A Simple Method of Radial Distortion Correction with Centre of Distortion EstimationOutlineIntroductionModel and ApproachFurther DiscussionExperiments and ResultsConclusionsIntroductionLens distortion usually can be classified into three types :radial distortion (predominant)decentering distortionthin prism distortion
Wang, J., Shi, F., Zhang, J., Liu, Y.: A new calibration model and method of camera lens distortion.
Usually, a ideal pinhole model is assumed in vary algorithms based on camera geometry. In reality, however, most lenses suffer from small or large amounts of distortion.When the lens has a nonnegligible distortion, using the ideal pinhole model may result in high measurement error.
Radial distortion, whilst primarily dominated by low order radial components, can be corrected using Brown's distortion model. Brown's model caters for both radial distortion and for tangential distortion caused by physical elements in a lens not being perfectly aligned. The latter is thus also known as decentering distortion.
it is likely that the distortion function is totally dominatedby the radial components, and especially dominatedby the first term. It has also been found that any more elaboratedmodeling not only would not help (negligible whencompared with sensor quantization), but also would causenumerical instability.3IntroductionMethod of obtaining the parameters of the radial distortion function and correcting the images. These previous works can be divided roughly into two strategic approachesmultiple views methodSingle view method multiple views method (emphasize the necessity of determining the radial distortion center and give a novel algorithm to estimate center of distortion)Since the multiple views method doesnt need to know especial condition in the scene, for example, straight line, there is a wide application range of this class of method. But the disadvantage of such method is that it needs multiple images which are sometimes not available.
Single view method based on the using of distorted straight lines
4IntroductionCorrect the radial distortionFormer approachbased on the collinearity of undistorted points.Need the camera intrinsic parameters and 3D-point correspondences.This paperbased on single images and the conclusion that distorted points are concyclic and uses directly the distorted points.uses the constraint, that straight lines in the 3D world project to circular arcs in the image plane, under the single parameter Division Model5Model and ApproachRadial Distortion ModelsPMDM
Distorted straight line is a circlecalibration procedure to estimate the center and the parameter of the radial distortionCircle fitting : LSLMDescribes the radial distortion model calibration procedure.6Radial Distortion ModelsPM : 1. works best for lens with small distortions2. When distortion is large, may necessary to take into account many terms7Radial Distortion ModelsDM1. express high distortion at much lower order.
? In particular, for many cameras one parameter sufcesIn order to simplify the equation we suppose that the distorted centre P is the origin of the image coordinates system(distorted centre P image center) so we have
8Radial Distortion ModelsP (0,0)9 The Figure of Distorted Straight LineIt is a most intuitive approach to investigate the distortion of an image that is to observe the image of a straight line whether it is still straight.
10 The Figure of Distorted Straight LineEquation (10) : indicates that a group of parameter (A,B,C) can be determined by fitting a circle to a straight linewhich extracted from the image,
consequently we obtain aconstraint equation (11) of distorted centre P : So theoretically the coordinates (x0, y0) of distorted centre P would be obtained so long as we can extract three straight linefrom the image14 (x0,y0)15Sum up whole algorithm16Circle fittingIt is a very important step to fit circle above algorithm.data extracted from image are only short arcs, it is hard to reconstruct a circle from the incomplete data.
MethodDirect Least Squares Method of Circle Fitting (LS)Levenberg-Marquardt Method of Circle Fitting (LM)
Circle to fitDistorted centerDistorted straight lineIt is a very important step to fit circle above algorithm.Since the data extracted from image are only short arcs,it is hard to reconstruct a circle from the incomplete data.17Circle fitting - LSCircle fitting - LS Circle fitting - LM Circle fitting - LMFurther DiscussionOnly One Straight Line (L1)Only Two Straight Lines (L2)24Only Two Straight Lines (L2)25Only Two Straight Lines (L2)26Only Two Straight Lines (L2)27Non-square PixelsNon-square PixelsExperiments and Results
The first experiment on synthetic data compared themethods (LS and LM) presented in this paper with themethod CK, proposed by C. Brauer-Burchardt and K. Vossin , at various noise levels. Because of using the sameDM model, it is comparable. Results from 30 random trialsare shown in Fig. 1.30Experiments and Results
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ConclusionsAdvantageNeither information about the intrinsic camera parameters nor 3D-point correspondences are required.based on single image and uses the distorted positions of collinear points.Algorithm is simple, robust and non-iterative.DisadvantageIt needs straight lines are available in the scene.