scholarly journals Build 3D Abstractions with Wireframes

2021 ◽  
Author(s):  
Roi Santos Mateos ◽  
Xose M. Pardo ◽  
Xose R. Fdez-Vidal
Keyword(s):  
Structural Information ◽  
Morphological Changes ◽  
Ground Truth ◽  
Optimization Methods ◽  
Straight Line Segment ◽  
Epipolar Constraint ◽  
Line Segments ◽  
Straight Line ◽  
Straight Lines ◽  
3D Representations

This chapter serves as an introduction to 3D representations of scenes or Structure From Motion (SfM) from straight line segments. Lines are frequently found in captures of man-made environments, and in nature are mixed with more organic shapes. The inclusion of straight lines in 3D representations provide structural information about the captured shapes and their limits, such as the intersection of planar structures. Line based SfM methods are not frequent in the literature due to the difficulty of detecting them reliably, their morphological changes under changes of perspective and the challenges inherent to finding correspondences of segments in images between the different views. Additionally, compared to points, lines add the dimensionalities carried by the line directions and lengths, which prevents the epipolar constraint to be valid along a straight line segment between two different views. This chapter introduces the geometrical relations which have to be exploited for SfM sketch or abstraction based on line segments, the optimization methods for its optimization, and how to compare the experimental results with Ground-Truth measurements.

Planar Lattices

1975 ◽  
Vol 27 (3) ◽  
pp. 636-665 ◽  
Author(s):  
David Kelly ◽  
Ivan Rival
Keyword(s):  
Line Segment ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Straight Line Segment ◽  
Line Segments ◽  
Small Circle ◽  
Partially Ordered ◽  
Straight Line ◽  
Finite Partially Ordered Set ◽  
Planar Lattices

A finite partially ordered set (poset) P is customarily represented by drawing a small circle for each point, with a lower than b whenever a < b in P, and drawing a straight line segment from a to b whenever a is covered by b in P (see, for example, G. Birkhoff [2, p. 4]). A poset P is planar if such a diagram can be drawn for P in which none of the straight line segments intersect.

Three-dimensional extension of Bresenham's algorithm and its application in straight-line interpolation

2002 ◽  
Vol 216 (3) ◽  
pp. 459-463 ◽  
Author(s):  
X-W Liu ◽  
K Cheng
Keyword(s):  
Line Segment ◽  
Three Dimensional ◽  
Straight Line Segment ◽  
Numerical Control ◽  
Interpolation Algorithm ◽  
Straight Line ◽  
Actual Error ◽  
Potential Applications ◽  
Sample Position ◽  
Straight Lines

Conventional straight-line generating algorithms, such as the digital differential analyser (DDA), Bresenham's algorithm and the mid-point algorithm, are suitable only for planer straight lines on the coordinate planes, of which Bresenham's algorithm is the most efficient. In this paper, the authors have extended Bresenham's algorithm to spatial straight lines. Given a spatial straight-line segment with two end-points, the authors have applied Bresenham's algorithm to the projections of the line segment on two of the three coordinate planes, which is determined by the largest of the coordinate lengths of the line segment, thereby obtaining a three-dimensional extension of the algorithm. In a case study, the authors calculated the distance between each sample position and the given line segment. The result reveals that the actual error at each sample position is smaller than the maximum theoretical error, and the performance of the three-dimensional extension of Bresenham's algorithm is as good as that of Bresenham's original planer algorithm. One of its potential applications is the three-dimensional step straight-line interpolation used in computer numerical control (CNC) systems of machine tools and rapid prototyping machines. Application of the algorithm is contrasted with that of the traditional DDA step straight-line interpolation algorithm. The result confirms that the three-dimensional extension of Bresenham's algorithm is much better than the DDA straight-line interpolation algorithm.

The Calculation of the Magnetic Field Produced by an Arbitrary Shaped Current-Carrying Wire in its Plane

2013 ◽  
Vol 756-759 ◽  
pp. 3687-3691 ◽  
Author(s):  
Zhou Yu ◽  
Chang Han Xiao ◽  
Huan Wang ◽  
Yao Zhong Zhou
Keyword(s):  
Magnetic Field ◽  
Straight Line Segment ◽  
Computational Time ◽  
Improved Method ◽  
New Approach ◽  
Line Segments ◽  
Steady Current ◽  
Straight Line ◽  
Coordinate Rotation ◽  
The Magnetic Field

Instead of performing the integration explicitly to calculate the magnetic field from an arbitrary shaped wire, an improved method was proposed. The magnetic field generated by a straight line segment carrying steady current was calculated based on the Biot-Savart law. The new approach is to break the wire down into a number of straight line segments in its plane. According to the principle of vector superposition and coordinate rotation, the magnetic field from the complete current wire can then be calculated by summing the contribution from each of the separate straight line pieces. The simulation results show that the proposed numerical method has high accuracy and faster computational time and is efficient and convenient to the application in projects.

