A Full Scale Camera Calibration Technique with Automatic Model Selection – Extension and Validation

This thesis presents work on the testing and development of a complete camera calibration approach which can be applied to a wide range of cameras equipped with normal, wide-angle, fish-eye, or telephoto lenses. The full scale calibration approach estimates all of the intrinsic and extrinsic parameters. The calibration procedure is simple and does not require prior knowledge of any parameters. The method uses a simple planar calibration pattern. Closed-form estimates for the intrinsic and extrinsic parameters are computed followed by nonlinear optimization. Polynomial functions are used to describe the lens projection instead of the commonly used radial model. Statistical information criteria are used to automatically determine the complexity of the lens distortion model. In the first stage experiments were performed to verify and compare the performance of the calibration method. Experiments were performed on a wide range of lenses. Synthetic data was used to simulate real data and validate the performance. Synthetic data was also used to validate the performance of the distortion model selection which uses Information Theoretic Criterion (AIC) to automatically select the complexity of the distortion model. In the second stage work was done to develop an improved calibration procedure which addresses shortcomings of previously developed method. Experiments on the previous method revealed that the estimation of the principal point during calibration was erroneous for lenses with a large focal length. To address this issue the calibration method was modified to include additional methods to accurately estimate the principal point in the initial stages of the calibration procedure. The modified procedure can now be used to calibrate a wide spectrum of imaging systems including telephoto and verifocal lenses. Survey of current work revealed a vast amount of research concentrating on calibrating only the distortion of the camera. In these methods researchers propose methods to calibrate only the distortion parameters and suggest using other popular methods to find the remaining camera parameters. Using this proposed methodology we apply distortion calibration to our methods to separate the estimation of distortion parameters. We show and compare the results with the original method on a wide range of imaging systems

A Factorization Based Self-Calibration for Radially Symmetric Cameras

The paper proposes a novel approach for planar selfcalibration of radially symmetric cameras. We model these camera images using notions of distortion center and concentric distortion circles around it. The rays corresponding to pixels lying on a single distortion circle form a right circular cone. Each of these cones is associated with two unknowns; optical center and focal length (opening angle). In the central case, we consider all distortion circles to have the same optical center, whereas in the non-central case they have different optical centers lying on the same optical axis. Based on this model we provide a factorization based self-calibration algorithm for planar scenes from dense image matches. Our formulation provides a rich set of constraints to validate the correctness of the distortion center. We also propose possible extensions of this algorithm i

Application for photogrammetry of organisms

Single-camera photogrammetry is a well-established procedure to retrieve quantitative information from objects using photography. In biological sciences, photogrammetry is often applied to aid in morphometry studies, focusing on the comparative study of shapes and organisms. Two types of photogrammetry are used in morphometric studies: 2D photogrammetry, where distance and angle measurements are used to quantitatively describe attributes of an object, and 3D photogrammetry, where data on landmark coordinates are used to reconstruct an object true shape. Although there are excellent software tools for 3D photogrammetry available, software specifically designed to aid in the somewhat simpler 2D photogrammetry are lacking. Therefore, most studies applying 2D photogrammetry, still rely on manual acquisition of measurements from pictures, that must then be scaled to an appropriate measuring system. This is often a laborious multistep process, on most cases utilizing diverse software to complete different tasks. In addition to being time-consuming, it is also error-prone since measurement recording is often made manually. The present work aimed at tackling those issues by implementing a new cross-platform software able to integrate and streamline the photogrammetry workflow usually applied in 2D photogrammetry studies. Results from a preliminary study show a decrease of 45% in processing time when using the software developed in the scope of this work in comparison with a competing methodology. Existing limitations and future work towards improved versions of the software are discussed.Fotogrametria em câmera única é um procedimento bem estabelecido para recolher dados quantitativos de objectos através de fotografias. Em biologia, fotogrametria é frequentemente aplicada no contexto de estudos morfométricos, focando-se no estudo comparativo de formas e organismos. Nos estudos morfométricos são utilizados dois tipos de aplicação fotogramétrica: fotogrametria 2D, onde são utilizadas medidas de distância e ângulo para quantitativamente descrever atributos de um objecto, e fotogrametria 3D, onde são utilizadas coordenadas de referência de forma a reconstruir a verdadeira forma de um objeto. Apesar da existência de uma elevada variedade de software no contexto de fotogrametria 3D, a variedade de software concebida especificamente para a a aplicação de fotogrametria 2D é ainda muito reduzida. Consequentemente, é comum observar estudos onde fotogrametria 2D é utilizada através da aquisição manual de medidas a partir de imagens, que posteriormente necessitam de ser escaladas para um sistema apropriado de medida. Este processo de várias etapas é frequentemente moroso e requer a aplicação de diferentes programas de software. Além de ser moroso, é também susceptível a erros, dada a natureza manual na aquisição de dados. O presente trabalho visou abordar os problemas descritos através da implementação de um novo software multiplataforma capaz de integrar e agilizar o processo de fotogrametria presentes em estudos que requerem fotogrametria 2D. Resultados preliminares demonstram um decréscimo de 45% em tempo de processamento na utilização do software desenvolvido no âmbito deste trabalho quando comparado a uma metodologia concorrente. Limitações existentes e trabalho futuro são discutidos

