# Digital Image Processing

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quiz
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### Smoothing filter

* smothing filters are used for
* blurring
* noise reduction

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how to quantize the performance of a filter?
* SNR: Signal Noise Ratio
* $SNR = \log10 \frac {P.signal}{P.noise}$
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#### box kernal smoothing filter
* with $kernal = 3$
* $\frac{1}{9} \cdot\begin{bmatrix} 1&1&1\\ 1&1&1\\ 1&1&1 \end{bmatrix}$

* which will result one pixel be the mean of itself and its 8 neighborhood
* thus the difference between two neighboring pixels will become less
* image will be visually smoother and blur, and noiseless

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how to define a kernal size
* the closest number *larger* than $6 * \sigma$
* since $6 * \sigma$ covering $99 \%$ of data in the Normal Distribution Model/ Gaussian Distribution Model
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unfinished
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#### padding techniques
* zero padding
* mirror padding: mirrow the inside pixel
* replicate padding: copy the border
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#### usage of major filters
* LPF: blur the border
* HPF: enhance the border

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unfinished
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[havn't finish from](https://youtu.be/wkk9wH2F4bc?feature=shared&t=2362)

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### [Introduce Correlation& Convolution](https://zhuanlan.zhihu.com/p/33194385)

#### convolution
* general mask
* processing with dot prodoct

#### correlation
* an upside down& left right flipped convolution mask
* processing with star 🌟 prodoct as well

#### comparison of two
| Convolution | Method | Correlation |
| ----------- | ------ | ----------- |
| Y | Conmmutative 交換律 | N |
| Y | Associative 結合律 | N |
| Y | Distributive 分配律 | Y |

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* Conmmutative:
* $a* b = b* a$
* Associative:
* $a* (b* c) = (a* b)* c$
* Distributive:
* $a* (b+ c) = a* b+ a* c$
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### histogram equalization
[a more easy way to explaine](https://jason-chen-1992.weebly.com/home/-histogram-equalization)
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* sleeping
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### Chapter 2

####
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* .* : a MATLAB operator to do multiply element-wise.
* unlike mathmetic operator $*$, the elements of answer matrix should be the combinaion of multiple elements from original two matrix, $.*$ only multiply the elements from original two matrix of the same position.
* ROI: region of interest, frequently used in masking
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#### complimentary of not binary image
* let A(x, y, z)

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### Chapter 2

#### Connect Component

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### Chapter 1

#### typcal image processing system

#### REQUIREMENTS for Image Acquisition
1. band-limited
* since we can not save infinity digital data
2. sampling rate shout be equal or larger than the full range of data
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**Sampling Theory**
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#### ?
Level 0

Level 1
* image to image

Level 2
* to recognize some feature from images

Level 3
* to label a image