Announcements
• Assignment 1: Due on next thursday
• For this week, there is a link on the web
page for reading which isn’t yet active.
Analysis of Binary Images
Introduction to Computer Vision
CSE 152
Lecture 6
CSE152, Spr 05
Intro Computer Vision
CSE152, Spr 05
Intro Computer Vision
Light Spectrum
The appearance of colors
• Color appearance is strongly affected by
(at least):
–
–
–
–
Spectrum of lighting striking the retina
other nearby colors (space)
adaptation to previous views (time)
“state of mind”
CSE152, Spr 05
Intro Computer Vision
CSE152, Spr 05
Talking about colors
Color Reflectance
Measured color spectrum is
a function of the spectrum
of the illumination and
reflectance
1. Spectrum –
•
•
Intro Computer Vision
A positive function over interval 400nm700nm
“Infinite” number of values needed.
2. Names
•
•
red, harvest gold, cyan, aquamarine, auburn,
chestnut
A large, discrete set of color names
3. R,G,B values
•
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Just 3 numbers
From Foundations of Vision, Brian Wandell, 1995, via B. Freeman slides
Intro Computer Vision
CSE152, Spr 05
Intro Computer Vision
1
Color Matching Functions
RGB
• Primaries are
monochromatic,
wavelengths are 645.2nm,
526.3nm, 444.4nm.
• Color matching functions
have negative parts ->
some colors can be
matched only
subtractively.
Primary light = p1P1(λ) + p2P2(λ) + p3P3(λ)
Where pi is the strength of each primary, and
Pi(λ) is the spectrum of primary i
slideIntro
from
T. Darrel
Computer
Vision
CSE152, Spr 05
CSE152, Spr 05
RGB Color Cube
YIQ Model
• Block of colours for (r, g,
b) in the range (0-1).
• Convenient to have an
upper bound on
coefficient of each
primary.
• In practice:
– primaries given by monitor
phosphors
– (phosphors are the materials
on the face of the monitor
screen that glow when
struck by electrons)
CSE152, Spr 05
Intro Computer Vision
0.114   R 
Y  0.299 0.587
 I  = 0.596 − 0.275 − 0.321 G 
  
 
Q  0.212 − 0.532 0.311   B 
• Used by NTSC TV standard
• Separates Hue & Saturation (I,Q) from
Luminance (Y)
CSE152, Spr 05
Intro Computer Vision
CIE xyY (Chromaticity Space)
CIE -XYZ and x-y
CSE152, Spr 05
Intro Computer Vision
Intro Computer Vision
CSE152, Spr 05
Intro Computer Vision
2
HSV Hexcone
RGB-> HSV
[[ Note that for HW1 you may find different ways to do this convertion in the
literature. If you use something different, just inclue a citation so we can know
where your equations came from ]]
Hue, Saturation, Value
AKA: Hue, Saturatation, Intensity (HIS)
Let MAX=max(R,G,B), let MIN=min(R,G,B)
S=(max-min)/max
V= max
Hexagon arises from projection of cube onto plane
orthogonal to (R,G,B) = (1,1,1)
CSE152, Spr 05
Intro Computer Vision
Metameric Lights
(Metamers)
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Intro Computer Vision
Blob Tracking for Robot Control
Intro Computer Vision
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Intro Computer Vision
Basic Steps
1. Labeling pixels as foreground/background
(0,1).
2. Morphological operators (sometimes)
3. Find pixels corresponding to a region
4. Compute properties of each region
Binary Image Processing
CSE152, Spr 05
Intro Computer Vision
CSE152, Spr 05
Intro Computer Vision
3
How do we select a Threshold?
Histogram-based Segmentation
• Manually determine threshold
experimentally.
Ex: bright object on dark background:
Histogram
• Select threshold
• Create binary image:
Number of pixels
– Good when lighting is stable and high contrast.
