depth imaging with ophthalmic applications", J. Biomed. Opt. 17 046013 (2012). CrossRef

Planar lower envelope of monotone polygonal chains

A simple linear search algorithm running in O(n+mk) time is proposed for constructing the lower envelope of k vertices from m monotone polygonal chains in 2D with n vertices in total. This can be applied to output-sensitive construction of lower envelopes for n arbitrary line segments in optimal O(nlog⁡k) time, where k is the output size. Compared to existing output-sensitive algorithms for lower envelopes, this is simpler to implement, does not require complex data structures, and is a constant factor faster.

Line coverage measures in wireless sensor networks

The coverage problem in wireless sensor networks addresses the problem of covering a region with sensors. Many different definitions of coverage are there in the literature depending on the goal of the coverage. In this paper, we address the problem of determining the quality of a sensor deployment against an intruder who can walk along a straight line. A line segment ℓ is said to be k-covered if it intersects the sensing regions of at least k sensors distributed in R. Similarly, it is said to be k-uncovered if it intersects the sensing regions, that is assumed to be circular, of at most k−1 sensors. We introduce two new metrics, smallestk-covered line segment and longestk-uncovered line segment, for measuring the quality of line coverage achieved by a sensor deployment. The intruder can walk a distance less than the smallestk-covered line segment without ever being detected by k sensors. So, this metric gives an estimate on the distance an intruder can walk in a straight line path before being detected by k sensors. On the other side, the defender would want to deploy sensors so that the length of the longestk-uncovered line segment is minimized. Given a deployment of n sensors, we propose deterministic algorithms to determine the smallestk-covered line segment and longestk-uncovered line segment where the line segments can be of the following types: (i) axis-parallel (horizontal and vertical) line segments, (ii) line segments whose one endpoint is fixed and is of arbitrary orientation and (iii) arbitrary line segments. The time complexities for the first and second types of line segments are O((n+χ)logn) for both smallestk-covered line segment and longestk-uncovered line segment, where χ is the number of intersections among n circles. For the arbitrary line segment case, the smallestk-covered segment can be determined in O(χ2logn+n113+ϵ) time, whereas, the longestk-uncovered segment can be determined in O(χ2logn+n2+β+ϵ) time, where β=log2(1+5)−1 and ϵ is a small value greater than or equal to 0. All our algorithms take linear space.

Changing the scattering of sheltered targets

In this paper, we propose a kind of illusion cloak that does not provide invisibility but instead changes the scattering of a coated target to that of a totally different one. Different from other illusion cloaks such as those based on ``anti-object'' or active sources, the proposed one is independent of the information of concealed targets or incident waves and can reshape the scattering of any targets. In addition, we also provide a general method to imitate arbitrary conductor line segments, as a special case of conductor reshaper. Electromagnetic (EM) simulations by a finite-element solver on detailed examples have been carried to validate the design.

Dynamic Connectivity: Connecting to Networks and Geometry

Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions. In this paper, we study two more challenging, yet equally fundamental, problems. Subgraph connectivity asks us to maintain an understanding of connectivity under vertex updates: updates can turn vertices on and off, and queries refer to the subgraph induced by on vertices. (For instance, this is closer to applications in networks of routers, where node faults may occur.) We describe a data structure supporting vertex updates in $\widetilde{O}(m^{2/3})$ amortized time, where m denotes the number of edges in the graph. This greatly improves upon the previous result [T. M. Chan, in Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC), 2002, pp. 7–13], which required fast matrix multiplication and had an update time of $O(m^{0.94})$. The new data structure is also simpler. Geometric connectivity asks us to maintain a dynamic set of n geometric objects and query connectivity in their intersection graph. (For instance, the intersection graph of balls describes connectivity in a network of sensors with bounded transmission radius.) Previously, nontrivial fully dynamic results were known only for special cases like axis-parallel line segments and rectangles. We provide similarly improved update times, $\widetilde{O}(n^{2/3})$, for these special cases. Moreover, we show how to obtain sublinear update bounds for virtually all families of geometric objects which allow sublinear time range queries. In particular, we obtain the first sublinear update time for arbitrary two-dimensional line segments: $O^*(n^{9/10})$; for d-dimensional simplices: $O^*(n^{1-\frac{1}{d(2d+1)}})$; and for d-dimensional balls: $O^*(n^{1-\frac{1}{(d+1)(2d+3)}})$.

