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Multimedia Systems & Interfaces. Karrie G. Karahalios Spring 2007. Overview. Filters Edge Detection Non Photo-realistic Rendering. Image Filtering Overview. http://www.courses.fas.harvard.edu/~ext12559/lectures/2005-11-29-Filtering.pdf by Chris Wren. Spatial domain - PowerPoint PPT Presentation
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Multimedia Systems &Interfaces
Karrie G. KarahaliosSpring 2007
Overview
• Filters
• Edge Detection
• Non Photo-realistic Rendering
Image Filtering Overview
http://www.courses.fas.harvard.edu/~ext12559/lectures/2005-11-29-Filtering.pdf
by Chris Wren
Spatial and Frequency Domains
• Spatial domain– refers to planar region of
intensity values
• Frequency domain– think of each color plane
as a sinusoidal function of changing intensity values
– apply DFT to subsets of pixels for compression
Convolution Filters
• Filter an image by replacing each pixel in the source with a weighted sum of its neighbors
• Define the filter using a convolution mask, also referred to as a kernel– non-zero values in small neighborhood, typically
centered around a central pixel– generally have odd number of rows/columns
Mean Filter
Convolution filterSubset of image
9549648
22813455
33191545
23141220
111
111
111
9
1
Mean Filter
Convolution filterSubset of image
9549648
22813455
33191545
23141220
111
111
111
9
1
Common 3x3 Filters
• Low/High pass filter
• Blur operator
• H/V Edge detector
121
212
121
13
1
111
191
111
121
000
121
101
202
101
111
111
111
9
1
Edge Detection
• Identify areas of strong intensity contrast– filter unecessary data;
preserve important properties
• Fundamental technique– object recognition, orientation– image segmentation– e.g., use gestures as input– identify shapes, match to
templates, invoke commands
Characteristics of Edges
• Identify high slope in first derivative
• Pixel is on an edge if value of the gradient exceeds a threshold
http://www.pages.drexel.edu/~weg22/edge.html
Basic Method
• Step 1: filter noise using mean filter
• Step 2: compute spatial gradient
• Step 3: mark points > threshold as edges
Compute Spatial Gradient
• Compute partials
• Compute gradient
• Compute length
• Divide by length
jy
Iix
II
y
I
x
IyxI
),(
y
I
x
II
22
I
IG
Compute Partials
121
000
121
4
1
y
I
987
654
321
PPP
PPP
PPP
101
202
101
4
1
x
I P3 – P1 + 2*P6 – 2*P4+ P9 – P7
987
654
321
PPP
PPP
PPPP7 – P1 + 2*P8 – 2*P2
+ P9 – P3
Mark Edge Points
• Given gradient at each pixel and threshold – mark pixels where gradient
> threshold as edges
• Canny algorithm extends basic method
http://www.cee.hw.ac.uk/hipr/html/sobel.html
Compute Edge Direction
• Compute direction of maximum change
y
x
G
G1tan
xG
yG
Apply Non-Max Suppression
• For each pixel– If G(x,y) < either neighbor
along Normal direction, then set G(x,y) = 0
• Suppress local change when larger change nearby – helps reduce false positives
Hysteresis
• Oscillation of gradient at threshold
• Use two thresholds – T1 and T2 with T2 > T1
• Mark pixel as edge pixel if G(x,y) > T2 – keep pixels along normal direction with
G(x,y) > T1