Showing papers on "Line segment published in 2006"

The Geometry of Musical Chords

Abstract: A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.

Line-Based Structure from Motion for Urban Environments

Abstract: We present a novel method for recovering the 3D-line structure of a scene from multiple widely separated views. Traditional optimization-based approaches to line-based structure from motion minimize the error between measured line segments and the projections of corresponding 3D lines. In such a case, 3D lines can be optimized using a minimum of 4 parameters. We show that this number of parameters can be further reduced by introducing additional constraints on the orientations of lines in a 3D scene. In our approach, 2D-lines are automatically detected in images with the assistance of an EM-based vanishing point estimation method which assumes the existence of edges along mutally orthogonal vanishing directions. Each detected line is automatically labeled with the orientation (e.g. vertical, horizontal) of the 3D line which generated the measurement, and it is this additional knowledge that we use to reduce the number of degrees of freedom of 3D lines during optimization. We present 3D reconstruction results for urban scenes based on manually established feature correspondences across images.

A fast line segment based dense stereo algorithm using tree dynamic programming

Abstract: Many traditional stereo correspondence methods emphasized on utilizing epipolar constraint and ignored the information embedded in inter-epipolar lines. Actually some researchers have already proposed several grid-based algorithms for fully utilizing information embodied in both intra- and inter-epipolar lines. Though their performances are greatly improved, they are very time-consuming. The new graph-cut and believe-propagation methods have made the grid-based algorithms more efficient, but time-consuming still remains a hard problem for many applications. Recently, a tree dynamic programming algorithm is proposed. Though the computation speed is much higher than that of grid-based methods, the performance is degraded apparently. We think that the problem stems from the pixel-based tree construction. Many edges in the original grid are forced to be cut out, and much information embedded in these edges is thus lost. In this paper, a novel line segment based stereo correspondence algorithm using tree dynamic programming (LSTDP) is presented. Each epipolar line of the reference image is segmented into segments first, and a tree is then constructed with these line segments as its vertexes. The tree dynamic programming is adopted to compute the correspondence of each line segment. By using line segments as the vertexes instead of pixels, the connection between neighboring pixels within the same region can be reserved as completely as possible. Experimental results show that our algorithm can obtain comparable performance with state-of-the-art algorithms but is much more time-efficient.

On Macroblock Partition for Motion Compensation

Abstract: In the H.264/AVC video coding standard, motion compensation can be performed by partitioning macroblocks into square or rectangular sub-macroblocks in a quadtree decomposition. This paper studies a motion compensation method using wedges, i.e. partitioning macroblocks or sub-macroblocks into two regions by an arbitrary line segment. This technique allows the shapes of the divided regions to better match the boundaries between moving objects. However, there are a large number of ways to slice a block and searching exhaustively over all of them would be an extremely computer-intensive task. Thus, we propose a fast algorithm which detects the predominant edge orientations within a block in order to pre-select candidate wedge lines. Finally a comparison among macroblock partition methods is performed, which points to the higher performance of the wedge partition method.

Real-time model-based SLAM using line segments

Abstract: Existing monocular vision-based SLAM systems favour interest point features as landmarks, but these are easily occluded and can only be reliably matched over a narrow range of viewpoints. Line segments offer an interesting alternative, as line matching is more stable with respect to viewpoint changes and lines are robust to partial occlusion. In this paper we present a model-based SLAM system that uses 3D line segments as landmarks. Unscented Kalman filters are used to initialise new line segments and generate a 3D wireframe model of the scene that can be tracked with a robust model-based tracking algorithm. Uncertainties in the camera position are fed into the initialisation of new model edges. Results show the system operating in real-time with resilience to partial occlusion. The maps of line segments generated during the SLAM process are physically meaningful and their structure is measured against the true 3D structure of the scene.

Real-Time Model-Based SLAM Using Line Segments

Abstract: Existing monocular vision-based SLAM systems favour interest point features as landmarks, but these are easily occluded and can only be reliably matched over a narrow range of viewpoints. Line segments offer an interesting alternative, as line matching is more stable with respect to viewpoint changes and lines are robust to partial occlusion. In this paper we present a model-based SLAM system that uses 3D line segments as landmarks. Unscented Kalman filters are used to initialise new line segments and generate a 3D wireframe model of the scene that can be tracked with a robust model-based tracking algorithm. Uncertainties in the camera position are fed into the initialisation of new model edges. Results show the system operating in real-time with resilience to partial occlusion. The maps of line segments generated during the SLAM process are physically meaningful and their structure is measured against the true 3D structure of the scene.