Non-parametric Models of Distortion in Imaging Systems.

Traditional radial lens distortion models are based on the physical construction of lenses. However, manufacturing defects and physical shock often cause the actual observed distortion to be different from what can be modeled by the physically motivated models. In this work, we initially propose a Gaussian process radial distortion model as an alternative to the physically motivated models. The non-parametric nature of this model helps implicitly select the right model complexity, whereas for traditional distortion models one must perform explicit model selection to decide the right parametric complexity. Next, we forego the radial distortion assumption and present a completely non-parametric, mathematically motivated distortion model based on locally-weighted homographies. The separation from an underlying physical model allows this model to capture arbitrary sources of distortion. We then apply this fully non-parametric distortion model to a zoom lens, where the distortion complexity can vary across zoom levels and the lens exhibits noticeable non-radial distortion. Through our experiments and evaluation, we show that the proposed models are as accurate as the traditional parametric models at characterizing radial distortion while flexibly capturing non-radial distortion if present in the imaging system.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120690/1/rpradeep_1.pd

Correction of radially asymmetric lens distortion with a closed form solution and inverse function

The current paradigm in the lens distortion characterization industry is to use simple radial distortion models with only one or two radial terms. Tangential terms and the optimal distortion centre are also seldom determined. Inherent in the models currently used is the assumption that lens distortion is radially symmetrical. The reason for the use of these models is partly due to the perceived instability of more complex lens distortion models. This dissertation shows, in the first of its three hypotheses, that higher order models are indeed beneficial, when their parameters are determined using modern numerical optimization techniques. They are both stable and provide superior characterization. Although it is true that the first two radial terms dominate the distortion characterization, this work proves superior characterization is possible for those applications that may require it. The third hypothesis challenges the assumption of the radial symmetry of lens distortion. Building on the foundation provided by the first hypothesis, a sample of lens distortion models of similar and greater complexity to those found in literature are modified to have a radial gain, allowing the distortion corrections to vary both with polar angle and distance from the distortion centre. Four angular gains are evaluated, and two provide better characterization. The elliptical gain was the only method to both consistently improve the characterization and not ‘skew’ the corrected images. This gain was shown to improve characterization by as much as 50% for simple (single radial term) models and by 7% for even the most complex models. To create an undistorted image from a distorted image captured through a lens which has had its distortion characterized, one needs to find the corresponding distorted pixel for each undistorted pixel in the corrected image. This is either done iteratively or using a simplified model typically based on the Taylor expansion of a simple (one or two radial coefficients) distortion model. The first method is accurate yet slow and the second, the opposite. The second hypothesis of this research successfully combines the advantages of both methods without any of their disadvantages. It was shown that, using the superior characterization of high order radial models (when fitted with modern numerical optimization methods) together with the ‘side-effect’ undistorted image points created in the lens distortion characterization, it is possible to fit a ‘reverse’ model from the undistorted to distorted domains. This reverse characterization is of similar complexity to the simplified models yet provides characterization equivalent to the iterative techniques. Compared to using simplified models the reverse mapping yields an improvement of more than tenfold - from the many tenths of pixels to a few hundredths.Dissertation (MEng)--University of Pretoria, 2009.Electrical, Electronic and Computer Engineeringunrestricte

