RATIONAL RADIAL DISTORTION MODELS OF CAMERA LENSES WITH ANALYTICAL SOLUTION FOR DISTORTION CORRECTION

2004 ◽  
Vol 01 (02) ◽  
pp. 135-147 ◽  
Author(s):  
LILI MA ◽  
YANGQUAN CHEN ◽  
KEVIN L. MOORE
Keyword(s):  
Analytical Solution ◽  
Polynomial Approximation ◽  
Distortion Correction ◽  
Camera Model ◽  
Distortion Model ◽  
Radial Distortion ◽  
New Class ◽  
Comparable Accuracy ◽  
The Common ◽  
Distortion Parameters

The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial distortion is to find a radial distortion model that allows easy undistortion as well as satisfactory accuracy. This paper presents a new class of rational radial distortion models with easy analytical undistortion formulae. Experimental results are presented to show that with this class of rational radial distortion models, satisfactory and comparable accuracy can be achieved.

scholarly journals HYPERBOLIC DISTORTION MODEL FOR RADIAL DISTORTION CORRECTION

2019 ◽  
Vol XLII-2/W13 ◽  
pp. 1667-1671
Author(s):  
G. B. Ikokou ◽  
J. Smit
Keyword(s):  
Mathematical Formulation ◽  
Distortion Correction ◽  
Wide Angle ◽  
Distortion Model ◽  
Radial Distortion ◽  
New Class ◽  
Image Shape ◽  
Straight Lines ◽  
Positive Coefficients ◽  
The Impact

<p><strong>Abstract.</strong> When information derived from the imagery is used for metric purposes and not as communication tools the impact of small imaging errors can be significant on the accuracy of derived information. As the number of photogrammetry applications grows and the technology advances, camera calibration becomes more complex. In fact, most lenses suffer from at least one kind of distortion profile such as barrel, pincushion or ‘moustache’ profiles. Commonly observed on wide angle lenses, barrel distortions curve straight lines inwards to give the image shape of barrel, however most lenses are prone to more than one distortion profile. Proposals for lens correction have been made using line-based approaches as well as division and rational models. The limitations of some of the techniques include the very limited number of distortion profiles they can handle due to their mathematical formulations. For example some can only handle distortion with positive coefficients and would exhibit instabilities when dealing with barrel distortions describe by negative distortion coefficients. In this paper we propose a new class of hyperbolic radial distortion model which handles several distortion profiles. The mathematical formulation of the new approach offers stability of the model since it can handle both positive and negative distortion coefficients -an improvement on some of the current techniques. The calibration results show that the approach produced the best distortion coefficients <i>k</i><sub>1</sub> and <i>k</i><sub>2</sub>. The model can handle distortions from panorama imagery as well as ‘moustache ’profile produced by wide angle lenses.</p>

scholarly journals ANALYTICAL SOLUTION OF THE FREQUENCY OF THE LOAD OSCILLATION AT AN ARBITRARY GIRDER NODE IN THE SYSTEM MAPLE

2019 ◽  
pp. 3-3
Author(s):  
Mikhail N. Kirsanov ◽  
Dmitriy V. Tinkov
Keyword(s):  
Analytical Solution ◽  
Arbitrary Number ◽  
Analytical Form ◽  
Labor Costs ◽  
Induction Method ◽  
Regular Type ◽  
Final Formula ◽  
The Common ◽  
Two Stages ◽  
Elastic Lattice

Introduction. We study the oscillations of a massive load on a planar statically definable symmetric truss of a regular type with parallel belts. Truss weight is not included. Free vertical oscillations are considered. The stiffness of the truss rods is assumed to be the same, the deformations are elastic. Lattice of the truss is double with descending braces and racks. New in the formulation and solution of the problem is the analytical form of the solution, which makes it possible in practice to easily evaluate the frequency characteristics of the structure depending on an arbitrary number of truss panels and the location of the load. Materials and methods. The operators and methods of the system of computer mathematics Maple are used. To determine the forces in the rods, the knotting method is used. The common terms of the sequence of coefficients of solutions for different numbers of panels are obtained from solving linear homogeneous recurrent equations of various order, obtained by special operators of the Maple system. Dependence on two arbitrary natural parameters is revealed in two stages. First, solutions for fixed load positions are found, then these solutions are summarized into one final formula for frequency. Results. By a series of individual solutions to the problem of load oscillation using the double induction method, it was possible to find common members of all sequences. The solution is polynomial in both natural parameters. Graphs constructed for particular cases, showed the adequacy of the approach. The discontinuous non-monotonic nature of the intermittent change depending on the number of truss panels and some other features of the solution are noted. Conclusions. It is shown that the induction method, previously applicable mainly to statics problems with one parameter (number of truss panels), is fully operational to the problems of the oscillations of system with two natural parameters. It should be noted that significant labor costs and a significant increase in the time symbolic transformations in such tasks

Compression Ultrasonography of the Leg Veins in Patients with Clinically Suspected Pulmonary Embolism

2000 ◽  
Vol 84 (12) ◽  
pp. 973-976 ◽  
Author(s):  
Bernd-Jan Sanson ◽  
Harry Büller ◽  
Dees P. Brandjes ◽  
Melvin Mac Gillavry ◽  
Keyword(s):  
Pulmonary Embolism ◽  
Femoral Vein ◽  
Suspected Pulmonary Embolism ◽  
Common Femoral Vein ◽  
Comparable Accuracy ◽  
The Common ◽  
Point Compression ◽  
Multi Center Study ◽  
Additional Value ◽  
Compression Ultrasonography