A Probabilistic Approach to Robust Shape Matching

Abstract: We present a probabilistic approach to shape matching that is invariant to rotation, translation and scaling. Shapes can be represented by unlabeled point sets, so discontinuous boundaries and non-boundary points do not pose a problem. Occlusion, significant dissimilarities between shapes and image clutter are explained by a background model, and hence, their impact on the overall match is limited. The ability to operate on incomplete shape representations and ignore part of the input means that, unlike many matching algorithms, our technique performs well on real images. We derive a continuous version of the model which can be used when the `query shape' is more accurately described by a set of line segments ? e.g. a boundary polygon or line drawing. The effectiveness of the algorithms is demonstrated using the benchmark MPEG-7 data set and real images.

Text line extraction in handwritten document with Kalman filter applied on low resolution image

Abstract: In this paper we present a method to extract text lines in handwritten documents. Indeed, line extraction is a first interesting step in document structure recognition. Our method is based on a notion of perceptive vision: at a certain distance, text lines of documents can be seen as line segments. Therefore, we propose to detect text line using a line segment extractor on low resolution images. We present our extractor based on the theory of Kalman filtering. Our method makes it possible to deal with difficulties met in ancient damaged documents: skew, curved lines, overlapping text lines. We present results on archive documents from the 18th and 19th century.

Convex and Concave Parts of digital Curves

Abstract: Decomposition of a digital curve into convex and concave parts is of relevance in several scopes of image processing. In digital plane convexity cannot be observed locally. It becomes an interesting question, how far one can decide whether a part of a digital curve is convex or concave by a method which is "as local as possible". In a previous paper, it was proposed to define the meaningful parts of a digital curve as meaningful parts of the corresponding polygonal representation. This technique has an approximative character. In our considerations, we use geometry of arithmetical discrete line segments. We will introduce an exact method to define convex and concave parts of a digital curve.

The head-body-tail intersection for spatial relations between directed line segments

Abstract: Directed line segments are fundamental geometric elements used to model through their spatial relations such concepts as divergence, confluence, and interference A new model is developed that captures spatial relations between pairs of directed line segments through the intersections of the segments' heads, bodies, and tails This head-body-tail intersection identifies 68 classes of topological relations between two directed line segments highlighting two equal-sized subsets of corresponding relations that differ only by their empty and non-empty body-body intersections The relations' con-ceptual neighborhood graph takes the shape of a torus inside a torus, one for each subset Another 12 classes of topological relation classes are distinguished if the segments' exteriors are considered as well, lining up such that their conceptual neighborhood graph forms another torus that contains the other two tori These conceptual neighborhoods as well as the relations' composition table enable spatial inferences and similarity assessments in a consistent and reasoned manner

Image-based Structural Analysis of Building using Line Segments and their Geometrical Vanishing Points

Abstract: This paper describes an approach to detect and analyze the properties of building in image. We use line segments and belongings in the appearance of building as geometrical and physical properties respectively. The geometrical properties are represented as principal component parts (PCPs) as a set of door, window, wall and so on. As the physical properties, color, intensity, contrast and texture of regions are used. Analysis process is started by detecting straight line segments. We use MSAC to group such parallel line segments which have a common vanishing point. We calculate one dominant vanishing point for vertical direction and five dominant vanishing points in maximum for horizontal direction. A mesh of basic parallelograms is created by one of horizontal groups and vertical group. Each mesh represents one face of building. The PCPs are formed by merging neighborhood of basic parallelograms which have similar colors. The wall regions of PCPs are detected. Finally, the structure of building is described as a system of hierarchical features. The building is represented by number of faces. Each face is regarded by a color histogram vector. The color histogram vector just is computed by wall region of face. The proposed approach was used to recognize a database containing 1005 images and 115 queried images. It has been confirmed with various kinds of images taken for different conditions like camera systems, weather and seasons.

Coded structure light

Abstract: The present invention is a system and method for creating a three-dimensional model of a surface comprising a light source 1.2 that projects a pattern of continuous line segments onto the surface, wherein each line segment is coded with a unique pattern along the line segment, a detector 1.3 that records an image of the surface with said projected pattern, and a computer for transforming said image to a three-dimensional model of the surface utilizing said projected pattern.

