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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.
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.
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.
14235163
Robust controllability of interval fractional order linear time invariant systems
We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in state-space form. We revisit the controllability problem for the case when there is no interval uncertainty. It turns out that the controllability check for FO-LTI systems amounts to checking the controllability of conventional integer order state space. Based on this fact, we further show that, for interval FO-LTI systems, the key is to check the linear dependency of a set of interval vectors. Illustrative examples are presented.
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.
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.
13128744
Bayesian Networks for Knowledge-Based Authentication
Knowledge-based authentication (KBA) has gained prominence as a user authentication method for electronic transactions. This paper presents a Bayesian network model of KBA grounded in probabilistic reasoning and information theory. The probabilistic semantics of the model parameters naturally lead to the definitions of two key KBA metrics-guessability and memorability. The statistical modeling approach allows parameter estimation using methods such as the maximum likelihood estimator (MLE). The information-theoretic view helps to derive the closed-form solutions to estimating the guessability and guessing entropy metrics. The results related to KBA metrics and the models under different attacking strategies and factoid distributions are unified under a game-theoretic framework that yields lower and upper bounds of optimal guessability. The paper also proposes a methodology for implementing a Bayesian network-based KBA system. Further, an empirical evaluation of the relative merits of two Bayesian network structures for KBA, the Naive Bayes (NB) and the Tree Augmented Naive Bayes (TAN), confirms the hypothesis that the TAN structure is superior in terms of authentication accuracy and error rates. The results of the theoretical analysis and the empirical study provide insights into the KBA design problem and establish a foundation for future research in the KBA area.
16649809
Relative difference sets fixed by inversion and Cayley graphs
Using graph theoretical technique, we present a construction of a (30, 2, 29, 14)-relative difference set fixed by inversion in the smallest finite simple group--the alternating group A5. To our knowledge this is the first example known of relative difference sets in the finite simple groups with a non-trivial forbidden subgroup. A connection is then established between some relative difference sets fixed by inversion and certain antipodal distance-regular Cayley graphs. With the connection, several families of antipodal distance-regular Cayley graphs which are coverings of complete graphs are presented.
14540904
Camera calibration with a motorized zoom lens
This paper presents a simple and efficient method of calibrating the intrinsic camera parameters for all the lens settings of a motorized zoom lens. We fix the aperture setting and perform the camera calibration, adaptively, over the ranges of the room and focus settings. Bilinear interpolation is used to provide the values of the intrinsic camera parameters for those lens settings where no observations are taken. Our experiments show that the proposed method can provide accurate intrinsic camera parameters for all the lens settings, even though camera calibration is performed only for a small number of sampled lens settings. A calibration object suitable for zoom lens calibration is also presented.
31930663
Minimization of resource consumption for multidatabase query optimization
Due to the autonomy of individual databases, a multidatabase system (MDBS) has no control over the task execution within each database system. This complicates the issue of query optimization in a MDBS. Past researchers tackled this problem mainly by regenerating the cost model of each participating database systems. However a completely autonomous participating database system does nor own the information (data) as well as the mechanism (software) for converting data of one database to another to resolve the data type conflict problems that can occur in any MDBS environment. In addition, unpredictable factors that can drastically deviate the accuracy of a regenerated cost model (in the past research) come into play at unknown time. This confines the processing of an intersite operation (such as a join over two relations of different databases) to the MDBS only. The participating database systems will not be able to share the workload of the MDBS under this circumstance. Hence, minimizing the consumption of system resources of the MDBS is an urgent problem. The authors propose three scheduling algorithms that are used in the MDBS to reduce the processing cost of a multidatabase query. A major difference between the strategies and the past methods is that ours do not require the knowledge of the cost models of the participating databases.
10148394
Generating C Code from LOGS Specifications
This paper introduces a tool that automatically translates a concrete form of specifications into C code linked with BSPlib. The translation tool is rigorously developed with important safety properties proved. A Logs specification for Bulk-Synchronous Parallelism is a relation of an initial state, a final state and some intermediate states. Nondeterminism and parallelism correspond to disjunction and conjunction respectively. Various advanced specification commands can be derived from the basic ones. The translator checks syntax, freedom of communication interference, type consistency and communication dependencies before generating the target code. Static analysis (including both static checkings and translation) is presented in abstract interpretation. It is shown that a few laws are complete for transforming any specification into a normal form. These laws are satisfied by the abstract functions. We demonstrate the actual effects of the abstract functions by applying them on the normal form. The approach has been implemented using an object-oriented language.