有关时间序列的零碎
时间序列特性
- Auto-regressive model coefficient values
- (Shannon) Entropy values; entropy values can be taken as a measure of complexity of the signal.
- Statistical features like:
- variance
- standard deviation
- Mean
- Median
- \(25^{\text{th}}\) percentile value
- \(75^{\text{th}}\) percentile value
- Root Mean Square value; square of the average of the squared amplitude values
- The mean of the derivative
- Zero crossing rate, i.e. the number of times a signal crosses y=0
- Mean crossing rate, i.e. the number of times a signal croesses y = mean(y)
Amplitude
percent beyond 1 std
percent close to median
skew
max slope
2D filters
Gabor filters
定义：在图像处理中，Gabor函数是一个用于边缘提取的线性滤波器。Gabor滤波器十分适合纹理表达及分离。在空间域中，一个二维Gabor滤波器是一个正弦平面波调制的高斯核函数。
Gabor滤波器的脉冲响应，可以定义为一个正弦波（对于二维Gabor滤波器是正弦平面波）乘以高斯函数。由于成分卷积性质，Gabor滤波器的脉冲响应的傅里叶变换和高斯函数傅里叶变换的卷积。该滤波器有实部和虚部组成，两者相互正交。一组不同频率不同方向的Gabor函数数组对于函数特征提取非常有用。
complex
\(g(x,y;\lambda,\theta,\psi,\sigma,\gamma)=\exp\left(-\frac{x^{'2}+\gamma^{2}y^{'2}}{2\sigma^{2}}\right)\exp\left( i\left ( 2\pi\frac{x^{'}}{\lambda} + \psi \right ) \right)\)
Real
\(g(x,y;\lambda,\theta,\psi,\sigma,\gamma)=\exp\left(-\frac{x^{'2}+\gamma^{2}y^{'2}}{2\sigma^{2}}\right) \cos\left ( 2\pi\frac{x^{'}}{\lambda} + \psi \right )\)
Imaginary
\(g(x,y;\lambda,\theta,\psi,\sigma,\gamma)=\exp\left(-\frac{x^{'2}+\gamma^{2}y^{'2}}{2\sigma^{2}}\right) \sin\left ( 2\pi\frac{x^{'}}{\lambda} + \psi \right )\)
where \(x^{'}=x\cos\theta + y\sin\theta\) and \(y^{'} = -x\sin\theta + y\cos\theta\).
In this equation, \(\lambda\) represents the wavelength of the sinusoidal factor, \(\theta\) represents the orientation of the normal to the normal to the parallel stripes of a Gabor function, \(\psi\) is the phase offset, \(\sigma\) is the sigma/standard deviation of the Gaussian envelope and \(\gamma\) is the spatial aspect ratio, and specificies the ellipticity of the support of the Gabor function.
Wiki:Gaborfilter
波长（\(\lambda\)）:它的值以像素为单位指定，通常大于等于2，但是不能大于输入图像尺寸的\(\frac{1}{5}\);
方向（\(\theta\)）:这个参数指定了Gabor函数并行条纹方向，它的取值为\(0-360^{\circ}\)；
相位偏移\(\psi\)：它的取值范围为\(-180-180^\circ\)。其中，\(0^{\circ}\)和\(180^{\circ}\)分别对应中心对称的center-on function 和center-off function，而\(-90^{\circ}\)和\(90^{\circ}\)对应反对称函数。
长宽比（\(\gamma\)）:空间纵横比，决定了Gabor函数形状（support，这里译为形状）的椭圆率（ellipticity）。当\(\gamma =1\)时，形状是圆的，当\(\gamma < 1\) 时，形状随着平行条纹方向拉长，通常该值设定为0.5.
带宽（\(b\)）:Gabor滤波器的半响应空间频率带宽\(b\)和\(\frac{\sigma}{\lambda}\)的比率有关，其中\(\sigma\)表示Gabor函数的高斯因子的标准差，如下：
\(b=\log_2 \frac{ \frac{\sigma}{\lambda}\pi + \sqrt{\frac{\ln 2}{2}} }{ \frac{\sigma}{\lambda}\pi - \sqrt{\frac{\ln 2}{2}}^{'} }\) ， \(\frac{\sigma}{\lambda}=\frac{1}{\pi}\sqrt{\frac{\ln 2}{2}}\cdot \frac{2^{b}+1}{2^{b}-1}\)。
\(\sigma\)的值不能直接设置，它随着带宽\(b\)变化。带宽值必须是正实数，通常设置为1，此时，标准差和波长的关系为: \(\sigma=0.56\lambda\)。带宽越小，标准差越大，Gabor的形状越大，可见平行兴奋和抑制区域条纹数量越多。
Gabor详解
Gabor详解2
Gabor function
Applied Gabor function
wavelet function
Morlet function
\(\exp^{-0.5x^{2}}\cos(5x)\)
matlab wavefun
[psi,xval] = wavefun(wname,iter) returns the wavelet approximation psi for those wavelets that do not have an associated scaling function, such as Morlet, Mexican Hat, Gaussian derivatives wavelets, or complex wavelets.
