712
Rational Radial Distortion Models with Analytical Undistortion Formulae
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 is achieved.
18628154
A Family of Simplified Geometric Distortion Models for Camera Calibration
The commonly used radial distortion model for camera calibration is in fact an assumption or a restriction. In practice, camera distortion could happen in a general geometrical manner that is not limited to the radial sense. This paper proposes a simplified geometrical distortion modeling method by using two different radial distortion functions in the two image axes. A family of simplified geometric distortion models is proposed, which are either simple polynomials or the rational functions of polynomials. Analytical geometric undistortion is possible using two of the distortion functions discussed in this paper and their performance can be improved by applying a piecewise fitting idea. Our experimental results show that the geometrical distortion models always perform better than their radial distortion counterparts. Furthermore, the proposed geometric modeling method is more appropriate for cameras whose distortion is not perfectly radially symmetric around the center of distortion.
1374
Flexible camera calibration using a new analytical radial undistortion formula with application to mobile robot localization
Most algorithms in 3D computer vision rely on the pinhole camera model because of its simplicity, whereas virtually all imaging devices introduce a certain amount of nonlinear distortion, where the radial distortion is the most severe part. 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 radial distortion model with an easy analytical undistortion formula, which also belongs to the polynomial approximation category. Experimental results are presented to show that with this radial distortion model, satisfactory accuracy is achieved. An application of the new radial distortion model is non-iterative yellow line alignment with a calibrated camera on ODIS, a robot built in our CSOIS.
3264554
An Analytical Piecewise Radial Distortion Model for Precision Camera Calibration
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 article presents a new piecewise radial distortion model with easy analytical undistortion formula. The motivation for seeking a piecewise radial distortion model is that, when a camera is resulted in a low quality during manufacturing, the nonlinear radial distortion can be complex. Using low order polynomials to approximate the radial distortion might not be precise enough. In contrast, higher order polynomials suffer from the inverse problem. With the new piecewise radial distortion function, more flexibility is obtained and the radial undistortion can be performed analytically. Experimental results are presented to show that with this new piecewise radial distortion model, better performance can be achieved than using the single function. Further, a comparable performance with the conventional polynomial model using two coefficients can also be accomplished.
669399
Camera Calibration: a USU Implementation
The task of camera calibration is to estimate the intrinsic and extrinsic parameters of a camera model. Though there are some restricted techniques to infer the 3-D information about the scene from uncalibrated cameras, effective camera calibration procedures will open up the possibility of using a wide range of existing algorithms for 3-D reconstruction and recognition. The applications of camera calibration include vision-based metrology, robust visual platooning and visual docking of mobile robots where the depth information is important.
5638961
Blind Detection and Compensation of Camera Lens Geometric Distortions
Author(s): Ma, Lili; Chen, YangQuan; Moore, Kevin L | Abstract: This paper presents a blind detection and compensation technique for camera lens geometric distortions. The lens distortion introduces higher-order correlations in the frequency domain and in turn it can be detected using higher-order spectral analysis tools without assuming any specific calibration target. The existing blind lens distortion removal method only considered a single-coefficient radial distortion model. In this paper, two coefficients are considered to model approximately the geometric distortion. All the models considered have analytical closed-form inverse formulae.
6045052
Basis pursuit for tracking
This paper introduces a novel adaptive texture feature selection algorithm for tracking. Specifically, we provide a statistical wavelet basis paradigm to maximally separate statistical characteristics of the object-in-interest and its background. The algorithm is based upon nonlinearly selecting basis elements out of dual dictionaries in an iterative fashion to continually improve a cost function that is suitable for tracking. We demonstrate that such a selection is effective with several difficult sequences that are affected by lighting changes, occlusion and background motion.
17642380
Evolutionary Modeling of Ordinary Differential Equations for Dynamic Systems
This paper presents a new idea of modeling one-dimensional dynamic systems by higher-order ordinary differential equation (HODE) models in stead of by the ARMA models used in the traditional time series analysis. Accordingly, based on the idea of hybrid evolutionary modeling, we modify the HEMA algorithm in (Cao et al., 1998a; Cao et al., 1998b) to approach the modeling problem of HODEs for dynamic systems. Two applications of time series are used to demonstrate its effectiveness and advantages.
17662809
Hierarchical Organisation of Predicate-Semantic Models
This paper introduces techniques to organise predicate- semantic models in a hierarchical structure so that a new model can inherit the laws of the existing ones. Generic composition is used to simplify the manipulation of predicates. Necessary restrictions are imposed on the definition of each model so that the inheritance relation can be established by checking a few conditions on the healthiness conditions and the commands. Much of the checking can be supported by laws of generic composition. The techniques also help simplify the proof of well-definedness of program combinators (i.e. their closure in the semantic space) so that we no longer need to prove it (in predicate calculus) for every new model.
46601989
Analysis of Lotka's law: The Simon-Yule approach
Abstract A major difficulty in using the well-known Lotka's law in information science is in the estimation of parameters. In this paper, we argue that the difficulty arises from the misuse of goodness-of-fit tests. As an alternative, we adopt Simon's five-step modeling process for the study of Lotka's law. Three significant contributions can be identified. First, an index approach is used to identify a general formulation of Lotka's law. Second, a time series approach is used to identify two influential variables associated with the empirical data. Third, the constructive mechanism proposed by Simon is used to derive a distribution resembling the general formulation of Lotka's law. Further research on refining the constructive mechanism is suggested.
8351589
Using automatic clustering to produce high-level system organizations of source code
We describe a collection of algorithms that we developed and implemented to facilitate the automatic recovery of the modular structure of a software system from its source code. We treat automatic modularization as an optimization problem. Our algorithms make use of traditional hill-climbing and genetic algorithms.