Camera Calibration with Non-Central Local Camera Models

Kamerakalibrierung ist eine wichtige Grundvoraussetzung für viele Computer-Vision-Algorithmen wie Stereo-Vision und visuelle Odometrie. Das Ziel der Kamerakalibrierung besteht darin, sowohl die örtliche Lage der Kameras als auch deren Abbildungsmodell zu bestimmen. Das Abbildungsmodell einer Kamera beschreibt den Zusammenhang zwischen der 3D-Welt und der Bildebene. Aktuell werden häufig einfache globale Kamera-Modelle in einem Kalibrierprozess geschätzt, welcher mit vergleichsweise geringem Aufwand und einer großen Fehlertoleranz durchgeführt werden kann. Um das resultierende Kameramodell zu bewerten, wird in der Regel der Rückprojektionsfehler als Maß herangezogen. Jedoch können auch einfache Kameramodelle, die das Abbildungsverhalten von optischen Systemen nicht präzise beschreiben können, niedrige Rückprojektionsfehler erzielen. Dies führt dazu, dass immer wieder schlecht kalibrierte Kameramodelle nicht als solche identifiziert werden. Um dem entgegen zu wirken, wird in dieser Arbeit ein neues kontinuierliches nicht-zentrales Kameramodell basierend auf B-Splines vorgeschlagen. Dieses Abbildungsmodell ermöglicht es, verschiedene Objektive und nicht-zentrale Verschiebungen, die zum Beispiel durch eine Platzierung der Kamera hinter einer Windschutzscheibe entstehen, akkurat abzubilden. Trotz der allgemeinen Modellierung kann dieses Kameramodell durch einen einfach zu verwendenden Schachbrett-Kalibrierprozess geschätzt werden. Um Kalibrierergebnisse zu bewerten, wird anstelle des mittleren Rückprojektionsfehlers ein Kalibrier-Benchmark vorgeschlagen. Die Grundwahrheit des Kameramodells wird durch ein diskretes Sichtstrahlen-basiertes Modell beschrieben. Um dieses Modell zu schätzen, wird ein Kalibrierprozess vorgestellt, welches ein aktives Display als Ziel verwendet. Dabei wird eine lokale Parametrisierung für die Sichtstrahlen vorgestellt und ein Weg aufgezeigt, die Oberfläche des Displays zusammen mit den intrinsischen Kameraparametern zu schätzen. Durch die Schätzung der Oberfläche wird der mittlere Punkt-zu-Linien-Abstand um einen Faktor von mehr als 20 reduziert. Erst dadurch kann das so geschätzte Kameramodell als Grundwahrheit dienen. Das vorgeschlagene Kameramodell und die dazugehörigen Kalibrierprozesse werden durch eine ausführliche Auswertung in Simulation und in der echten Welt mithilfe des neuen Kalibrier-Benchmarks bewertet. Es wird gezeigt, dass selbst in dem vereinfachten Fall einer ebenen Glasscheibe, die vor der Kamera platziert ist, das vorgeschlagene Modell sowohl einem zentralen als auch einem nicht-zentralen globalen Kameramodell überlegen ist. Am Ende wird die Praxistauglichkeit des vorgeschlagenen Modells bewiesen, indem ein automatisches Fahrzeug kalibriert wird, das mit sechs Kameras ausgestattet ist, welche in unterschiedliche Richtungen zeigen. Der mittlere Rückprojektionsfehler verringert sich durch das neue Modell bei allen Kameras um den Faktor zwei bis drei. Der Kalibrier-Benchmark ermöglicht es in Zukunft, die Ergebnisse verschiedener Kalibrierverfahren miteinander zu vergleichen und die Genauigkeit des geschätzten Kameramodells mithilfe der Grundwahrheit akkurat zu bestimmen. Die Verringerung des Kalibrierfehlers durch das neue vorgeschlagene Kameramodell hilft die Genauigkeit weiterführender Algorithmen wie Stereo-Vision, visuelle Odometrie oder 3D-Rekonstruktion zu erhöhen

Experimental and data analysis techniques for deducing collision-induced forces from photographic histories of engine rotor fragment impact/interaction with a containment ring

An analysis method termed TEJ-JET is described whereby measured transient elastic and inelastic deformations of an engine-rotor fragment-impacted structural ring are analyzed to deduce the transient external forces experienced by that ring as a result of fragment impact and interaction with the ring. Although the theoretical feasibility of the TEJ-JET concept was established, its practical feasibility when utilizing experimental measurements of limited precision and accuracy remains to be established. The experimental equipment and the techniques (high-speed motion photography) employed to measure the transient deformations of fragment-impacted rings are described. Sources of error and data uncertainties are identified. Techniques employed to reduce data reading uncertainties and to correct the data for optical-distortion effects are discussed. These procedures, including spatial smoothing of the deformed ring shape by Fourier series and timewise smoothing by Gram polynomials, are applied illustratively to recent measurements involving the impact of a single T58 turbine rotor blade against an aluminum containment ring. Plausible predictions of the fragment-ring impact/interaction forces are obtained by one branch of this TEJ-JET method; however, a second branch of this method, which provides an independent estimate of these forces, remains to be evaluated