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Regions and Binary Images

Hao Jiang

Computer Science Department

Sept. 25, 2014

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);Slides 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);

Slides 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

Sequential connected components

Slide from J. Neira

Sequential connected components

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

Region properties

Given connected components, can compute simple features per blob, such as: Area (num pixels in the region) Centroid (average x and y position of pixels in the region) Bounding box (min and max coordinates)

How could such features be useful?

A1=200

A2=170

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

Morphological operators

Change the shape of the foreground regions/ objects.

Useful to clean up result from thresholding

Basic operators are: Dilation Erosion

Dilation

Expands connected components Grow features Fill holes

Before dilation After dilation

Erosion

Erode connected components Shrink features Remove bridges, branches, noise

Before erosion After erosion

Structuring elements

Masks of varying shapes and sizes used to perform morphology, for example:

Scan mask across foreground pixels to transform the binary image

>> help strel

Dilation

At each position: Dilation: OR (MAX) of everything inside the

structuring element mask.

Example for Dilation (1D)

SExfxg )()(

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1Output Image

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Adapted from T. Moeslund

Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1Output Image

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Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0Output Image

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Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0 1Output Image

111

Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0 1 1Output Image

111

Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0 1 1 1Output Image

111

Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0 1 1 1 1Output Image

111

Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0 1 1 1 1 1Output Image

111

Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0 1 1 1 1 1 1Output Image

111

Note that the object gets bigger and holes are filled.>> help imdilate

Example for Dilation

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

1 1 0 1 1 1 1 1 1 1Output Image

111

Note that the object gets bigger and holes are filled.>> help imdilate

Erosion

At each position: Erosion: AND (MIN) of everything inside the

structuring element mask.

Example for Erosion (1D)

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0Output Image

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SExfxg O)()( _

Example for Erosion (1D)

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0Output Image

111

SExfxg O)()( _

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0Output Image

111

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0 0Output Image

111

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0 0 0Output Image

111

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0 0 0 1Output Image

111

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0 0 0 1 0Output Image

111

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0 0 0 1 0 0Output Image

111

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0 0 0 1 0 0 0Output Image

111

Example for Erosion

1 0 0 0 1 1 1 0 1 1Input image

Structuring Element

0 0 0 0 0 1 0 0 0 0Output Image

111

Note that the object gets smaller>> help imerode

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