A Method of Multi-View Images 3D Restructuring of Discrete Line Segments

2014 ◽  
Vol 644-650 ◽  
pp. 2359-2365
Author(s):  
Xiao Bo Lin
Keyword(s):  
Renewal Process ◽  
Analytical Method ◽  
High Efficiency ◽  
Target Function ◽  
Optimal Result ◽  
Simulation Data ◽  
Linear Restriction ◽  
Line Segments ◽  
Straight Line ◽  
Straight Lines

In this paper, the average reprojection geometrical errors on all images of a spatial straight line is taken as the restructuring and optimization target function to ensure the optimal result to be acquired; a spatial straight line is expressed by use of the Plücker coordinates for the proposal of the analytical method of correcting the double linear restriction on the Plücker coordinates of noise-included spatial straight lines; during the optimization process, to ensure parameters that meet double linear restriction, the iteration renewal process is expressed by at least 4 parameters, to increase the precision of restructuring results. Experiments results derived from simulation data and real images have all demonstrated the high efficiency and precision of the algorithm proposed in this paper.

scholarly journals Digital straight lines in the Khalimsky plane

2005 ◽  
Vol 96 (1) ◽  
pp. 49 ◽  
Author(s):  
Erik Melin
Keyword(s):  
Line Segment ◽  
Straight Line Segment ◽  
Integer Points ◽  
Straight Line ◽  
Digital Plane ◽  
Straight Lines ◽  
Khalimsky Topology

We consider the digital plane of integer points equipped with the Khalimsky topology. We suggest a digitization of straight lines such that the digitized image is homeomorphic to the Khalimsky line and a digitized line segment is a Khalimsky arc. It is demonstrated that a Khalimsky arc is the digitization of a straight line segment if and only if it satisfies a generalized version of the chord property introduced by Rosenfeld.

Optical equiphase filter approximation using segments of straight lines

1985 ◽  
Vol 63 (2) ◽  
pp. 246-249
Author(s):  
M. Lévesque ◽  
G. April ◽  
H. H. Arsenault
Keyword(s):  
Wave Front ◽  
Phase Distribution ◽  
Complex Amplitude ◽  
Optimum Length ◽  
Line Segments ◽  
Phase Filter ◽  
Straight Line ◽  
Arbitrary Phase ◽  
Filter Approximation ◽  
Straight Lines

Phase filters may be used to modify the phase distribution on a wave front in order to correct distortions on the wave front or to create arbitrary phase distributions. Under certain conditions, the phase filter may be made by plotting the equiphases of the complex amplitude as lines of equal width, which may be done with a simple digital plotter. Such equiphase filters cause two types of problems: the overlapping of diffraction orders and the additional aberrations introduced when the equiphases are approximated by segments of straight lines plotted by a computer. The parameters that determine the useful field of the filtered phase distribution and the aberrations introduced by the filter are used to obtain an expression for the optimum length of the straight line segments that approximate the curved equiphases.

Reasoning with uncertain points, straight lines, and straight line segments in 2D

2009 ◽  
Vol 64 (2) ◽  
pp. 125-139 ◽  
Author(s):  
Jochen Meidow ◽  
Christian Beder ◽  
Wolfgang Förstner
Keyword(s):  
Line Segments ◽  
Straight Line ◽  
Straight Lines

scholarly journals Uncertainty Analysis of 3D Line Reconstruction in a New Minimal Spatial Line Representation

2020 ◽  
Vol 10 (3) ◽  
pp. 1096
Author(s):  
Hang Zhou ◽  
Keju Peng ◽  
Dongxiang Zhou ◽  
Weihong Fan ◽  
Yunhui Liu
Keyword(s):  
Uncertainty Analysis ◽  
Structural Information ◽  
Ground Truth ◽  
Image Sequences ◽  
Compact Representation ◽  
Simulation Data ◽  
Line Segments ◽  
Urban Scenes ◽  
Reprojection Error ◽  
World Image

