Learning OpenCV: Chapter 11 Camera Models and Calibration

Learning OpenCV ebook
: Chapter 11 Camera Models and Calibration


ref.
opencv v2.1 documentation » cv. Image Processing and Computer Vision » Camera Calibration and 3D Reconstruction (c reference / cpp reference)
Noah Kuntz's OpenCV Tutorial 10 - Chapter 11


370p

detection of light from the world:
light source -> reflected light from a object -> our eye or camera (lens -> retina or imager)

cf. http://en.wikipedia.org/wiki/Electronic_imager


geometry of the ray's travel
 
pinhole camera model

ref. O'Connor 2002
al-Hytham (1021)
Descartes
Kepler
Galileo
Newton
Hooke
Euler
Fermat
Snell

ref.
Trucco 1998
Jaehne 1995;1997
Hartley and Zisserman 2006
Forsyth and Ponce 2003
Shapiro and Stockman 2002
Xu and Zhang 1996


projective geometry

lens distortion

camera calibration
1) to correct mathematically for the main deviations from the simple pinhole model with lenses
2) to relate camera measurements with measurements in the real, 3-dimensional world

3-D scene reconstruction


: Camera Model (371p)

camera calibration => model of the camera's geometry & distortion model of the lens : intrinsic parameters

homography transform

OpenCV function cvCalibrateCamera2() or cv::calibrateCamera

pinhole camera:
single ray -> image plane (projective plane)

(...) the size of the image relative to the distant object is given by a single parameter of the camera: its focal length. For our idealized pinhole camera, the distance from the pinhole aperture to the screen is precisely the focal length.

The point in the pinhole is reinterpreted as the center of projection.

The point at the intersection of the image plane and the optical axis is refereed to as the principal point.

(...) the individual pixels on a typical low-cost imager are rectangular rather than square. The focal length(fx) is actually the product of the physical focal length(F) of the lens and the size (sx) of the individual imager elements. (*sx converts physical units to pixel units.)

: Basic Projective Geometry (373p)

projective transform

homogeneous coordinates

The homogeneous coordinates associated with a point in a projective space of dimension n are typically expressed as an (n+1)-dimensional vector with the additional restriction that any two points whose values are proportional are equivalent.

camera intrinsics matrix (of parameters defining our camera, i.e., fx,fy,cx,and cy)

ref. Heikkila and Silven 1997


OpenCV function cvConvertPointsHomogeneous() or cv::convertPointsHomogeneous

cf. cvReshape or cv::reshape

For a camera to form images at a faster rate, we must gather a lot of light over a wider area and bend (i.e., focus) that light to converge at the point of projection. To accomplish this, we uses a lens. A lens can focus a large amount of light on a point to give us fast imaging, but it comes at the cost of introducing distortions.

: Lens Distortions (375p)

Radia distortions arise as a result of the shape of lens, whereas tangential distortions arise from the assembly process of the camera as a whole.

radial distortion:

External points on a frontfacing rectangular grid are increasingly displaced inward as the radial distance from the optical center increases.

"barrel" or "fish-eye" effect -> barrel distortion


tangential distortion:

due to manufacturing defects resulting from the lens not being exactly parallel to the imaging plane.

plumb bob (연직 추, 측량 추) model
ref. D. C. Brown, "Decentering distortion of lenses", Photogrammetric Engineering 32(3) (1966). 7: 444–462.
http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/parameters.html

distortion vector (k1, k2, p1, p2, k3); 5-by-1 matrix


: Calibration (378p)

ref. http://www.vision.caltech.edu/bouguetj/calib_doc/

cvCalibrateCamera2() or cv::calibrateCamera
The method of calibration is to target the camera on a known structure that has many individual and identifiable points. By viewing this structure from a variety of angles, it is possible to then compute the (relative) location and orientation of the camera at the time of each image as well as the intrinsic parameters of the camera.


얘네는 뭔 있다 없다 하니...

cv::initCameraMatrix2D

cvFindExtrinsicCameraParams2



: Rotation Matrix and Translation Vector (379p)

Ultimately, a rotation is equivalent to introducing a new description of a point's location in a different coordinate system.

Using a planar object, we'll see that each view fixed eight parameters. Because the six parameters on two additional parameters that we use to resolve the camera intrinsic matrix. We'll then need at least two views to solve for all the geometric parameters.

: Chessboards (381p)

OpenCV opts for using multiple view of a planar object (a chessboard) rather than one view of  a specially constructed 3D object. We use a pattern of alternating black and white squares, which ensures that there is no bias toward one side or the other in measurement. Also, the resulting gird corners lend themselves naturally to the subpixel localization function.

use a chessboard grid that is asymmetric and of even and odd dimensions - for example, (5,6). using such even-odd asymmetry yields a chessboard that has only one symmetry axis, so the board orientation can always be defined uniquely.

The chessboard interior corners are simply a special case of the more general Harris corners; the chessboard corners just happen to be particularly easy to find and track.

cf. Chapter 10: Tracking and Motion: Subpixel Corners

319p: If you are processing images for the purpose of extracting geometric measurements, as opposed to extracting features for recognition, then you will normally need more resolution than the simple pixel values supplied by cvGoodFeaturesToTrack().

fitting a curve (a parabola)
ref. newer techniques
Lucchese02
Chen05


cvFindCornerSubpix() or cv::cornerSubPix (cf. cv::getRectSubPix )

ref.
Zhang99; Zhang00
Sturm99


: Homography (384p)