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CSE152, Spr. 2010
Intro Computer Vision
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Introduction to Computer Vision
CSE 152
Lecture 8
CSE152, Spr. 2010
Intro Computer Vision
Announcements
• HW 1 is due today
• HW2 will be available later today or tomorrow
• See links on web page for reading on binary
image processing (ereserves)
• Midterm May 5
CSE152, Spr 2010
Intro Computer Vision
Binary System Summary
1.
Acquire images and binarize (tresholding, color
labels, etc.).
2.
Possibly clean up image using morphological
operators.
3.
Determine regions (blobs) using connected
component exploration
4.
Compute position, area, and orientation of each
blob using moments
5.
Compute features that are rotation, scale, and
translation invariant using Moments (e.g.,
Eigenvalues of normalized moments).
CSE152, Spr 2010
Intro Computer Vision
Four & Eight Connectedness
Eight Connected
Four Connected
CSE152, Spr 2010
Intro Computer Vision
Recursive Labeling
Connected Component Exploration
2
1
CSE152, Spr 2010
Intro Computer Vision
Properties extracted from binary image
•
A tree showing containment of regions
•
Properties of a region
1.
Genus – number of holes
2.
Centroid
3.
Area
4.
Perimeter
5.
Moments (e.g., measure of elongation)
6.
Number of “extrema” (indentations, bulges)
7.
Skeleton
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CSE152, Spr 2010
Intro Computer Vision
Moments
(related to moments of intertia)
B(x,y)
• Fast way to implement
computation over n by m
image or window
• One object
The order of the M
jk
moment is j +k.
CSE152, Spr 2010
Intro Computer Vision
Central Moments
μ
jk
=
i
m
Λ
Ν
Μ
Ξ
Π
Ο
n
=
1
j
∑
m
=
1
i
∑
j
n
Λ
Ν
Μ
Ξ
Π
Ο
(
−
x
)
(
i
−
m
)
(
−
y
)
(
j
−
n
)
M
mn
CSE152, Spr 2010
Intro Computer Vision
Normalized Moments
CSE152, Spr 2010
Intro Computer Vision
Region orientation from Second Moment
Matrix
1.
Compute second centralized moment matrix
2.
Compute Eigenvectors of Moment Matrix to obtain orientation
3.
Eigenvalues are independent of orientation, translation!
• Symmetric, positive definite matrix
• Positive Eigenvalues
• Orthogonal Eigenvectors
m
20
m
11
m
11
m
02
Ρ
Σ
Τ
Φ
Υ
CSE152, Spr 2010
Intro Computer Vision
Moments
• Regular Moments M
jk
• Central Moments μ
jk
: Translation invariant
• Normalized Moments m
jk
: Translation and
scale Invariant
• Eigenvalues of Second Moment Matrix:
translation, scale, and rotation invariant.
• Hu Moments: Higher than second order,
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 Spring '08
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 Image processing

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