SummaryWe performed a multi-center study in consecutive patients with suspected pulmonary embolism to compare the diagnostic accuracy of a two-point compression ultrasonography (only the common femoral vein and popliteal vein) with an extensive examination of compressibility (from the common femoral vein until the trifurcation of calf veins). A total of 479 patients underwent the two-point compression ultrasonography. The prevalence of pulmonary embolism was 32%. The sensitivity and specificity of this procedure were 23% (95% CI 19-26) and 98% (95% CI 96-99), respectively. Extensive compression ultrasonography was performed in 461 (96%) of these 479 patients and showed comparable accuracy indices (sensitivity 25%, 95% CI 20-28 and specificity 97%, 95% CI 95-99). We conclude that compression ultrasonography has a limited sensitivity for the detection of thrombosis in patients with acute pulmonary embolism within 24 h of presentation. A more extensive assessment of compressibility of the leg veins in these patients has no additional value as compared to the two-point assessment.

scholarly journals DoF-Dependent and Equal-Partition Based Lens Distortion Modeling and Calibration Method for Close-Range Photogrammetry

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5934
Author(s):  
Xiao Li ◽  
Wei Li ◽  
Xin’an Yuan ◽  
Xiaokang Yin ◽  
Xin Ma
Keyword(s):  
Optical Axis ◽  
Focal Length ◽  
Calibration Method ◽  
Depth Of Field ◽  
Model Parameters ◽  
Lens Distortion ◽  
Camera Model ◽  
Distortion Model ◽  
Manual Adjustment ◽  
Close Range

Lens distortion is closely related to the spatial position of depth of field (DoF), especially in close-range photography. The accurate characterization and precise calibration of DoF-dependent distortion are very important to improve the accuracy of close-range vision measurements. In this paper, to meet the need of short-distance and small-focal-length photography, a DoF-dependent and equal-partition based lens distortion modeling and calibration method is proposed. Firstly, considering the direction along the optical axis, a DoF-dependent yet focusing-state-independent distortion model is proposed. By this method, manual adjustment of the focus and zoom rings is avoided, thus eliminating human errors. Secondly, considering the direction perpendicular to the optical axis, to solve the problem of insufficient distortion representations caused by using only one set of coefficients, a 2D-to-3D equal-increment partitioning method for lens distortion is proposed. Accurate characterization of DoF-dependent distortion is thus realized by fusing the distortion partitioning method and the DoF distortion model. Lastly, a calibration control field is designed. After extracting line segments within a partition, the de-coupling calibration of distortion parameters and other camera model parameters is realized. Experiment results shows that the maximum/average projection and angular reconstruction errors of equal-increment partition based DoF distortion model are 0.11 pixels/0.05 pixels and 0.013°/0.011°, respectively. This demonstrates the validity of the lens distortion model and calibration method proposed in this paper.

Robust Multibit Image Watermarking Based on Contrast Modulation and Affine Rectification

2019 ◽  
Vol 33 (14) ◽  
pp. 1954036
Author(s):  
Xin Zhong ◽  
Frank Y. Shih
Keyword(s):  
Image Processing ◽  
Lower Bound ◽  
State Of The Art ◽  
Image Watermarking ◽  
Center Of Mass ◽  
Experimental Results ◽  
Superior Performance ◽  
The Common ◽  
Distortion Parameters ◽  
Watermarking Scheme

In this paper, we present a robust multibit image watermarking scheme to undertake the common image-processing attacks as well as affine distortions. This scheme combines contrast modulation and effective synchronization for large payload and high robustness. We analyze the robustness, payload, and the lower bound of fidelity. Regarding watermark resynchronization under affine distortions, we develop a self-referencing rectification method to detect the distortion parameters for reconstruction by the center of mass in affine covariant regions. The effectiveness and advantages of the proposed scheme are confirmed by experimental results, which show the superior performance as comparing against several state-of-the-art watermarking methods.

Uncertainty Estimation for the Optical System of Optical Measuring Machines

2014 ◽  
Vol 615 ◽  
pp. 95-101
Author(s):  
Jesús Caja ◽  
Emilio Gómez ◽  
Piera Maresca ◽  
Miguel Berzal
Keyword(s):  
Optical System ◽  
Calibration Procedure ◽  
Uncertainty Estimation ◽  
Geometric Distortion ◽  
Camera Model ◽  
Optical Measuring ◽  
The Monte Carlo Method ◽  
Measuring Machine ◽  
Machine Calibration ◽  
Distortion Parameters

This paper presents the problem of optical measuring machine calibration, emphasizing the calibration of the "optical system", omitting the calibration of the "machine system". The calibration of an optical measuring machine is the first step before using the instrument for any application. For this purpose, a mathematical model has been developed to transform the coordinates of a point in space (3D) into coordinates of a point in an image (2D). Using this camera model, a calibration procedure has been developed using a grid distortion pattern. Finally, a procedure for calculating the uncertainty of the camera and geometric distortion parameters based on the Monte Carlo method has been developed.

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