Page 148 - Introduction to Autonomous Mobile Robots

Perception

 x l y l  y r 133
 r ---- + r ---- + r 23  z' + r 02 = ----z' r (4.33)
l
22
21
f
f
f
 x l y l 
 r ---- + r ---- + r 33  z' + r 03 = z' r (4.34)
31
32
l
f
f
y'
x'
The same process can be used to identify values for and , yielding complete infor-
mation about the position of point . However, using the above equations requires us to
P
have identified conjugate pairs in the left and right camera images: image points that orig-
P
inate at the same object point in the scene. This fundamental challenge, identifying the
conjugate pairs and thereby recovering disparity, is the correspondence problem. Intu-
itively, the problem is, given two images of the same scene from different perspectives,
how can we identify the same object points in both images? For every such identified object
point, we will be able to recover its 3D position in the scene.
The correspondence problem, or the problem of matching the same object in two differ-
ent inputs, has been one of the most challenging problems in the computer vision field and
the artificial intelligence fields. The basic approach in nearly all proposed solutions
involves converting each image in order to create more stable and more information-rich
data. With more reliable data in hand, stereo algorithms search for the best conjugate pairs
representing as many of the images’ pixels as possible.
The search process is well understood, but the quality of the resulting depth maps
depends heavily upon the way in which images are treated to reduce noise and improve sta-
bility. This has been the chief technology driver in stereo vision algorithms, and one par-
ticular method has become widely used in commercially available systems.

The zero crossings of Laplacian of Gaussian (ZLoG). ZLoG is a strategy for identify-
ing features in the left and right camera images that are stable and will match well, yielding
high-quality stereo depth recovery. This approach has seen tremendous success in the field
of stereo vision, having been implemented commercially in both software and hardware
with good results. It has led to several commercial stereo vision systems and yet it is
extremely simple. Here we summarize the approach and explain some of its advantages.
The core of ZLoG is the Laplacian transformation of an image. Intuitively, this is noth-
ing more than the second derivative. Formally, the Laplacian Lx y,( ) of an image with
intensities Ix y,( ) is defined as

2 2
(
,
Lxy) = ∂ I + ∂ I (4.35)
x ∂ 2 ∂ y 2