# Other Materials

Part 1 (Convolution): Link
Part 2 (Gradient Filters): Link
Part 3 (Computer Vision): Link
Part 4 (Computer Vision): Link
Part 5 (Viola Jones): Link
Part 6 (Convolutional Neural Net): Link

Image Filter: Link
Canny Edge Detection: Link
SIFT: PDF
HOG: PDF
Conv Net on MNIST: Link
Conv Net Vis: Link
LeNet: PDF, Link
Google Inception Net: PDF
CNN Architectures: Link
Image to Image: Link
Image segmentation: Link
Image colorization: Link, Link 
Image Reconstruction: Link
Style Transfer: Link
Move Mirror: Link
Pose Estimation: Link
YOLO Attack: YouTube

# Keywords and Notations

Convolution (1D): $a=x\star w$, $a_j={\displaystyle \sum _{t=-k}^k{w}_t{x}_{j-t}}$, where $w$ is the filter, and $k$ is half of the width of the filter.
Convolution (2D): $A=X\star W$, $A_{j{j}^{\prime }}={\displaystyle \sum _{s=-k}^k{\displaystyle \sum _{t=-k}^k{W}_{s,t}{X}_{j-s,j^{\prime }-t}}}$, where $W$ is the filter, and $k$ is half of the width of the filter.
Sobel filter: $W_x=\left[\begin{array}{ccc}-1& 0& 1\\ -2& 0& 2\\ -1& 0& 1\end{array}\right]$ and $W_y=\left[\begin{array}{ccc}-1& -2& -1\\ 0& 0& 0\\ 1& 2& 1\end{array}\right]$.
Image gradient: ${\mathrm{\nabla }}_{x}X=W_x\star X$, ${\mathrm{\nabla }}_{y}X=W_y\star X$, with gradient magnitude $G=\sqrt{{\mathrm{\nabla }}_x^2+{\mathrm{\nabla }}_y^2}$ and gradient direction $\mathrm{\Theta }=arctan\left({\displaystyle \frac{{\mathrm{\nabla }}_y}{{\mathrm{\nabla }}_x}}\right)$.

Fully connected layer: $a=g(w^{\mathrm{\top }}x+b)$, where $a$ is the activation unit, $g$ is the activation function.
Convolution layer: $A=g(W\star X+b)$, where $A$ is the activation map.
Pooling layer: (max-pooling) $a={\displaystyle max\{x_1,...,x_m\}}$, (average-pooling) $a={\displaystyle \frac{1}{m}}{\displaystyle \sum _{j=1}^m{x}_j}$.