A general imaging model and a method for finding its parameters
Summary (2 min read)
- After describing the general imaging model and its properties, the authors present a simple method for finding the parameters of the model for any arbitrary imaging system:.
- It is important to note that, given the non-perspective nature of a general device, conventional calibration methods based on known scene points [251 or self-calibration techniques that use unknown scene points [51, [lo] , [151, cannot be directly applied.
- Since the authors are interested in the mapping from rays to image points, they need a ruy-bused calibration method.
- The authors describe a simple and effective ray-based approach that uses structured light patterns.
- This method allows a user to obtain the geometric, radiometric, and optical parameters of an arbitrarily complex imaging system in a matter of minutes.
2 General Imaging Model: Geometry
- If the imaging system is perspective, all the incoming light rays are projected directly onto to the detector plane through a single point, namely, the effective pinhole of the perspective system.
- The goal of this section is to present a geometrical model that can represent such imaging systems.
- Each raxel includes a pixel that measures light energy and imaging optics (a lens) that collects the bundle of rays around an incoming ray.
- The authors will focus on the geometric properties (locations and orientations) of raxels.
- Each raxel can posses its own radiometric (brightness and wavelength) response as well as optical (point spread) properties.
- These non-geometric properties will be discussed in subsequent sections.
Figure 3: (a)
- It may be placed along the line of a principle ray of light entering the imaging system.
- In addition to location and orientation, a raxel may have radiometric and optical parameters.
- The notation for a raxel used in this paper.
- Multiple raxels may be located at the same point (p1 = p~ = p3), but have different directions.
- The choice of intersecting the incoming rays with a refer-3Many of the arrays of photo-sensitive elements in the imaging devices described in section 1 are one or two-dimensional.
- 41ntensities usually do not change much along a ray (particularly when the medium is air) provided the the displacement is small with respect to the total length of the ray.
- In 191 and [141, it was suggested that the plenoptic function could also be restricted to a plane.
- The important thing is to choose some reference surface so that each incoming ray intersects this surface at only one point.
- 'For example, when light refracts through shallow water of a pool, bnght curves can be seen where the caustics intersect the bottom Figure 5 :.
- The caustic is a good candidate for the ray surface of an imaging system as it is closely related to the geometry of the incoming rays; the incoming ray directions are tangent to the caustic.
4.1 Local Focal Length and Point Spread
- An arbitrary imaging system cannot be expected to have a single global focal length.
- Each raxel may be modeled to have its own focal length.
- The authors can compute each raxel's focal length by measuring its point spread function for several depths.
- A flexible approach models the point spread as an elliptical Gaussian.
4.3 Complete Imaging Model
- In the case of perspective projection, the essential [51 or fundamental [ 101 matrix provides the relationship between points in one image and lines in another image (of the same scene).
- In the general imaging model, this correspondence need no longer be projective.
5 Finding the Model Parameters
- The major axis makes an angle 1c, with the x-axis in the image.
- Each raxel has two focal lengths, f a , hThe angle $ is only defined if the major and minor axis have different.
- In section the authors described how to compute The authors model for a known optical system.
- In contrast, their goal in this section lengths.
Figure 7: (a)
- If these positions are known, the direction of the ray qf may be determined for each pixel.
- Now, the authors construct a calibration environment where the geometric and radiometric parameters can be efficiently estimated.
- If a display has N locations, the authors can make each point distinct in logN images using simple grey coding or bit coding.
- The authors may then compute the fall-off function across all the points.
- The authors compute both the radiometric response function and the falloff from seventeen uniform brightness levels.
5.1 Experimental Apparatus
- The laptop was oriented so as to give the maximum screen resolution along the axis of symmetry.
- Figure 8 (b) shows a sample binary pattern as seen from the parabolic catadioptric system.
- The perspective imaging system, consisting of just the camera itself, can be seen in Figure 1 l(a).
Did you find this useful? Give us your feedback
Cites methods from "A general imaging model and a metho..."
...The techniques we consider are the generalized camera (Grossberg and Nayar 2001) and the pose averaging (Viksten et al....
Cites background from "A general imaging model and a metho..."
...Many natural camera systems, including catadioptric systems made with conical mirrors and incorrectly aligned lenses in standard cameras, have a set of viewpoints well characterized by a caustic ....
...The main contribution of this paper is to express a multi-camera system in this framework and then to derive the structure from motion constraint equations for this model....