# Different Convolutions

### Pointwise Convolution or 1x1 convolution

It is a 1x1 convolution kernel. This helps in acquiring pixel by pixel level feature extraction. But the main purpose is, 1. When the number channels in the previous layers needs to be shrinked , then we use 1x1 convolution. This reduces the problem of computational cost.
2. For all the features learned from the previous layer, 1x1 convolution indroduces more nonlinearity ( through activation function ). This inturn increases the network’s nonlinearity with the previous layers.

Andrew Ng’s coursera video on 1x1 convolution

### Dilated Convolution A kernel with spaces in between each cell is called dilation. 1-Dilated kernel has 1 cell spaces around pixels. 1-Dilated kernels have the capacity to extract higher spatial information from an effective receptive field. Dilated kernels can be used along with regular kernels. Since, a 0-Dilated kernel is a regular kernel .

Dilated convolution are used for applications like semantic segmentation with one label per pixel , image super resolution , denoising etc.

$$Dilated \ Kernel = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 \\ 0 & 0& 0&0&0\\ 1 & 0 & 1 & 0 & 1 \\ 0 & 0& 0&0&0\\ 1 & 0 & 1 & 0 & 1 \\ \end{bmatrix}$$ CS231n Notes on Dilated convolution

Dilated Convolution Blog Post

This paper infers that the architecture assumes the fact that dilated convolution increases the receptive field exponentially through the network.

### Transposed convolution layer / Deconvolution

From the paper Deconvolution Networks

Convolutional networks are a bottom-up approach where the input signal is subjected to multiple layers of convolutions, non-linearities and sub-sampling. By contrast, each layer in our Deconvolutional Network is top-down; it seeks to generate the input signal by a sum over convolutions of the feature maps (as opposed to the input) with learned filters.