Motion‐compensated video coding using sliced blocks

AbstractIn international standards for video coding such as MPEG‐4 and H.264, motion compensation is performed by partitioning macroblocks (square pixel sets) into multiple areas. In this paper, we propose motion compensation using sliced blocks as a new method for macroblock‐based motion compensation. The partition shape is not restricted to squares or other patterns; instead, macroblocks are sliced by arbitrary line segments. This produces better agreement in shape between partitions and moving objects, as well as better motion compensation performance. In addition, when partition data are described in bitstream, adaptive prediction of segments based on partition shape of neighbor macroblocks is applied, aiming at reduction of the overhead caused by partition data. In the proposed method, coding is performed at the macroblock level, and therefore, coding mode selection and other related algorithms of conventional rate distortion optimization can be used unaltered. The proposed method was applied to forward‐prediction picture coding (basic algorithm of H.264), and an improvement of coding efficiency by about 5% was confirmed. © 2007 Wiley Periodicals, Inc. Syst Comp Jpn, 38(7): 12– 22, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20714

Optimal estimation of line segments in noisy lidar data

Lidar data usually is obtained by independently measuring distance r and angle ϕ . Therefore, measurements of r and ϕ are statistically independent. However, in most approaches measurements in x and y are assumed to be uncorrelated thus not taking properly into account the noise characteristic. This article investigates the application of least squares (LS), total least squares (TLS), mixed-LS–TLS (MTLS), structured total least norm (STLN) and maximum-likelihood (ML) estimators to the problem of estimating line segments in noisy lidar data and compares their performance from a theoretical point of view. This analysis is supported by simulation results. A new approach of estimating an arbitrary line segment without the need of parametric constraints is proposed.

Transversals to Line Segments in Three-Dimensional Space

We completely describe the structure of the connected components of transversals to a collection of n line segments in ℝ3. Generically, the set of transversals to four segments consists of zero or two lines. We catalog the non-generic cases and show that n≥ 3 arbitrary line segments in ℝ3 admit at most n connected components of line transversals, and that this bound can be achieved in certain configurations when the segments are coplanar, or they all lie on a hyperboloid of one sheet. This implies a tight upper bound of n on the number of geometric permutations of line segments in ℝ3.

Exact lower bound for proportion of maximally embedded beamlet

We prove that the maximal inscribed beamlet is at least 1/7 of an arbitrary line segment (i.e., beam). The implication of this result is addressed.

Fast computation of the ambiguity function and the Wigner distribution on arbitrary line segments

By using the fractional Fourier transformation of the time-domain signals, closed-form expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections of the auto and cross Wigner distributions and the well known two-dimensional (2-D) Fourier transformation relationship between the ambiguity and Wigner domains, closed-form expressions are obtained for the slices of both the Wigner distribution and the ambiguity function. By using discretization of the obtained analytical expressions, efficient algorithms are proposed to compute uniformly spaced samples of the Wigner distribution and the ambiguity function located on arbitrary line segments. With repeated use of the proposed algorithms, samples in the Wigner or ambiguity domains can be computed on non-Cartesian sampling grids, such as polar grids.

