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Regions and Binary Images

Hao Jiang

Computer Science Department

Sept. 24, 2009

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

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