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Alper Yilmaz, Fall 2005 UCF
CAP 5415 Computer Vision
Fall 2005
Dr. Alper Yilmaz
Univ. of Central Florida
www.cs.ucf.edu/courses/cap5415/fall
Office: CSB 250
Alper Yilmaz, Fall 2005 UCF
Recap (Filtering)
z Modify pixels based on the neighborhood
f ( p )
Alper Yilmaz, Fall 2005 UCF
Linear Filtering
z The output is the linear combination of the
neighborhood pixels
Image
Kernel
Filter Output
convolution
Alper Yilmaz, Fall 2005 UCF
Filtering Examples
Alper Yilmaz, Fall 2005 UCF
Filtering Examples
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1
1 1 1
1 1 1
1 1 1
Alper Yilmaz, Fall 2005 UCF
Blurring Examples
original
original
pixel offset
pixel offset
filtered
filtered
0
0
8
8 4
8 4
6
Alper Yilmaz, Fall 2005 UCF
Filtering Gaussian
Alper Yilmaz, Fall 2005 UCF
Gaussian vs. Smoothing
Gaussian Smoothing Smoothing by Averaging
Alper Yilmaz, Fall 2005 UCF
Edge Detection
Alper Yilmaz, Fall 2005 UCF
Example
Alper Yilmaz, Fall 2005 UCF
An Application
z What is an object?
z How can we find it?
Alper Yilmaz, Fall 2005 UCF
Edge Detection in Images
z Can occur due to different sources
– Shadows
– Texture
Alper Yilmaz, Fall 2005 UCF
Derivative in Two-Dimensions
z Definition
z Approximation
z Convolution kernels
= ⎛^ + −
ε
fx y fx y
x
f x , y lim , ,
0
= ⎛^ + −
ε
fxy fx y
y
f x , y lim , ,
0
x
fx y f x y
x
f xy n m n m
x
fx y f x y
y
f xy n m n m
f x = [ 1 − 1 ] ⎥
f y
Alper Yilmaz, Fall 2005 UCF
Image Derivatives
I x = I * [ 1 − 1 ] ⎥
I I *^1
Image I y
Alper Yilmaz, Fall 2005 UCF
Derivatives and Noise
z Strongly affected by noise
- obvious reason: pixels look very different from their neighbors
z The larger the noise is the
stronger the response
z What is to be done?
- Neighboring pixels look alike
- Pixel along an edge look alike
- Image smoothing should help
z Force pixels different to
their neighbors (possibly
noise) to look like
neighbors
Alper Yilmaz, Fall 2005 UCF
Derivatives and Noise
Zero mean additive gaussian noise
Increasing noise
Alper Yilmaz, Fall 2005 UCF
Gaussian Smoothing (Examples)
Alper Yilmaz, Fall 2005 UCF
Edge Detectors
z Gradient operators
– Prewit
– Sobel
z Laplacian of Gaussian (Marr-Hildreth)
z Gradient of Gaussian (Canny)
z Facet Model Based Edge Detector (Haralick)
Alper Yilmaz, Fall 2005 UCF
Prewitt and Sobel Edge Detector
z Compute derivatives
– In x and y directions
z Find gradient magnitude
z Threshold gradient magnitude
Alper Yilmaz, Fall 2005 UCF
Prewitt Edge Detector
image averagesmoothing in x blurred derivativefiltering in x edges in x
[ 1 − 1 ]
⎢⎣⎡−^11 ⎥⎦⎤
and results
image averagesmoothing in y blurred derivativefiltering in y edges in x
and
results
Alper Yilmaz, Fall 2005 UCF
Sobel Edge Detector
dxd^ I
dydI
Alper Yilmaz, Fall 2005 UCF
Sobel Edge Detector
2 2 ∆ = ⎜⎝⎛ dxdI ⎟⎠⎞+⎜⎜⎝⎛ dydI ⎟⎟⎠⎞
∆ ≥ Threshold = 100
Alper Yilmaz, Fall 2005 UCF
Exercise
z Code Sobel and Prewitt edge detectors.
– Reading images
– Use of convolution
z Gradient computation
– Thresholding
Alper Yilmaz, Fall 2005 UCF
Suggested Reading
z Chapter 4, Emanuele Trucco, Alessandro
Verri, "Introductory Techniques for 3-D
Computer Vision"
z Chapter 2, Mubarak Shah, “Fundamentals of
Computer Vision”
