Validation of polynomial-based equidistance fish-eye models
Martin Glavin2009
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
The majority of computer vision applications assume that the camera adheres to the pin-hole camera model. However, most real optical systems will introduce some undesirable effects, rendering the assumption of the pin-hole camera model invalid. By far the most evident of these effects is radial distortion, particularly in fish-eye camera systems where the level of this distortion is relatively extreme. The aim of fish-eye distortion correction is, therefore, to transform the distorted view of fish-eye cameras to the desired rectilinear pin-hole perspective view. To perform this distortion correction, several authors have developed models of fish-eye distortion. It is the aim of this paper to examine the accuracy of several of the polynomial-based models against the equidistance mapping function, which is the most common mapping function that fish-eye lenses are designed to follow. __________________________________________________________________________________________
Related papers
Review of geometric distortion compensation in fish-eye cameras
IET Irish Signals and Systems Conference (ISSC 2008), 2008
The majority of computer vision applications assume the pin-hole camera model. However, most optics will introduce some undesirable effects, rendering the assumption of the pin-hole camera model invalid. This is particularly evident in cameras with wide fields-of-view. The aim of distortion correction is, therefore, to transform the distorted view of wide-angle cameras to the pin-hole perspective view. Fish-eye cameras are those with "super-wide" fields-of-view, e.g. those cameras with fields-of-view of up to 180 degrees. However, these lenses exhibit severe forms of distortion. The most evident of these is radial distortion, but several other distortions, such as uneven illumination and inaccurate estimation of the centre of distortion, should also be considered when using a fish-eye camera. In this paper, we review and discuss methods of correcting radial and other distortions for fish-eye cameras and illustrate the effect of these methods on a test image exhibiting multiple types of distortion.
Accuracy of fish-eye lens models
Applied Optics, 2010
The majority of computer vision applications assumes that the camera adheres to the pinhole camera model. However, most optical systems will introduce undesirable effects. By far, the most evident of these effects is radial lensing, which is particularly noticeable in fish-eye camera systems, where the effect is relatively extreme. Several authors have developed models of fish-eye lenses that can be used to describe the fish-eye displacement. Our aim is to evaluate the accuracy of several of these models. Thus, we present a method by which the lens curve of a fish-eye camera can be extracted using well-founded assumptions and perspective methods. Several of the models from the literature are examined against this empirically derived curve.
Equidistant fish-eye perspective with application in distortion centre estimation
Image and Vision Computing, 2010
Radial distortion in an image is a geometric distortion that causes a non-linear variation in resolution across the image, with a higher spatial resolution in the central areas of the image, and lower resolution in the peripheral areas of the image. This is particularly evident in fish-eye cameras, with very wide fields-of-view. Equidistant fish-eye cameras are designed such that the distance between a projected point and the distortion centre of the image is proportional to the incident angle of the projected ray, scaled only by the focal length. The perspective of the projection of a given scene in an equidistant fish-eye camera differs greatly from the projection of the same scene in a rectilinear pin-hole camera. For example, while the field-of-view is significantly larger for a fish-eye camera, the non-linear radial distortion of the scene results in straight lines mapping to curves of a particular shape in the equidistant fish-eye image. In this paper, we describe equidistant fish-eye perspective in terms of the projection of sets of parallel lines to the equidistant fish-eye plane, and derive an equation that describes the projection of a straight line. We also demonstrate how the shape of a projected straight line can be accurately described by arcs of circles on the distorted image plane. We also describe an application of the equidistant perspective properties, by showing that the distortion centre of an equidistant fish-eye camera can be estimated by the extraction of the vanishing points. Additionally, we examine the accuracy of this estimation procedure on a large set of synthetically created images and a smaller set of real images from fish-eye cameras.
A generic camera calibration method for fish-eye lenses
Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., 2004
Fish-eye lenses are convenient in such computer vision applications where a very wide angle of view is needed. However, their use for measurement purposes is limited by the lack of an accurate, generic, and easy-to-use calibra- tion procedure. We hence propose a generic camera model for cameras equipped with sh-e ye lenses and a method for calibration of such cameras.
A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000
Fish-eye lenses are convenient in such applications where a very wide angle of view is needed but their use for measurement purposes has been limited by the lack of an accurate, generic, and easy-to-use calibration procedure. We hence propose a generic camera model, which is suitable for fish-eye lens cameras as well as for conventional and wide-angle lens cameras, and a calibration method for estimating the parameters of the model. The achieved level of calibration accuracy is comparable to the previously reported state-of-the-art.
