October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Demo Website

I highly recommend taking a look at this website:

http://users.ecs.soton.ac.uk/msn/book/new_demo/

It has nice interactive demonstrations of the Fourier transform, the Hough transform, edge detection, and many other useful operations.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Region Detection

There are two basic – and often complementary – approaches to segmenting an image into individual objects or parts of objects: region-based segmentation and boundary estimation.

Region-based segmentation is based on region detection, which we will discuss in this lecture.

Boundary estimation is based on edge detection, which we already discussed earlier.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Region Detection

We have already seen the simplest kind of region detection.

It is the labeling of connected components in binary images.

Of course, in general, region detection is not that simple.

Successful region detection through component labeling requires that we can determine an intensity threshold in such a way that all objects consist of 1-pixels and do not touch each other.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Region Detection

We will develop methods that can do a better job at finding regions in real-world images.

In our discussion we will first address the question of how to segment an image into regions.

Afterwards, we will look at different ways to represent the regions that we detected.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Region Detection

How shall we define regions?

The basic idea is that within the same region the intensity, texture, or other features do not change abruptly.

Between adjacent regions we do find such a change in at least one feature.

Let us now formalize the idea of partitioning an image into a set of regions.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Region Detection

A partition S divides an image I into a set of n regions Ri. Regions are sets of connected pixels meeting three requirements:

• The union of regions includes all pixels in the image,

IRn

ii

1

• Each region Ri is homogeneous, i.e., satisfies a homogeneity predicate P so that P(Ri) = True.

• The union of two adjacent regions Ri and Rj never satisfies the homogeneity predicate, i.e., P(Ri Rj) = False.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Region Detection

The homogeneity predicate could be defined as, for example, the maximum difference in intensity values between two pixels being no greater than a some threshold .

Usually, however, the predicate will be more complex and include other features such as texture.

Also, the parameters of the predicate such as may be adapted to the properties of the image.

Let us take a look at the split-and-merge algorithm of image segmentation.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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The Split-and-Merge Algorithm

First, we perform splitting:• At the start of the algorithm, the entire image is

considered as the candidate region.• If the candidate region does not meet the

homogeneity criterion, we split it into four smaller candidate regions.

• This is repeated until there are no candidate regions to be split anymore.

Then, we perform merging:• Check all pairs of neighboring regions and merge

them if it does not violate the homogeneity criterion.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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The Split-and-Merge Algorithm

Sample image to be segmented with = 1

1 1 1 1 1 1 1 2

1 1 1 1 1 1 1 0

3 1 4 9 9 8 1 0

1 1 8 8 8 4 1 0

1 1 6 6 6 3 1 0

1 1 5 6 6 3 1 0

1 1 5 6 6 2 1 0

1 1 1 1 1 1 0 0

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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The Split-and-Merge Algorithm

First split

1 1 1 1 1 1 1 2

1 1 1 1 1 1 1 0

3 1 4 9 9 8 1 0

1 1 8 8 8 4 1 0

1 1 6 6 6 3 1 0

1 1 5 6 6 3 1 0

1 1 5 6 6 2 1 0

1 1 1 1 1 1 0 0

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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The Split-and-Merge Algorithm

Second split

1 1 1 1 1 1 1 2

1 1 1 1 1 1 1 0

3 1 4 9 9 8 1 0

1 1 8 8 8 4 1 0

1 1 6 6 6 3 1 0

1 1 5 6 6 3 1 0

1 1 5 6 6 2 1 0

1 1 1 1 1 1 0 0

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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The Split-and-Merge Algorithm

Third split

1 1 1 1 1 1 1 2

1 1 1 1 1 1 1 0

3 1 4 9 9 8 1 0

1 1 8 8 8 4 1 0

1 1 6 6 6 3 1 0

1 1 5 6 6 3 1 0

1 1 5 6 6 2 1 0

1 1 1 1 1 1 0 0

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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The Split-and-Merge Algorithm

Merge

1 1 1 1 1 1 1 2

1 1 1 1 1 1 1 0

3 1 4 9 9 8 1 0

1 1 8 8 8 4 1 0

1 1 6 6 6 3 1 0

1 1 5 6 6 3 1 0

1 1 5 6 6 2 1 0

1 1 1 1 1 1 0 0

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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The Split-and-Merge Algorithm

Final result

1 1 1 1 1 1 1 2

1 1 1 1 1 1 1 0

3 1 4 9 9 8 1 0

1 1 8 8 8 4 1 0

1 1 6 6 6 3 1 0

1 1 5 6 6 3 1 0

1 1 5 6 6 2 1 0

1 1 1 1 1 1 0 0

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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A Better Criterion

The split-and-merge algorithm is a straightforward way of finding a segmentation of an image that provides homogeneity within regions and non-homogeneity of neighboring regions.

In practice, it is not a good idea to use a maximum intensity difference as the criterion.

A single outlier pixel (black or white) could decide about splitting or merging large regions.

Instead, we should use the standard deviation of pixel intensities within a region.

Our criterion could be that max.

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Examples

Input image(512×512 pixels)

Image after splitting (max= 40)

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Examples

Input image(512×512 pixels)

Image after split/merge (max= 40)

October 28, 2014 Computer Vision Lecture 13: Image Segmentation III

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Examples

Input image(512×512 pixels)

Image after split/merge (max= 10)