Structure and View Estimation for Tomographic Reconstruction: A Bayesian Approach

Abstract: This paper addresses the problem of reconstructing the density of a scene from multiple projection images produced by modalities such as x-ray, electron microscopy, etc. where an image value is related to the integral of the scene density along a 3D line segment between a radiation source and a point on the image plane. While computed tomography (CT) addresses this problem when the absolute orientation of the image plane and radiation source directions are known, this paper addresses the problem when the orientations are unknown - it is akin to the structure-from-motion (SFM) problem when the extrinsic camera parameters are unknown. We study the problem within the context of reconstructing the density of protein macro-molecules in Cryogenic Electron Microscopy (cryo-EM), where images are very noisy and existing techniques use several thousands of images. In a non-degenerate configuration, the viewing planes corresponding to two projections, intersect in a line in 3D. Using the geometry of the imaging setup, it is possible to determine the projections of this 3D line on the two image planes. In turn, the problem can be formulated as a type of orthographic structure from motion from line correspondences where the line correspondences between two views are unreliable due to image noise. We formulate the task as the problem of denoising a correspondence matrix and present a Bayesian solution to it. Subsequently, the absolute orientation of each projection is determined followed by density reconstruction. We show results on cryo-EM images of proteins and compare our results to that of Electron Micrograph Analysis (EMAN) - a widely used reconstruction tool in cryo-EM.

Farthest-point queries with geometric and combinatorial constraints

Abstract: In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log2 n) time. Our data structure needs O(n log n) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.

Offline sorting buffers on line

Abstract: We consider the offline sorting buffers problem. Input to this problem is a sequence of requests, each specified by a point in a metric space. There is a “server” that moves from point to point to serve these requests. To serve a request, the server needs to visit the point corresponding to that request. The objective is to minimize the total distance travelled by the server in the metric space. In order to achieve this, the server is allowed to serve the requests in any order that requires to “buffer” at most k requests at any time. Thus a valid reordering can serve a request only after serving all but k previous requests. In this paper, we consider this problem on a line metric which is motivated by its application to a widely studied disc scheduling problem. On a line metric with N uniformly spaced points, our algorithm yields the first constant-factor approximation and runs in quasi-polynomial time O(mNkO(logN)) where m is the total number of requests. Our approach is based on a dynamic program that keeps track of the number of pending requests in each of O(logN) line segments that are geometrically increasing in length.

K-Separability

Abstract: Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane. For complex data with multimodal distributions this transformation is difficult to learn. Projection on k ≥2 line segments is the simplest extension of linear separability, defining much easier goal for the learning process. The difficulty of learning non-linear data distributions is shifted to separation of line intervals, making the main part of the transformation much simpler. For classification of difficult Boolean problems, such as the parity problem, linear projection combined with k-separability is sufficient.

Multi-scale point and line range data algorithms for mapping and localization

Abstract: This paper presents a multi-scale point and line based representation of two-dimensional range scan data. The techniques are based on a multi-scale Hough transform and a tree representation of the environment's features. The multi-scale representation can lead to improved robustness and computational efficiencies in basic operations, such as matching and correspondence, that commonly arise in many localization and mapping procedures. For multi-scale matching and correspondence we introduce a chi2 criterion that is calculated from the estimated variance in position of each detected line segment or point. This improved correspondence method can be used as the basis for simple scan-matching displacement estimation, as a part of a SLAM implementation, or as the basis for solutions to the kidnapped robot problem. Experimental results (using a Sick LMS-200 range scanner) show the effectiveness of our methods

3D from Line Segments in Two Poorly-Textured, Uncalibrated Images

Abstract: This paper addresses the problem of camera self-calibration, bundle adjustment and 3D reconstruction from line segments in two images of poorly-textured indoor scenes. First, we generate line segment correspondences, using an extended version of our previously proposed matching scheme. The first main contribution is a new method to identify polyhedral junctions resulting from the intersections of the line segments. At the same time, the images are segmented into planar polygons. This is done using an algorithm based on a Binary Space Partitioning (BSP) tree. The junctions are matched end points of the detected line segments and hence can be used to obtain the epipolar geometry. The essential matrix is considered for metric camera calibration. For better stability, the second main contribution consists in a bundle adjustment on the line segments and the camera parameters that reduces the number of unknowns by a maximum flow algorithm. Finally, a piecewise-planar 3D reconstruction is computed based on the segmentation of the BSP tree. The system?s performance is tested on some challenging examples.