<title>Geometry of binocular imaging III: wide-angle and fish-eye lenses</title>
Stereoscopic Displays and Virtual Reality Systems III, 1996
We address the issue of creating stereo imagery on a screen that, when viewed by naked human eyes, will be indistinguishable from the original scene as viewed through a visual accessory. In doing so we investigate effects that appear because real optical systems are not ideal. Namely, we consider optical systems that are not free from geometric aberrations. We present an analysis and confirming computational experiments of the simulations of stereoscopic optical accessories in the presence of aberrations. We describe an accessory in the framework of the Seidel-Schwarzschild theory. That means that we represent its deviation from an ideal (Gaussian) device by means of five constants. Correspondingly, we are able to simulate five fundamental types of monochromatic geometric aberrations: spherical aberration, coma, astigmatism, curvature-of-field, and distortion (barrel and pincushion). We derive and illustrate how these aberrations in stereoscopic optical systems, can lead to anomalous perception of depth, e. g., the misperception of planar surfaces as curved, or even twisted, as well as to circumstances under which stereoscopic perception is destroyed. The analysis and numerical simulations also allow us to simulate the related but not identical effects that occur when lenses with aberrations are used in stereoscopic cameras.
Geometry of binocular imaging III: wide-angle and fish-eye lenses
Proceedings of SPIE, 1996
We address the issue of creating stereo imagery on a screen that, when viewed by naked human eyes, will be indistinguishable from the original scene as viewed through a visual accessory. In doing so we investigate effects that appear because real optical systems are not ideal. Namely, we consider optical systems that are not free from geometric aberrations. We present an analysis and confirming computational experiments of the simulations of stereoscopic optical accessories in the presence of aberrations. We describe an accessory in the framework of the Seidel-Schwarzschild theory. That means that we represent its deviation from an ideal (Gaussian) device by means of five constants. Correspondingly, we are able to simulate five fundamental types of monochromatic geometric aberrations: spherical aberration, coma, astigmatism, curvature-of-field, and distortion (barrel and pincushion). We derive and illustrate how these aberrations in stereoscopic optical systems, can lead to anomalous perception of depth, e. g., the misperception of planar surfaces as curved, or even twisted, as well as to circumstances under which stereoscopic perception is destroyed. The analysis and numerical simulations also allow us to simulate the related but not identical effects that occur when lenses with aberrations are used in stereoscopic cameras.
An Experimental Foveated Vision System using Fish-Eye Lens
This paper present an experimental foveated vision system which simulates eye movement and non-uniform sampling of human vision system. Fish-eye lens is utilized to simulate eye movement by taking a partial image around the xation point. This makes the development of the active vision system easy. The log-polar sampling is employed to simulate the non-uniform sampling of retina. Then the successive space-variant retinal images are combined in an iconic buer which is represented as the two dimensional array of the equidistant image.
Recognition of landmarks distorted by fish-eye lens
1999
The paper deals with recognition of artificial landmarks using fish-eye lens. The proposed recognition model is based on algebraic affine moment invariants (AMIs). Landmarks are used for the navigation of an autonomous robot, equipped with a fisheye lens camera. The recognition ability of the AMIs regarding the deformation introduced by the fish-eye lens image acquisition is investigated. The results of the experiments in real situations, which proved the discriminability and the stability of the recognition model, are shown.
Parameter-Free Lens Distortion Calibration of Central Cameras
2017 IEEE International Conference on Computer Vision (ICCV), 2017
At the core of many Computer Vision applications stands the need to define a mathematical model describing the imaging process. To this end, the pinhole model with radial distortion is probably the most commonly used, as it balances low complexity with a precision that is sufficient for most applications. On the other hand, unconstrained non-parametric models, despite being originally proposed to handle specialty cameras, have been shown to outperform the pinhole model, even with the simpler setups. Still, notwithstanding the higher accuracy, the inability of describing the imaging model by simple linear projective operators severely limits the use of standard algorithms with unconstrained models. In this paper we propose a parameter-free camera model where each imaging ray is constrained to a common optical center, forcing the camera to be central. Such model can be easily calibrated with a practical procedure which provides a convenient undistortion map that can be used to obtain a virtual pinhole camera. The proposed method can also be used to calibrate a stereo rig with a displacement map that simultaneously provides stereo rectification and corrects lens distortion.
