Week 7: Image Segmentation

class: center, middle
 ##   Image Segmentation
 By: Eslam Adel 
        
 email: eslam.a.mahmoud@eng1.cu.edu.eg
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* Image to segments (objects)

* Classification problem.

* Medical applications (3D Segmentation)

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class: top, left
### Example
Orthodontic treatment plan

3D reconstruction.
<img style="width:65%" src="../../images/Selection_061.png">
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class: top, left
### Example cont'd
Orthodontic treatment plan
<img style="width:90%" src="../../images/results.png  ">
An Optimized Technique of 3D Segmentation for Orthodontic Treatment Plan. Eslam Adel 2017 
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* Image Binarization

* Only two classes (object , background)

* Basic Idea 
$$
I(x,y) = 
\begin{cases}
0, I(x,y) < T \\\ 
1, I(x,y) > T 
\end{cases}
$$

* How to select threshold ?

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class: left, top
## Optimal Threshold
* Object, background histogram 
<img style="width:85%" src="../../images/Selection_065.png">

* Example

<img style="width:85%" src="../../images/Selection_064.png"> 
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* Optimal threshold in range 0 to 255

* Recall (We have two classes)

* Criteria 
1. Select t that minimize within class variance.

2. Select t that maximize between class variance.

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## Otsu Thresholding cont'd
* Calculating within class variance 
$$
\sigma_w^2  = c_1 \sigma_1^2 + (1-c_1) \sigma_2^2 
$$
* Calculating Between class variance 
$$
\sigma_b^2  = c_1 (1-c_1) (\mu_1 - \mu_2)^2  
$$
Where $$c_1$$ is cumulative sum at t 
* Recall 
$$
E[x] = \sum x p(x)
$$
and 
$$
\sigma^2 = E[x^2] - \mu^2
$$

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class: top, left
## Basic Algorithm 
* Basic algorithm is 
* Maximize between class variance 
```python 
Get Histogram of the image
Get relative histogram (PDF)
Get cumulative Histogram (CDF)
initialize OptThreshold = 1 and maxVariance = 0
For each t in range 1 to 255 
  m1 =  mean value class 1 
  m2 =  mean value class 2  
  c1 = CDF[t]
  varBet = c1 * (1-c1) * (m1 - m2)**2   
  if value > maxVariance 
      maxVariance = value
      OptThreshold = t  
```

**Lets try to implement it**

* What about minimizing within class variance 
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class: top, left
## Seed Pixels (Region Growing)
* Initial Seed 
* Check connected pixels 
* Add them to region (Intensity , colored based)
* repeat.

<img style="width:85%" src="../../images/Selection_066.png"> 
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