Week 4: Image Filtering and Edge Detection

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

Inspired by slides of TA.Mohamed Hisham 2016
        
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## 2D Convolution 
<img style="width:100%" src="../../images/2DConv.png">

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Basic Steps are :

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1. Flip the Kernel in both horizontal and vertical directions (center of the kernel must be provided)

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2. Move over the array with kernel centered at interested point.

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3. Multiply kernel data with overlapped area.

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4. Sum or accumulate the output.

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Clear Image

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## Image Denoising Cont'd

Adding Noise

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Derived from 2D gaussian function $$\begin{equation}
h(u,v) = \frac{1}{2 \pi \sigma^2} e^{(- \frac{u^2 + v^2}{\sigma^2})}
\end{equation}
$$

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* Nonlinear digital filter
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* efficient in removal of salt and pepper noise.

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## Edge detection kernels

Edges represents the object boundaries.

Edge detection is a very important preprocessing step object detection

### Prewitt operator

For Ix(x,y) and Iy(x,y)

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For Ix(x,y) and Iy(x,y)

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## Edge detection kernels Cont'd
### Laplacian 
It is an approximation of second order derivative that defines zeros crossing. 
For Example 3x3 laplacian is :

Laplacian usually is applied after gaussian smoothing. So LOG refers to laplacian of gaussian.
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Gradient magnitude is given by

$$
\begin{equation}
I_{xy} = \sqrt{I_x(x,y)^2 + I_y(x,y)^2}
\end{equation}
$$

and Gradient direction:

$$
\begin{equation}
I_{\theta} = tan^{-1}(\frac{I_y(x,y)}{I_x(x,y)})
\end{equation}
$$
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It was developed by [John F. Canny](https://en.wikipedia.org/wiki/John_Canny) in 1986.

**Stages**
1. **Smoothing for noise removal.**
2. Finding Gradients.
3. None-maximum suppression.
4. Double Thresholding.
5. Edge Tracking by hysteresis.
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## Smoothing 
The first stage in canny edge detection algorithm is smoothing to remove noise that may cause false edges. Kernel used in this step is 5x5 gaussian kernel with $\sigma = 1.4$ and that it

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##Smoothing Cont'd
Original Image 
<img style="width:90%" src="../../images/Lines.jpg">

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**Stages**
1. Smoothing for noise removal.
2. **Finding Gradients.**
3. None-maximum suppression.
4. Double Thresholding.
5. Edge Tracking by hysteresis.
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### Finding Gradients

using sobel operator in both x and y .

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**Stages**
1. Smoothing for noise removal.
2. Finding Gradients.
3. **None-maximum suppression.**
4. Double Thresholding.
5. Edge Tracking by hysteresis.
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Compare pixel with pixels in the gradient directions and Suppress if not max.

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### None-maximum suppression Cont'd

Direction must be quantized to 8 directions or angles to use 8-Connectivity.

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### None-maximum suppression Cont'd
The result of this stage would be an edge image with thin edges.

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**Stages**
1. Smoothing for noise removal.
2. Finding Gradients.
3. None-maximum suppression.
4. **Double Thresholding.**
5. Edge Tracking by hysteresis.

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We have two threshlods $T_l$ and $T_h$ selected by user.

```python
if image[x,y] < TL:
    image[x,y] = 0
elif image(x,y) > TH:
    image[x,y] = 1
```
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### Double thresholding Cont'd

What about pixels with in-between values ?

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**Stages**
1. Smoothing for noise removal.
2. Finding Gradients.
3. None-maximum suppression.
4. Double Thresholding.
5. **Edge Tracking by hysteresis.**

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### Edge tracking by hysteresis

For in-between $T_l$ and $T_h$ check neighbors keep it if strong else Suppress.
<img style="width:95%" src="../../images/FinalCanny.jpg">

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## Demo 
```bash
$ git clone https://github.com/sbme-tutorials/cv-week4-demo
```
## Useful links

* [matplotlib gallery](https://matplotlib.org/gallery/index.html)
* [scikit-image examples](http://scikit-image.org/docs/dev/auto_examples/)
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