Related papers
A Generic Non-linear Method for Fisheye Correction
International Journal of Computer Applications, 2012
With rapid advances in the field of vision based systems and ever increasing applications that they foster to; it brings along many challenges both in terms of algorithm design and associated hardware. One such widely used gadget is the fisheye camera that is used in myriad of applications in various fields owing to their wide Field of View. However, these lenses introduce distortions when any real-world object gets mapped on to the image plane. The amount of distortion in fish eye images increases while moving radially outward from the image centre. Therefore, the amount of correction to be applied should also vary accordingly based on the pixel location. This paper presents a fast and real-time implementable technique for fisheye correction. The proposed method uses non-linear radial stretching and scaling down of pixels thereafter; both in X and Y dimensions for correction. For real-time implementation of the proposed algorithm, we propose the use of inverse mapping matrix. This enables transformation of computationally extensive equations used for correction into a simple look-up table that can easily be implemented on a FPGA platform.
Automatic calibration of fish-eye cameras from automotive video sequences
IET Intelligent Transport Systems, 2010
A technique for calibrating a lens in the automotive environment to compensate for radial distortion introduced by wide-angle or fish-eye lenses, without the need for a dedicated calibration environment, is proposed. At present, car manufacturers are endeavouring to introduce systems that provide the driver with views of the car's surroundings that are not directly visible (blind zones). To achieve this, wide-angle/fish-eye lens cameras are fitted to many modern vehicles to maximise the field of view. However, fish-eye lenses introduce undesirable radial distortion to the resulting images that can be compensated for by postprocessing the images. Calibration of the camera is important for fish-eye compensation, because each camera has different intrinsic properties. However, in some situations, calibration via specific calibration setup can be undesirable. For example, in automotive mass production, where time and space on a production line have a direct impact on cost, even minutes spent on calibration is costly. In these situations, automatic calibration can reduce production time and alleviate the associated costs. It is proposed that the radial distortion introduced by fish-eye lenses can be calibrated using video normally captured by the camera on a vehicle. Here, it is proposed to heuristically extract real-world straight lines from image frames captured in an automotive environment and use these to calibrate the fish-eye camera for radial distortion. The two primary types of distortion introduced by wideangle cameras are radial distortion and tangential distortion. By far, the most obvious form of distortion is radial distortion, with tangential distortion commonly considered to be negligible [6-9]. It can be seen that although the fish-eye image shows a far larger portion of the 136
A generic fisheye camera model for robotic applications
2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2007
Omnidirectional cameras have a wide field of view and are thus used in many robotic vision tasks. An omnidirectional view may be acquired by a fisheye camera which provides a full image compared to catadioptric visual sensors and do not increase the size and the weakness of the imaging system with respect to perspective cameras. We prove that the unified model for catadioptric systems can model fisheye cameras with distortions directly included in its parameters. This unified projection model consists on a projection onto a virtual unitary sphere, followed by a perspective projection onto an image plane. The validity of this assumption is discussed and compared with other existing models. Calibration and partial Euclidean reconstruction results help to confirm the validity of our approach. Finally, an application to the visual servoing of a mobile robot is presented and experimented.
Equidistant Fish-Eye Calibration and Rectification by Vanishing Point Extraction
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000
In this paper, we describe a method to photogrammetrically estimate the intrinsic and extrinsic parameters of fish-eye cameras using the properties of equidistance perspective, particularly vanishing point estimation, with the aim of providing a rectified image for scene viewing applications. The estimated intrinsic parameters are the optical center and the fish-eye lensing parameter, and the extrinsic parameters are the rotations about the world axes relative to the checkerboard calibration diagram.
A novel camera calibration method for fish-eye lenses using line features
ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2014
In this paper, a novel method for the fish-eye lens calibration is presented. The method required only a 2D calibration plane containing straight lines i.e., checker board pattern without a priori knowing the poses of camera with respect to the calibration plane. The image of a line obtained from fish-eye lenses is a conic section. The proposed calibration method uses raw edges, which are pixels of the image line segments, in stead of using curves obtained from fitting conic to image edges. Using raw edges is more flexible and reliable than using conic section because the result from conic fitting can be unstable. The camera model used in this work is radially symmetric model i.e., bivariate non-linear function. However, this approach can use other single view point camera models. The geometric constraint used for calibrating the camera is based on the coincidence between point and line on calibration plane. The performance of the proposed calibration algorithm was assessed using si...
