# 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): \(A = X \star W\), \(A_{j j'} = \displaystyle\sum_{s=-k}^{k} \displaystyle\sum_{t=-k}^{k} W_{s,t} X_{j-s,j'-t}\), where \(W\) is the filter, and \(k\) is half of the width of the filter.
Sobel filter: \(W_{x} = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}\) and \(W_{y} = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}\).
Image gradient: \(\nabla_{x} X = W_{x} \star X\), \(\nabla_{y} X = W_{y} \star X\), with gradient magnitude \(G = \sqrt{\nabla_{x}^{2} + \nabla_{y}^{2}}\) and gradient direction \(\Theta = arctan\left(\dfrac{\nabla_{y}}{\nabla_{x}}\right)\).

Fully connected layer: \(a = g\left(w^\top x + b\right)\), where \(a\) is the activation unit, \(g\) is the activation function.
Convolution layer: \(A = g\left(W \star X + b\right)\), where \(A\) is the activation map.
Pooling layer: (max-pooling) \(a = \displaystyle\max\left\{x_{1}, ..., x_{m}\right\}\), (average-pooling) \(a = \dfrac{1}{m} \displaystyle\sum_{j=1}^{m} x_{j}\).