• Automatic thresholding
–
–
–
–
– I(x,y) < T -> O(x,y) = 0
– I(x,y) > T -> O(x,y) = 1
P-tile method
Mode method
Peakiness detection
Iterative algorithm
Gray value
T
CSE152, Spr 05
[ From Octavia Camps]
Intro Computer Vision
CSE152, Spr 05
P-Tile Method
Intro Computer Vision
Mode Method
• If the size of the object is approx. known, pick T
s.t. the area under the histogram corresponds to the
size of the object:
• Model intensity in each region Ri as
“constant” + N(0,σi):
T
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[ From Octavia Camps]
Intro Computer Vision
CSE152, Spr 05
• It is a not trivial problem:
Ideal histogram:
µ2 µ3
Add noise:
µ1
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Intro Computer Vision
Finding the peaks and valleys
Example: Image with 3 regions
µ1
[ From Octavia Camps]
µ2 µ3
[ From Octavia Camps]
The valleys are
good places for
thresholding to
separate regions.
Intro Computer Vision
CSE152, Spr 05
[ From Octavia Camps]
Intro Computer Vision
4
“Peakiness” Detection Algorithm
• Find the two HIGHEST LOCAL MAXIMA at a
MINIMUM DISTANCE APART:
gi and gj
Regions
• Find lowest point between them: gk
• Measure “peakiness”:
– min(H(gi),H(gj))/H(gk)
• Find (gi,gj,gk) with highest peakiness
gi
[ From Octavia Camps]
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gk gj
Intro Computer Vision
CSE152, Spr 05
What is a region?
Connected Regions
• “Maximal connected set of points in the image
with same brightness value” (e.g., 1)
1 1 1
1 1 1
1 1 1
• Two points are connected if there exists a
continuous path joining them.
• Regions can be simply connected (For every pair
of points in the region, all smooth paths can be
smoothly and continuously deformed into each
other). Otherwise, region is multiply connected
(holes)
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Intro Computer Vision
1 1
1 1 1
1
1
1 1
1
1
1 1
1
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Intro Computer Vision
Four & Eight Connectedness
1 1 1 1 1
1
1 1
1 1 1 1 1
Four Connected
• What the connected regions in this binary image?
• Which regions are contained within which region?
CSE152, Spr 05
1 1 1
1 1
1 1
1 1 1
• What are the connected regions in this binary image?
• Which regions are contained within which region?
Connected Regions
1
1 1
1 1
1 1
Intro Computer Vision
Intro Computer Vision
CSE152, Spr 05
Eight Connected
Intro Computer Vision
5
Jordan Curve Theorem
Problem of 4/8 Connectedness
• “Every closed curve in R2 divides the plane
into two region, the ‘outside’ and ‘inside’ of
the curve.”
• 8 Connected:
1
1
– 1’s form a closed curve,
but background only
forms one region.
1
1
1
1
1
1
1
• 4 Connected
– Background has two
regions, but ones form
four “open” curves (no
closed curve)
1
Almost obvious
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Intro Computer Vision
To achieve consistency w.r.t. Jordan
Curve Theorem
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Recursive Labeling
Connected Component Exploration
1. Treat background as
4-connected and
foreground as 8connected.
2. Use 6-connectedness
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Intro Computer Vision
1
Intro Computer Vision
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Recursive Labeling
Connected Component Exploration
Procedure Label (Pixel)
BEGIN
Mark(Pixel) <- Marker;
FOR neighbor in Neighbors(Pixel) DO
IF Image (neighbor) = 1 AND Mark(neighbor)=nil THEN
Label(neighbor)
END
2
Intro Computer Vision
Some notes
• How deep does stack go?
• Iterative algorithms (See reading from
Horn)
• Parallel algorithms
BEGIN Main
Marker <- 0;
FOR Pixel in Image DO
IF Image(Pixel) = 1 AND Mark(Pixel)=nil THEN
BEGIN
Globals:
Marker <- Marker + 1;
Marker: integer
Label(Pixel);
Mark: Matrix same size as Image,
END;
initialized to NIL
END
CSE152, Spr 05
Intro Computer Vision
CSE152, Spr 05
Intro Computer Vision
6