Extended fisheye lens model for practical geometric correction and image enhancement
Optics Letters, 2014
An extended fisheye lens model is presented to control the size ratio between the distorted and virtually undistorted images based on orthographic projection. The optimum size ratio is derived to correct the barrel distortion of a fisheye lens so that the maximum amount of the peripheral region is reconstructed with the minimum visual distortion. The geometric correction generates an aliasing artifact in the central region and a jagging artifact in the peripheral region. Based on the proposed lens model, a novel image enhancement algorithm is also presented to remove the aliasing and jagging artifacts in the geometrically corrected image. Experimental results demonstrate that the proposed enhancement method outperforms existing methods in the sense of objective and subjective measures.
Digital deformation model for fisheye image rectification
Optics Express, 2012
Fisheye lens can provide a wide view over 180 • . It then has prominence advantages in three dimensional reconstruction and machine vision applications. However, the serious deformation in the image limits fisheye lens's usage. To overcome this obstacle, a new rectification method named DDM (Digital Deformation Model) is developed based on two dimensional perspective transformation. DDM is a type of digital grid representation of the deformation of each pixel on CCD chip which is built by interpolating the difference between the actual image coordinate and pseudo-ideal coordinate of each mark on a control panel. This method obtains the pseudo-ideal coordinate according to two dimensional perspective transformation by setting four mark's deformations on image. The main advantages are that this method does not rely on the optical principle of fisheye lens and has relatively less computation. In applications, equivalent pinhole images can be obtained after correcting fisheye lens images using DDM.
Techniques for Fisheye Lens Calibration using a Minimal Number of Measurements
A method is discussed describing how different types of Omni-Directional "fisheye" lenses can be calibrated for use in robotic vision. The technique discussed will allow for full calibration and correction of x,y pixel coordinates while only taking two uncalibrated and one calibrated measurement. These are done by finding the observed x,y coordinates of a calibration target. Any Fisheye lens that has a roughly spherical shape can have its distortion corrected with this technique. Two measurements are taken to discover the edges and centroid of the lens. These can be done automatically by the computer and does not require any knowledge about the lens or the location of the calibration target. A third measurement is then taken to discover the degree of spherical distortion, This is done by comparing the expected measurement to the measurement obtained and then plotting a curve that describes the degree of distortion. Once the degree of distortion is known and a simple curve has been fitted to the distortion shape, the equation of that distortion and the simple dimensions of the lens are plugged into an equation that remains the same for all types of lenses. The technique has the advantage of needing only one calibrated measurement to discover the type of lens being used.
Improvising Field of View of Camera using Fisheye Image Correction
Fisheye cameras have very good properties like wide angle view capture , cost effectiveness etc. hence they are used in variety of applications including automobile rear view imaging system , surveillance and robotics. But the produced images have some distortion and lead to have hemispherical scenes projected on flat surface and looking curvilinear. These distortions result into viewer's confusion. Hence the distortion should be corrected to rectilinear corrected version. The proposed work aims to devise a method for fisheye correction along with the enhancement of the distorted images and hence to improve the Field of View (FoV) of the camera. Referring fisheye type images like Hemispherical and Full Circular images the method will be designed considering the aspects of imaging, projection model, distortion model, bilinear interpolation adjusting etc. The resulting image is expected to have a high resolution and homogeneous illumination distribution.
Comparison and Calibration of Mobile Phone Fisheye Lens and Regular Fisheye Lens via Equidistant Model
Journal of Sensors, 2016
Nowadays, mobile phones are more than a device that can only satisfy the communication need between people. In addition to providing ease to human lives with various applications, lens kits that can be integrated to mobile phones have recently been introduced. Fisheye lenses that are compliant with mobile phones are one of these new types of equipment. Since fisheye lenses integrated with mobile phones are lightweight and easy to use, they are advantageous. In addition to this advantage, whether fisheye lens and mobile phone combination can be used in a photogrammetric way is experimented, and if so, what will be the result. The main purpose of this study is to test fisheye lens equipment used with mobile phones. In this study, standard calibration of “Olloclip 3 in one” fisheye lens used with iPhone 4S mobile phone and “Nikon FC-E9” fisheye lens used with Nikon Coolpix8700 are compared based on equidistant model. The results of these calibrations are analyzed, using photogrammetric...
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.