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Polyhedral Geometry and the Two-Plane Parameterization [chapter]

Xianfeng Gu, Steven J. Gortler, Michael F. Cohen
1997 Eurographics  
These systems use the intersection points of the lines on two planes to parameterize the lines in space. This paper explores the structure of the two-plane parameterization in detail.  ...  More generally, in an n dimensional linear space, there are nk + n ; k 2 ; k degrees of freedom in choosing a k dimensional affine subset [11] .  ...  Words such as point, line, segment, and plane will describe sets in 3D geometric space.  ... 
doi:10.1007/978-3-7091-6858-5_1 fatcat:kf32ujiycnhqnkcusy4f5zmsoa

The 3D visibility complex : a new approach to the problems of accurate visibility [chapter]

Frédo Durand, George Drettakis, Claude Puech
1996 Eurographics  
In this paper we propose a new way of describing and studying the visibility of 3D space by a dual space of the 3D lines, such that all the visibility events are described.  ...  More recently analytic approaches efficiently encoding visibility have appeared for 2D (the visibility complex) and for certain limited cases in 3D (aspect graph, discontinuity meshes).  ...  Since such segments are collinear to the same line, they are projected on the same point in the 4D line dual space.  ... 
doi:10.1007/978-3-7091-7484-5_25 fatcat:lkeyv72nkrervpt36bvccrmbiq

Discrete analytical curve reconstruction without patches

Isabelle Sivignon, Rodolphe Breton, Florent Dupont, Eric Andrès
2005 Image and Vision Computing  
From a discrete 4-connected curve in 2D, or 6-connected curve in 3D, the proposed algorithms compute a polygonal line which digitization with the standard model is equal to all the pixels or voxels of  ...  The framework of this method is the discrete analytical geometry and parameter spaces are used in order to simplify the algorithms.  ...  (c) The solution p 0 k in the parameter space is a Euclidean line (in (a)) going through p 0 k .  ... 
doi:10.1016/j.imavis.2004.06.014 fatcat:n3gpwyh6ufb5tjgmx44qjvi5jm

Reversible Polygonalization of a 3D Planar Discrete Curve: Application on Discrete Surfaces [chapter]

Isabelle Sivignon, Florent Dupont, Jean-Marc Chassery
2005 Lecture Notes in Computer Science  
One 3D line in the Euclidean space E is represented by another 3D line in the parameter space P.  ...  3D line in the Euclidean Example of dual segments reductions according to the carrier plane P space.  ... 
doi:10.1007/978-3-540-31965-8_32 fatcat:mwxft6vlsffkvkmd6ywzblf2sy

Estimating motion and structure from correspondences of line segments between two perspective images

Zhengyou Zhang
1995 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The assumption we use is that two matched line segments contain the projection of a common part of the corresponding line segment in space, i.e. they overlap.  ...  We present in this paper an algorithm for determining 3D motion and structure from correspondences of line segments between two perspective images.  ...  Indeed, each line segment de nes a generalized triangle in space with the rst side passing through the optical center C and the starting point s of the line segment, the second side passing through C and  ... 
doi:10.1109/34.476506 fatcat:42pd37zmunhjtn6ujasxpbqmba

Reversible vectorisation of 3D digital planar curves and applications

Isabelle Sivignon, Florent Dupont, Jean-Marc Chassery
2007 Image and Vision Computing  
A dual space representation of lines and planes is used to ensure that the computed curve remains inside the digital curve, and this tool enables to define a very efficient algorithm.  ...  The proposed transformation also provides an analytical modelling of a digital plane segment as a discrete polygon composed of a face, edges and vertices.  ...  Similarly to the continuous case, modelling a DPC is done through the de- composition of the DPC into 3D digital line segments. 3D digital lines are also well-defined in the digital space according to  ... 
doi:10.1016/j.imavis.2006.06.022 fatcat:7fmoa24b3bduhhrimyew63z3y4

COMPACT - A Surface Representation Scheme

P. Grossman
1988 Procedings of the Alvey Vision Conference 1988  
Maximal sets of segments supporting different surfaces are then identified. In this we make a novel use of the Dual Space Representation.  ...  This paper describes the continuation of our work on extracting simple surfaces from a 3D line-segment representation of stereo image data.  ...  Thus a set of coplanar lines in space is mapped onto a set of lines intersecting in a single point in Dual Space.  ... 
doi:10.5244/c.2.15 dblp:conf/bmvc/Grossmann88 fatcat:6f7ueynrrfh5zbsk5sguourh64

Compact —a surface representation scheme

P Grossmann
1989 Image and Vision Computing  
Maximal sets of segments supporting different surfaces are then identified. In this we make a novel use of the Dual Space Representation.  ...  This paper describes the continuation of our work on extracting simple surfaces from a 3D line-segment representation of stereo image data.  ...  Thus a set of coplanar lines in space is mapped onto a set of lines intersecting in a single point in Dual Space.  ... 
doi:10.1016/0262-8856(89)90005-x fatcat:tezroveojrdq5ewmdc2qm7itua