Calibration system for image capture apparatus and method thereof

Abstract: A calibration system and a method to be used in an image capture apparatus are disclosed The calibration system includes a calibration appliance, a feature extraction unit and a processor The calibration appliance has a plurality of mark points The plurality of mark points is on the same plane to form a line segment with a known length The image capture apparatus captures an image Then based on the captured image, the feature extraction unit extracts at least three image feature points corresponding to the mark points The processor calculates the inclination angle of the image capture apparatus, and the height between the image capture apparatus and the plane Besides a line segment with a known length, the mark points corresponding to the image feature points may form a corner with a known angle, two corners with unknown but equal angles, or two line segments with unknown but equal lengths Convenience for the calibration system is therefore improved

Method and apparatus for identifying the rotation angle and bounding rectangle of a digitized form

Abstract: Methods and apparatus for determining the skew angle of a digitized form scanned at an angle to the original page are described. The method determines a rotation angle and a boundary rectangle of best fit. Sections of the digital image in the form of thin strips are examined for the boundary between the page and the region of the scanned image beyond the original page. The Hough transform is employed to determined candidate edge line segments for the page from the sets of perimeter points. These line segments are then combined to select the best rectangle enclosing the page, from which the skew angle is determined. The algorithm also determines a rotated bounding box enclosing the page. An innovation of the invention is the use of fuzzy logic, whereby several candidates for perimeter points, candidate edges, and bounding rectangles are determined in each step of the computation with associated confidence values and the final skew angle is selected by choosing the bounding rectangle with the highest confidence values.

Routing display facilitating task of removing error

Abstract: A layout editor apparatus draws line segments constituting a first interconnect line connecting between an output pin and a first input pin so as to draw the first interconnect line as a straight line formed of the line segments connected in a line extending from the output pin only in a first direction, and draws line segments constituting a second interconnect line connecting between a branch point and a second input pin so as to draw the second interconnect line as a straight line formed of the line segments connected in a line extending only in the first direction from a point that is displaced from the branch point on the first interconnect line in a second direction perpendicular to the first direction, wherein the displayed lengths of the line segments are proportional to their physical lengths, and the displayed widths of the line segments reflect their physical widths.

System and method of image processing, and scanning electron microscope

Abstract: A scanning electron microscope comprises an image processing system for carrying out a pattern matching between a first image and a second image. The image processing system comprises: a paint-divided image generator for generating a paint divided image based on the first image; a gravity point distribution image generator for carrying out a smoothing process of the paint divided image and generating a gravity point distribution image; an edge line segment group generation unit for generating a group of edge line segments based on the second image; a matching score calculation unit for calculating a matching score based on the gravity point distribution image and the group of edge line segments; and a maximum score position detection unit for detecting a position where the matching score becomes the maximum.

Robot controller and robot control method using spline interpolation

Abstract: A determining unit determines tangent vectors at one and the other end of one spline curve segment of each section such that a length of each tangent vector is proportional to that of a first straight line connecting one end and the other end of the one spline curve segment, and that the tangent vectors at one end and the other end of the one spline curve segment are directed to divide, by a predetermined ratio, a first angle and a second angle, respectively. The first angle is formed by the first straight line and an extension of a second straight line connecting one and the other ends of a previous spline curve segment. The second angle is formed by the fist straight line and an extension of a third straight line connecting one and the other ends of a next spline curve segment.

Method for handwritten character recognition, system for handwritten character recognition, program for handwritten character recognition and storing medium

Abstract: In a case in which handwritten character recognition such as online handwritten character recognition is implemented, simple and high performance character recognition by which transformation such as remarkable transformation and rotation is able to be treated and which recognizes an input that is written in a single stroke such as kaisho-writing, is provided Because of this, the present invention performs: capturing an input handwritten character with parameter representation for each stroke and applying a polygonal approximation to each stroke; assuming each polygonal line segment approximated by the polygonal approximation to be vector that reaches an end point from a start point, and obtaining an angle between an axis that becomes a reference and each line segment as a polygonal line segment angle sequence; obtaining an exterior angle sequence of vertices of the obtained polygonal line segments; making a sum of exterior angles of the same sign, where the same sign of plus or minus in the exterior angle sequence continues, to be a winding angle sequence; extracting a global feature according to each obtained sequence and a localized or quasi-localized feature in each curved portion divided corresponding to the winding angle sequence, hierarchically and divisionally; and performing the character recognition by comparing the extracted result with a template of an object character for recognition that is provided in advance