UNet 3+¶
浙大的论文，非要用英文写，想要看懂还得翻译回来，难受。
先导知识¶
Up-Sampling¶
There are four major ways of upsampling: bilinear interpolation, transposed convolution, unpooling and dilated convolution.
Bilinear Interpolation¶
假设我们想得到未知数\(f\)在点\(P=(x, y)\)处的值，已知函数\(f\)在\(Q_{11}=(x_1, y_1)\), \(Q_{12}=(x_1, y_2)\), \(Q_{21}=(x_2, y_1)\), \(Q_{22}=(x_2, y_2)\)四个点的值，首先在\(x\)方向进行差值，得到
\[
f(R_1) \approx \frac{x_2-x}{x_2-x_1}f(Q_{11})+\frac{x-x_1}{x_2-x_1}f(Q_{21})\quad \text{where}\quad R=(x, y_1)
\]
\[
f(R_2) \approx \frac{x_2-x}{x_2-x_1}f(Q_{12})+\frac{x-x_1}{x_2-x_1}f(Q_{22})\quad \text{where}\quad R=(x, y_2)
\]
然后在\(y\)方向进行线性插值
\[
f(P) \approx \frac{y_2-y}{y_2-y_1}f(R_1) + \frac{y-y_1}{y_2-y_1}f(R_2)
\]
Deconvolution¶
Deconvolution 又称 Transposed Convolution
假设我们有一个\(3 \times 3\)的卷积核，
\[
k = \pmatrix{
w_{0, 0} & w_{0, 0} & w_{0, 0} \\
w_{0, 0} & w_{0, 0} & w_{0, 0} \\
w_{0, 0} & w_{0, 0} & w_{0, 0}
}
\]
TODO: 用一张纸算算这些\(w\)都是哪跟哪
\[
\begin{pmatrix}
w_{0,0} & 0 & 0 & 0 \\
w_{0,1} & w_{0,0} & 0 & 0 \\
w_{0,2} & w_{0,1} & 0 & 0 \\
0 & w_{0,2} & 0 & 0 \\
w_{1,0} & 0 & w_{0,0} & 0 \\
w_{1,1} & w_{1,0} & w_{0,1} & w_{0,0} \\
w_{1,2} & w_{1,1} & w_{0,2} & w_{0,1} \\
0 & w_{1,2} & 0 & w_{0,2} \\
w_{2,0} & 0 & w_{1,0} & 0 \\
w_{2,1} & w_{2,0} & w_{1,1} & w_{1,0} \\
w_{2,2} & w_{2,1} & w_{1,2} & w_{1,1} \\
0 & w_{2,2} & 0 & w_{1,2} \\
0 & 0 & w_{2,0} & 0 \\
0 & 0 & w_{2,1} & w_{2,0} \\
0 & 0 & w_{2,2} & w_{2,1} \\
0 & 0 & 0 & w_{2,2}
\end{pmatrix} ^ \intercal
\]
{loading=lazy}
Q: 转置卷积会更新权值吗？反向传播公式？
Unpooling¶
That's comparably easier.
Dilated Convolution¶
Down-Sampling¶
TODO: Tesla 系列和 GTX 系列性能对比