CAP 5415 Computer Vision Fall 2004

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CAP 5415 Computer VisionFall 2004

• Dr. Alper Yilmaz
• Univ. of Central Florida
• www.cs.ucf.edu/courses/cap5415/fall2004
• Office CSB 250

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RecapEstimation of Camera Parameters

• Relation between camera and image coordinates

(A)
(B)

• Estimate rij,ti,ox,oy,fx,fy.

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RecapEstimation of Camera Parameters

• Given corresponding world and image points
• Divide (A) to (B), rearrange result

(C)

• Rearrange into matrix and solve using SVD
• Estimate scale factor ? r2i and ty are there!!
• Compute ? similar to scale factor
• Compute r3i from r1i and r2i .
• Estimate fx , fy and ty .
• Finally compute ox and oy from other knowns

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RecapRotation around arbitrary axis
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RecapRotation around arbitrary axis
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Images
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General

• Binary
• Gray Scale
• Color

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Binary Images
Y
1
1
1
1
Row 1
q
X
0 Black 1 White
0
0
0
0
0
Row q
p
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Gray Level Image
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5
9
100
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Gray Scale Image
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Color ImageRed, Green, Blue Channels
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Image Histogram
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Image Noise

• Light Variations
• Camera Electronics
• Surface Reflectance
• Lens

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Image Noise

• I(x,y) the true pixel values
• n(x,y) the noise at pixel (x,y)

?
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Gaussian Noise
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Salt Pepper Noise

• p is uniformly distributed random variable
• l is threshold
• smin and smin are constant

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Image Derivatives Averages
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Definitions

• Derivative Rate of change
• Speed is a rate of change of a distance
• Acceleration is a rate of change of speed
• Average (Mean)
• Dividing the sum of N values by N

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Derivative
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Examples
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Discrete Derivative
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Discrete DerivativeFinite Difference
Backward difference
Forward difference
Central difference
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Example
Derivative Masks
Backward difference
-1 1
1 -1
Forward difference
-1 0 1
Central difference
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Derivatives in 2 Dimensions
Given function
Gradient vector
Gradient magnitude
Gradient direction
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Derivatives of Images
Derivative masks
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Derivatives of Images
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Convolution
f
h
x
x
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Averages

• Mean

• Weighted mean

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Gaussian Filter
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Properties of Gaussian

• Most common natural model
• Smooth function, it has infinite number of
  derivatives
• Fourier Transform of Gaussian is Gaussian.
• Convolution of a Gaussian with itself is a
  Gaussian.
• There are cells in eye that perform Gaussian
  filtering.