Generalized Zone Plates Focusing Light into Arbitrary Line Segments

Abstract A new computer-generated generalized zone plate is proposed, which is able to concentrate the incident beam into a line segment of various length and arbitrary inclination to the optical axis, as well as unrestricted distribution of the longitudinal intensity. The approach is based on the energy conservation principle and equations of the paraxial ray tracing, both considered in the cartesian coordinate system. Hyberbolic, elliptic, linear, and conical zone plates are shown to be limiting cases of the proposed element. Other specific cases, e.g. a new element focusing into a segment of the optical axis, are also derived.

Perspective angle transform: Principle of shape from angles

This paper introduces a new relation, called the perspective angle transform (PAT), to deal with shape-from-angle problems, together with its application to 3D configuration recovery from an image. Three main aspects of PAT are presented in this paper. The first is the derivation of PAT which holds between the apparent and real angles under perspective projection. A concept is proposed of a virtual image plane and a new coordinate system, named the first perspective moving coordinate (FPMC) system, for analysis of the shape-from-range problems. Characteristics of FPMC are discussed briefly. The second point is the analysis of PAT properties, for which the general PAT form is introduced on another new coordinate system, named the second perspective moving coordinate (SPMC) system. Using this general form, the gradient of the plane including the real angle is constrained on a curve (PAT curve) of the fourth degree in the virtual image plane. The characteristics of PAT curves and relations between the general PAT form and skewed symmetry are summarized briefly. The last point concerns an application of PAT. As an example, we treat 3D configuration recovery from three arbitrary line segments in the image plane. This recovery corresponds to a generalization of the right-angled interpretation problem proposed and discussed by S.T. Barnard. A solution to the problem is shown using the general PAT form in conjunction with the concept of a virtual crossing point. The right-angled interpretation problem is ascribed to a quadratic equation. A simplified solution is also provided for the case where three line segments have a common crossing point in the image plane. This solution is based on the primary PAT form and is applicable to interpretation of a trihedral vertex with at least two right angles.

Reporting and counting segment intersections

This paper partly settles the following question: Is it possible to compute all k intersections between n arbitrary line segments in time linear in k? We describe an algorithm for this problem whose running time is O(n( log 2 n log log n )+k) . This is the first solution with a time bound linear in the size of the output. To obtain this result we turn away from traditional, sweep-line-based schemes. Instead, we introduce a new hierarchical strategy for dealing with segments without reducing the dimensionality of the problem. This framework is also used to answer related questions. New results include an O( n 1.695) time algorithm for counting intersections (as opposed to reporting each of them explicitly) and an optimal algorithm for computing the intersections of a line arrangement with a query segment. Using duality arguments we also present an improved algorithm for a point enclosure problem.

Rectilinear line segment intersection, layered segment trees, and dynamization

The aim of the present paper is to provide an efficient solution to the following problem: “Given a family of n rectilinear line segments in two-space report all intersections in the family with a query consisting of an arbitrary rectilinear line segment.” We provide an algorithm which takes O( nlog 2 n) preprocessing time, o( nlog 2 n) space and O(log 2 n + k) query time, where k is the number of reported intersections. This solution serves to introduce a powerful new data structure, the layered segment tree, which is of independent interest. Second it yields, by way of recent dynamization techniques, a solution to the on-line version of the above problem, that is the operations INSERT and DELETE and QUERY with a line segment are allowed. Third it also yields a new nonscanning solution to the batched version of the above problem. Finally we apply these techniques to the problem obtained by replacing “line segment” by “rectangle” in the above problem, giving an efficient solution in this case also.

The range of values of a complex polynomial over a complex interval

We discuss algorithms for the computation of the range of values of a complex interval polynomial over a complex interval. The mathematical results needed are based upon a result by Rivlin [7] valid for the range of values of a complex polynomial over the line segment [0, 1]. In the present work we extend his results to an arbitrary line segment in the complex plane. Based upon these results we then generate algorithms suitable for both line segments and rectangular regions in the complex plane executed in rectangular complex interval arithmetic. The algorithms are then tested on a variety of complex interval polynomials and compared both to the true range of values and to the values obtained by the Horner scheme.