1 Regions and Binary Images Hao Jiang Computer Science Department Sept. 24, 2009.
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Transcript of 1 Regions and Binary Images Hao Jiang Computer Science Department Sept. 24, 2009.
1
Regions and Binary Images
Hao Jiang
Computer Science Department
Sept. 24, 2009
Figure Ground Separation
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Brightness Thresholding
3
=-
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
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
More Binary Images
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Slide from Kristen Grauman
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
Find Connected Regions
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Find Connected Regions
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Our target in this image is the largest blob.
Connected Components
Identify distinct regions of “connected pixels”
Shapiro and Stockman
Pixel Neighbors
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4 neighboring pixels of the blue pixel
Pixel Neighbors
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8 neighboring pixels of the blue pixel
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
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
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
Example
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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
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
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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)
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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)
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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
Example
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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)
Example
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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
Example
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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
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)
Morphology Operations
Define
At = { p + t | p is a point in A}
Erosion
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T = { t | At belongs to S}
S
What if A is
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)
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
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
What if A is
Opening
Erode, then dilate Remove small objects, keep original shape
Before opening After opening
Slide from Kristen Grauman
Closing
Dilate, then erode Fill holes, but keep original shape
Before closing After closing
Slide from Kristen Grauman
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
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
Example Using Binary Image Analysis:Bg subtraction + blob detection
…
Slide from Kristen Grauman
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