Line segments are common in urban scenes and contain rich structural information. However, different from point-based reconstruction, reconstructed 3D lines may have large displacement from the ground truth in spite of a very small sum of reprojection error. In this work, we present a method to analyze the uncertainty of line reconstruction and provide a quantitative evaluation of accuracy. A new minimal four-vector line representation based on Plücker line is introduced, which is tailed for uncertainty analysis of line reconstruction. Each component of the compact representation has a certain physical meaning about the 3D line’s orientation or position. The reliability of the reconstructed lines can be measured by the confidence interval of each component in the proposed representation. Based on the uncertainty analysis of two-view line triangulation, the uncertainty of multi-view line reconstruction is also derived. Combining the proposed uncertainty analysis with reprojection error, a more reliable 3D line map can be obtained. Experiments on simulation data, synthetic and real-world image sequences validate the feasibility of the proposed method.

Automatic Tread Gaging Machine

1979 ◽  
Vol 7 (1) ◽  
pp. 31-39
Author(s):  
G. S. Ludwig ◽  
F. C. Brenner
Keyword(s):  
Experimental Tests ◽  
Automatic Machine ◽  
Wear Rates ◽  
Handling Device ◽  
Straight Line ◽  
Component Systems ◽  
Before And After ◽  
Good Repeatability ◽  
The Difference ◽  
Straight Lines

Abstract An automatic tread gaging machine has been developed. It consists of three component systems: (1) a laser gaging head, (2) a tire handling device, and (3) a computer that controls the movement of the tire handling machine, processes the data, and computes the least-squares straight line from which a wear rate may be estimated. Experimental tests show that the machine has good repeatability. In comparisons with measurements obtained by a hand gage, the automatic machine gives smaller average groove depths. The difference before and after a period of wear for both methods of measurement are the same. Wear rates estimated from the slopes of straight lines fitted to both sets of data are not significantly different.

A NOVEL EXTENSIVE EX-VIVO OCT DATABASE FROM MURINE MODELS OF COLORECTAL CANCER

2021 ◽  
Vol 108 (Supplement_3) ◽  
Author(s):  
J Bote ◽  
J F Ortega-Morán ◽  
C L Saratxaga ◽  
B Pagador ◽  
A Picón ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Machine Learning ◽  
Structural Information ◽  
Ex Vivo ◽  
Ground Truth ◽  
Colon Polyps ◽  
Learning Methods ◽  
Non Invasive ◽  
Machine Learning Methods ◽  
In Situ Methods

Abstract INTRODUCTION New non-invasive technologies for improving early diagnosis of colorectal cancer (CRC) are demanded by clinicians. Optical Coherence Tomography (OCT) provides sub-surface structural information and offers diagnosis capabilities of colon polyps, further improved by machine learning methods. Databases of OCT images are necessary to facilitate algorithms development and testing. MATERIALS AND METHODS A database has been acquired from rat colonic samples with a Thorlabs OCT system with 930nm centre wavelength that provides 1.2KHz A-scan rate, 7μm axial resolution in air, 4μm lateral resolution, 1.7mm imaging depth in air, 6mm x 6mm FOV, and 107dB sensitivity. The colon from anaesthetised animals has been excised and samples have been extracted and preserved for ex-vivo analysis with the OCT equipment. RESULTS This database consists of OCT 3D volumes (C-scans) and 2D images (B-scans) of murine samples from: 1) healthy tissue, for ground-truth comparison (18 samples; 66 C-scans; 17,478 B-scans); 2) hyperplastic polyps, obtained from an induced colorectal hyperplastic murine model (47 samples; 153 C-scans; 42,450 B-scans); 3) neoplastic polyps (adenomatous and adenocarcinomatous), obtained from clinically validated Pirc F344/NTac-Apcam1137 rat model (232 samples; 564 C-scans; 158,557 B-scans); and 4) unknown tissue (polyp adjacent, presumably healthy) (98 samples; 157 C-scans; 42,070 B-scans). CONCLUSIONS A novel extensive ex-vivo OCT database of murine CRC model has been obtained and will be openly published for the research community. It can be used for classification/segmentation machine learning methods, for correlation between OCT features and histopathological structures, and for developing new non-invasive in-situ methods of diagnosis of colorectal cancer.

Sign in / Sign up

Export Citation Format

Share Document