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I have a homogeneity image that includes two regions $\Omega_1$ and $\Omega_2$. How to represent the image by decomposition of two regions?

For example, the famous way is representing by the mean feature. Image $I$ can be represented as follows:

$$I=u_1c_1+u_2c_2$$

$c_1$ is mean of region $\Omega_1$

$c_2$ is mean of region $\Omega_2$

$ u_1 = \begin{cases} 1 & \text{if is $\Omega_1$ }\\ 0 & \text{otherwise} \end{cases} $

$ u_2 = \begin{cases} 1 & \text{if is $\Omega_2$ }\\ 0 & \text{otherwise} \end{cases} $

Do you know another way to represent image $I$ without using mean feature. Thank you so much

As the question, I will show a simple example as following enter image description here

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  • $\begingroup$ Can you show an example image? $\endgroup$ – Adi Shavit May 6 '15 at 10:56
  • $\begingroup$ @AdiShavit: Let see the example. Note that, $I$ is homogeneity image. I am looking for a feature to represent the region of image, not mean intensity $\endgroup$ – John May 6 '15 at 12:39
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Your example seems to imply you are talking about mutually exclusive, non-overlapping regions.

In this case, given N such regions, use an image where each pixel has enough values (depth), to represent N regions. Just set the pixel value to the index of the region in that position.

You could think of the result image as a sum of N binary images, each multiplied by the $i$ subscript of the corresponding $\Omega_i$.

Alternatively, if you are asking about how to segment such an image into 2 (or more) regions, the you should use a connected component algorithm, which is common is most image processing libraries.

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  • $\begingroup$ So, How to model image $I$, for example, such as mean feature, $I$ can model as my formula $\endgroup$ – John May 6 '15 at 12:45
  • $\begingroup$ I'm sorry, I don't understand the question. Are you asking about image pixel representations or some mathematical abstraction? $\endgroup$ – Adi Shavit May 6 '15 at 12:46
  • $\begingroup$ Mathematical abstraction,sir $\endgroup$ – John May 6 '15 at 12:47
  • $\begingroup$ Well, in that case, you will have to be much more specific. An image, in general, is a non-parametric representation, much like a general matrix. $\endgroup$ – Adi Shavit May 6 '15 at 12:53
  • $\begingroup$ Yes,right. For other example, for rice noise image, they often used median feature. However, in my case, i assumed that my image is homogeneity image. It is more simple case $\endgroup$ – John May 6 '15 at 12:54

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