Week 6: Corner Detection

email: eslam.a.mahmoud@eng1.cu.edu.eg
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### Challenges

* Patch (image) matching
* Geometric transformations (Translation, Rotation, Scale)
* Photometric (Brightness, exposure )

<img style="width:90%" src="../../images/unique1.jpg">
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### Good Feature

* Distinctive (unique)
* Robust & efficient 
* General

<img style="width:90%" src="../../images/unique2.jpg">
[source](http://aishack.in/tutorials/features/)
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* Flat region

* Edge

* Corner

<img style="width:90%" src="../../images/Corners.png">
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Variation in all directions

Corner is a good feature
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## How to detect corners
* Hessian matrix
<img style="width:60%" src="../../images/Hmat.png">

* Eigen vectors and Eigen values

values (amount of variation), vector (variation direction)

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$$|H - \lambda I | = 0$$
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Complex computation.

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## Harris operator
* Instead of calculating $$\lambda_1, \lambda_2$$ 
* Lower complexity

$$  Harris = det(H(p)) - a * trace(H(p))$$

where a is  a constant.

* Trace is sum of diagonal elements

**Lets try to implement it**.

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## Harris and Stephens operator
* Instead of second order derivative Hessian matrix
* first-order derivatives of smoothed version (gaussian).

$$ H = \frac{det(G)}{trace(G)}  $$ 
 
 or 
 $$  H = det(G) - a * trace(G)$$

Select large values

**Lets See implementation**

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## FAST Corner Detector
* Features from Accelerated Segment Test (FAST)
* Real-time applications.

<img style="width:100%" src="../../images/fast.png">
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## FAST Corner Detector
* Basic Algorithm

```python
1. Select Pixel p with intensity $$I_p$$ 
2. Select Threshold t
3. Consider circle with 16 pixels.
4. Calculate absolute difference $$I_p - I_i$$ and i =1 to 16
5. P is a corner if n points have absolute difference > t and n >= 6
6. Suppress weak corners (None-Max suppression)
```

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* High Speed Test

```python
4. Calculate absolute difference $$I_p - I_i$$ Considering i =1, 9, 5, 13 only.
5. P is a corner if n points have absolute difference > t and n >= 3
6. Suppress weak corners (None-Max suppression)
```
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* None-Max suppression

```python
For successive corners.
1. For each corner point p
1. Compute score V which is sum of absolute difference between point p and 16 circle points.
2. Suppress if not local maximum. 
```
**Lets See Implementation**
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