Page 183 - Introduction to Autonomous Mobile Robots

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a) b) Chapter 4

2 2
x x
– --------- – --------- 2
1 2σ 2 x – 2σ
G x() = --------------e G ' x() = -----------------e
σ
σ
2πσ 2πσ 3
Figure 4.43
(a) A Gaussian function. (b) The first derivative of a Gaussian function.

a b c

,
,
(
,
(
G xy) = G x()G y() f xy) = G' x()G y() f ( xy) = G' y()G x()
σ
σ
σ
σ
σ
σ
σ
H
V
Figure 4.44
(a) Two-dimensional Gaussian function. (b) Vertical filter. (c) Horizontal filter.
2
2
,
2. Define the square of the gradient magnitude Rxy,( ) = R xy,( ) + R ( xy) .
V H
3. Mark those peaks in R x y,( ) that are above some predefined threshold .
T
Once edge pixels are extracted, the next step is to construct complete edges. A popular
next step in this process is nonmaxima suppression. Using edge direction information, the
process involves revisiting the gradient value and determining whether or not it is at a local