Hi, Community!
This topic describes the Fisheye camera imaging model.
Fisheye Lens Model
A fisheye lens is usually formed by a dozen of different lenses. During imaging, the incident light is projected to a limited-sized imaging plane by different degrees of refraction so that the fisheye lens has a wider range of vision than the ordinary lens. The following figure shows the general structure of a fisheye camera. The light refracts at the first two lenses to reduce the incidence angle, and the other lenses are equal to an imaging lens. The multi-component structure makes the analysis of the refraction relationship of the fisheye camera complex.
The research shows that the model of fisheye camera imaging can be approximated to the unit spherical projection model. The imaging process of the fisheye camera is as follows: Step 1: The three-dimensional space points are linearly projected to a spherical surface, which is a virtual unit sphere and whose spherical center coincides with the original point of the camera coordinate system. Step 2: Points on the unit sphere are projected to the image plane non-linearly. The following figure shows the imaging process of the fisheye camera.
As we know, common camera imaging follows a pinhole camera model. Straight lines in actual scenarios are still projected as straight lines on the image plane during the imaging process. However, if fisheye camera imaging follows a pinhole camera model, the projected image becomes very large. When the camera view angle reaches 180°, the image becomes infinitely large. Therefore, the projection model of the fisheye camera allows image distortion to project as large an image as possible onto a limited-sized image plane. The fisheye camera's radial distortion is very serious. Therefore, only radial distortion of the fisheye camera is considered, and other distortion is ignored.
Projection Function
In order to project as large an image as possible to a limited-sized image plane, the fisheye camera is designed according to a certain projection function. There are four design models of the fisheye camera based on the projection functions: equidistant projection model, isometric projection model, orthogonal projection model, and stereoscopic projection model. The following figures show how is point P in the space projected to the spherical surface and imaged on the image plane.
1. Equidistant projection model
rd=fθ
rd=fθ
In the preceding formulas, rd indicates a distance from a point to a distortion center in a fisheye image, which is a focal length of the fisheye camera and is an angle between an incident light and an optical axis of a fisheye camera, that is, an incident angle.
2. Isometric projection model
rd=2fsin(θ2)
rd=2fsin(θ2)
3. Orthogonal projection model
rd=fsin(θ)
rd=fsin(θ)
4. Stereoscopic projection model
rd=2ftan(θ2)
rd=2ftan(θ2)
Thanks for reading!
