图像的处理¶
Image processing basics¶
- Contrast：S curve，\(\mathrm{output}(x, y) = f(\mathrm{input}(x, y))\)
- Invert：\(\mathrm{output}(x, y) = 1 - \mathrm{input}(x, y)\)
- Blur 模糊
- Sharpen 锐化
- Edge detection 边缘检测
Gaussian Blur 高斯模糊¶
Obtain filter kernel by 2D Gaussian function:
\[
f(i, j) = \frac{1}{2\pi\sigma^2}e^{-\frac{i^2+j^2}{2\sigma^2}}
\]
3x3 Gaussian kernel:
\[
\begin{bmatrix}
.075 & .124 & .075 \\
.124 & .204 & .124 \\
.075 & .124 & .075
\end{bmatrix}
\]
Sharpen Filter 锐化滤波¶
\[
\begin{bmatrix}
0 & -1 & 0 \\
-1 & 5 & -1 \\
0 & -1 & 0
\end{bmatrix}
\]
Sharpening is adding high frequencies.
Bilateral Filter 双边滤波¶
Kernel depends on both spatial distance and intensity difference.
Image Sampling 图像采样¶
Reducing image size – down-sampling
Aliasing 混叠¶
产生原因：Signals are changing too fast but sampled too slow. 信号变化太快，采样太慢。
Higher frequency signals need faster sampling.
Under-sampling：高频信号采样不足，采样结果错误地显示低频信号。
Fourier Transform 傅里叶变换¶
Represent a function as a weighted sum of sines and cosines. 将函数表示为正弦和余弦的加权和。
\[
F(u) = \int_{-\infty}^{\infty} f(x)e^{-2\pi i ux}\mathrm{d}x
\]