Chapter 11. Reconstructing 3D
Scenes
In this chapter, we will cover the following recipes:
Calibrating a camera
Recovering camera pose
Reconstructing a 3D scene from calibrated cameras
Computing depth from stereo image
Introduction
We learned in the previous chapter how a camera captures a 3D scene
by projecting light rays on a 2D sensor plane. The image produced is an
accurate representation of what the scene looks like from a particular
point of view, at the instant the image was captured. However, by its
nature, the process of image formation eliminates all information
concerning the depth of the represented scene elements. This chapter
will teach how, under specific conditions, the 3D structure of the scene
and the 3D pose of the cameras that captured it, can be recovered. We
will see how a good understanding of projective geometry concepts
allows us to devise methods that enable 3D reconstruction. We will
therefore revisit the principle of image formation introduced in the
previous chapter; in particular, we will now take into consideration that
our image is composed of pixels.
Digital image formation
Let's now redraw a new version of the figure shown in Chapter 10 ,
Estimating Projective Relations in Images, describing the pin-hole
camera model. More specifically, we want to demonstrate the relation
between a point in 3D at position (X,Y,Z) and its image (x,y) on a
camera specified in pixel coordinates:
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