Incremental Line-based 3D Reconstruction using Geometric Constraints

Manuel Hofer, Andreas Wendel, Horst Bischof
2013 Procedings of the British Machine Vision Conference 2013  
scoring in the image space.  ...  For each putative match we compute a 3D line segment K h by triangulating the corresponding 2D line segments from I 1 and I 2 . Each match results in a new hypothesis h ∈ H.  ...  The radius r space (h) is defined as the maximum distance betweenK h , and the infinite line passing through K h .  ... 
doi:10.5244/c.27.92 dblp:conf/bmvc/HoferWB13 fatcat:xceset27pnds5lbwkwmg72qhdi

Extraction and Simplification of Building Façade Pieces from Mobile Laser Scanner Point Clouds for 3D Street View Services

Yan Li, Qingwu Hu, Meng Wu, Jianming Liu, Xuan Wu
2016 ISPRS International Journal of Geo-Information  
, such as smart city management, autonomous navigation through the urban environment, fly-through rendering, 3D street view, virtual tourism, urban mission planning, etc.  ...  . urban environment, fly-through rendering, 3D street view, virtual tourism, urban mission planning, etc. [5, 6] .  ...  segmentation line, as shown in Figure 10  ... 
doi:10.3390/ijgi5120231 fatcat:ungalwwssvfdlkkqm4hx3kql5e

Barriers detection method for stereovision-based ACC systems

Tiberiu Marita
2009 2009 IEEE 5th International Conference on Intelligent Computer Communication and Processing  
The detected barrier objects are reported as 3D cuboids which are further tracked along with other objects/obstacles detected through a 3D points grouping method integrated in a multifunction application  ...  Therefore the proposed method combines the detection of the horizontal structure of a barrier's boom in the 2D grayscale image space using a Hough based approach followed by a series of 3D validation steps  ...  The horizontal line segments detected in 2D will be used as search regions for 3D points.  ... 
doi:10.1109/iccp.2009.5284778 fatcat:5fc3zwhrmjbj3ctj3dxf74grfe

Object-Based Integration of Photogrammetric and LiDAR Data for Automated Generation of Complex Polyhedral Building Models

Changjae Kim, Ayman Habib
2009 Sensors  
This research is concerned with a methodology for automated generation of polyhedral building models for complex structures, whose rooftops are bounded by straight lines.  ...  The performance of the developed methodology is evaluated through qualitative and quantitative analysis of the generated building models from real data.  ...  After this process, each matching pair will define a matched 3D line by determining the extreme points among the projected endpoints along the line bisecting the space between the two line segments in  ... 
doi:10.3390/s90705679 pmid:22346722 pmcid:PMC3274126 fatcat:uupyeaq6fvb37hi475u5lfe2zm

Twister Segment Morphological Filtering. A New Method for Live Zebrafish Embryos Confocal Images Processing

M.A. Luengo-Oroz, E. Faure, B. Lombardot, R. Sance, P. Bourgine, N. Peyrieras, A. Santos
2007 2007 IEEE International Conference on Image Processing  
It consists in filtering a 3D+time image with the opening by all the possible rotations of a segment in the 4D space, given an initial segment and a rotation angle.  ...  We propose an extension of the classical morphological filtering based on openings by line segment structuring elements.  ...  in the 3D space in the present time.  ... 
doi:10.1109/icip.2007.4379813 dblp:conf/icip/Luengo-OrozFLSBPS07 fatcat:2i7c4gcb3fharc2jehbhmv6aay

A Spiking Neural Model of HT3D for Corner Detection

Pilar Bachiller-Burgos, Luis J. Manso, Pablo Bustos
2018 Frontiers in Computational Neuroscience  
It uses a 3D parameter space that enables the detection of segments instead of whole lines.  ...  HT3D is a recent variant of the Hough transform for the combined detection of corners and line segments in images.  ...  HT3D employs a 3D Hough space that offers a compact representation of line segments.  ... 
doi:10.3389/fncom.2018.00037 pmid:29910720 pmcid:PMC5992504 fatcat:jwvz6cy4gzhxllek7m55tjjoqy

EDGE BASED 3D INDOOR CORRIDOR MODELING USING A SINGLE IMAGE

A. Baligh Jahromi, G. Sohn
2015 ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
Many scene layout hypotheses are created through intersecting random line segments and virtual rays of vanishing points.  ...  The straight line segments are extracted from the single image and the orthogonal vanishing points are estimated by employing the RANSAC approach.  ...  In addition, the authors wish to extend gratitude to Miss Mozhdeh Shahbazi and Mr. Kivanc Babacan, who consulted on this research.  ... 
doi:10.5194/isprsannals-ii-3-w5-417-2015 fatcat:yopsyd44dreghanabrdwo6nkfu
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