1 regions and binary images hao jiang computer science department sept. 24, 2009
TRANSCRIPT
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1
Regions and Binary Images
Hao Jiang
Computer Science Department
Sept. 24, 2009
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Figure Ground Separation
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Brightness Thresholding
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=-
Thresholding Given a grayscale image or an intermediate matrix
threshold to create a binary output.
Example: background subtraction
Looking for pixels that differ significantly from the “empty” background.
fg_pix = find(diff > t);Slide from Kristen Grauman
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Thresholding Given a grayscale image or an intermediate matrix
threshold to create a binary output.
Example: color-based detection
Looking for pixels within a certain hue range.
fg_pix = find(hue > t1 & hue < t2);
Slide from Kristen Grauman
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More Binary Images
6
Slide from Kristen Grauman
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Issues
How to demarcate multiple regions of interest? Count objects Compute further features per
object
What to do with “noisy” binary outputs? Holes Extra small fragments
Slide from Kristen Grauman
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Find Connected Regions
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Find Connected Regions
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Our target in this image is the largest blob.
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Connected Components
Identify distinct regions of “connected pixels”
Shapiro and Stockman
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Pixel Neighbors
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4 neighboring pixels of the blue pixel
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Pixel Neighbors
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8 neighboring pixels of the blue pixel
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Recursive Method
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label = 2for i = 1 to rows for j = 1 to cols if I(i, j) == 1 labelConnectedRegion(i, j, label) label ++; endend
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Recursive Method
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function labelConnectedRegion(int i, int j, int label) if (i,j) is labeled or background or out of boundary return
I(i,j)=label for (m,n) belongs to neighbors of (i,j) labelConnectedRegion(m,n,label) end
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Two Pass Method
We check each pixel from left to right and up to bottom If a pixel has no left and up foreground neighbor, we assign a
new label to the pixel If a pixel has only one left or up foreground neighbor, we
assign the label of the neighbor to the pixel If a pixel has both left and up foreground neighbors, and their
labels are the same, we assign the label of the neighbor to the pixel
If a pixel has both left and up foreground neighbors, and their labels are the different, we assign the label of the left neighbor to the pixel and use the up-left label pair to update the equivalency table.
We go through another pass to replace the labels to corresponding labels in the equivalency table
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Example
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1 1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
17
2 1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
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2 2 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
19
2 2 3 1 1
1 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
20
2 2 3 3 1
1 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
21
2 2 3 3 3
1 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
22
2 2 3 3 3
2 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
23
2 2 3 3 3
2 2 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
24
2 2 3 3 3
2 2 2 1
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
25
2 2 3 3 3
2 2 2 2
1 1 1 1
1 1 1 1 1
1 1 1 1 1
2 3
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
(2,3)
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Example
26
2 2 3 3 3
2 2 2 2
2 1 1 1
1 1 1 1 1
1 1 1 1 1
2 3
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
27
2 2 3 3 3
2 2 2 2
2 2 1 1
1 1 1 1 1
1 1 1 1 1
2 3
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
28
2 2 3 3 3
2 2 2 2
2 2 4 1
1 1 1 1 1
1 1 1 1 1
2 3
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
29
2 2 3 3 3
2 2 2 2
2 2 4 4
1 1 1 1 1
1 1 1 1 1
2 3
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
30
2 2 3 3 3
2 2 2 2
2 2 4 4
5 1 1 1 1
1 1 1 1 1
2 3
3 3
4 4
5 5
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
31
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 1 1 1
1 1 1 1 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
(5,2)
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Example
32
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 1 1
1 1 1 1 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
33
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 4 1
1 1 1 1 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
34
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 4 4
1 1 1 1 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
35
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 4 4
5 1 1 1 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
36
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 4 4
5 5 1 1 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
37
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 4 4
5 5 5 1 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
38
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 4 4
5 5 5 5 1
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
(5,2)
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Example
39
2 2 3 3 3
2 2 2 2
2 2 4 4
5 5 2 4 4
5 5 5 5 4
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Example
40
3 3 3 3 3
3 3 3 3
3 3 4 4
3 3 3 4 4
3 3 3 3 4
2 3
3 3
4 4
5 3
6 6
7 7
8 8
9 9
Image Label equivalence table
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Morphology Operations
Define
At = { p + t | p is a point in A}
Erosion
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T = { t | At belongs to S}
A
S
Erosion(S, A)
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Morphology Operations
Define
At = { p + t | p is a point in A}
Erosion
42
T = { t | At belongs to S}
S
What if A is
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Morphology Operations
Define
At = { p + t | p is a point in A}
Dilation
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T = Union of At and S for all t in S
S
What if A is Erosion(S, A)
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Morphology Operations
Define
At = { p + t | p is a point in A}
Dilation
44
T = Union of At and S for all t in S
S
What if A is
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Morphology Operations Define
At = { p + t | p is a point in A}
Dilation
45
T = Union of At and S for all t in S
What if A is
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Opening
Erode, then dilate Remove small objects, keep original shape
Before opening After opening
Slide from Kristen Grauman
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Closing
Dilate, then erode Fill holes, but keep original shape
Before closing After closing
Slide from Kristen Grauman
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Morphology Operators on Grayscale Images
Dilation and erosion typically performed on binary images. If image is grayscale: for dilation take the neighborhood max, for erosion
take the min.
original dilated eroded
Slide from Kristen Grauman
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Matlab
Create structure element
se = strel(‘disk’, radius); Erosion
imerode(image, se); Dilation
imdilate(image, se); Opening
imopen(image, se); Closing
imclose(image, se); More possibilities
bwmorph(image, ‘skel’);
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Figure Ground Separation
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Brightness Thresholding
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Opening
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Find the Largest Connected Region
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Example Using Binary Image Analysis: segmentation of a liver
Slide credit: Li Shen Slide from Kristen Grauman
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Example Using Binary Image Analysis:Bg subtraction + blob detection
…
Slide from Kristen Grauman
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University of Southern Californiahttp://iris.usc.edu/~icohen/projects/vace/detection.htm
Example Using Binary Image Analysis:Bg subtraction + blob detection
Slide from Kristen Grauman