Graphics Reference
In-Depth Information
highly textured scenes, obtaining a mathematically sufficient number of features to
apply the algorithms discussed in this chapter shouldn't be a problem. However,
we'll obtain better results if the features are well distributed across the entire image
as opposed to being clustered in a small region. One option is to
grow matches
using the estimated epipolar geometry at each frame; that is, we search for feature
matches along conjugate epipolar lines using a less stringent criterion for descriptor
matching than we might have used when searching over the entire image. In the
worst case, it may be necessary to manually add feature tracks in a video sequence
in difficult regions to improve the matchmove result. Dobbert's book on the practice
of matchmoving [
122
] discusses several rules of thumb for obtaining suitable feature
tracks that produce high-quality results.
6.2
CAMERA PARAMETERS AND IMAGE FORMATION
To proceed, we must establish a mathematical model for how a camera creates an
image of a scene. Throughout this and the following chapters, we denote 3D points
in the scene by capital letter coordinates
(
X
,
Y
,
Z
)
and 2D points in an image plane
by lowercase coordinates
.
We assume that cameras for visual effects follow the rules of
perspective
projection
, resulting in the
pinhole model
illustrated in Figure
6.3
a. That is, 3D
points in the scene are projected through the
camera center
C
onto a 2D
image
plane
. The image plane is coincident with a CCD array in a digital camera, or with
the physical surface of the film in a film camera.
In a real camera, the camera center lies at the center of the circular shutter or
aperture that opens to allow light to fall onto the image plane. The physical distance
(
x
,
y
)
image plane
camera center
image plane
camera center
scene
scene
(a)
(b)
Figure 6.3.
The pinhole model of perspective projection. (a) Light rays pass through the cam-
era center and impinge on the image plane (a piece of film or a CCD). (b) For mathematical
convenience, we model the image plane as lying between the camera center and the scene.
