1
CSE152, Spr 11
Intro Computer Vision
Generalized Hough Transform,
line fitting
Introduction to Computer Vision
CSE 152
Lecture 11a
CSE152, Spr 11
Intro Computer Vision
Announcements
• Assignment 2: Due today
• Midterm: Thursday, May 5 in class
CSE152, Spr 11
Intro Computer Vision
What is region like if:
1.
λ
1
= 0?
2.
λ
2
= 0?
3.
λ
1
= 0
and
λ
2
= 0?
4.
λ
1
> 0
and
λ
2
> 0?
Corner Detection
C
(
x
,
y
)
=
I
x
2
∑
I
x
I
y
∑
I
x
I
y
∑
I
y
2
∑
Ρ
Σ
Τ
Φ
Υ
Υ
CSE152, Spr 11
Intro Computer Vision
So, to detect corners
•
Filter image with a Gaussian.
•
Compute the gradient everywhere.
•
Move window over image and construct C
over the window.
•
Use linear algebra to find
λ
1
and
λ
2
.
•
If they are both big, we have a corner.
1.
Let e(x,y) = min(
λ
1
(x,y),
λ
2
(x,y)
)
2.
(x,y) is a corner if it’s local maximum of e(x,y)
and e(x,y) >
τ
Parameters: Gaussian std. dev, window size, threshold
CSE152, Spr 11
Intro Computer Vision
• Segment linked edge chains into curve features
(e.g., line segments).
• Group unlinked or unrelated edges into lines (or
curves in general).
• Accurately fitting parametric curves (e.g., lines) to
grouped edge points.
What to do with edges?
CSE152, Spr 11
Intro Computer Vision
Hough Transform
[ Patented 1962 ]
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Finding lines in an image
Connection between image (x,y) and Hough (m,b) spaces
•
A line in the image corresponds to a point in Hough space
•
To go from image space to Hough space:
– given a set of points (x,y), find all (m,b) such that y = mx + b
x
y
m
b
(m
0
,b
0
)
image space
Hough space
Finding lines in an image
Connection between image (x,y) and Hough (m,b) spaces
•
A line in the image corresponds to a point in Hough space
•
To go from image space to Hough space:
– given a set of points (x,y), find all (m,b) such that y = mx + b
•
What does a point (x
0
, y
0
) in the image space map to?
x
y
m
b
image space
Hough space
– A:
the solutions of b = x
0
m + y
0
– this is a line in Hough space
(x
0
,y
0
)
CSE152, Spr 11
Intro Computer Vision
Hough transform algorithm
•
Typically use a different parameterization
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 Spring '08
 staff
 Computer vision, SPR

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