Convolutional Layer

A convolutional layer is a core component of a convolutional neural network (CNN) that extracts features from images. It's made up of a set of filters, or kernels, that are smaller than the image. Each filter convolves with the image to create an activation map, and the layer's main function is to apply a convolution operation to the input, passing the result to the next layer.

What is Convolution?

Convolution is a mathematical operation that combines two sets of information. In the context of CNNs, the operation involves combining an image matrix and a filter (also called a kernel) matrix. The filter is smaller than the image, and it is applied to each part of the image in a sliding window fashion. The filter is multiplied with the image values at each position, and the results are summed to produce a single output value in the activation map.

Convolutional Layer Architecture

Convolution Process (Cross-Correlation)

The picture belows shows how a convolution process works. We can see that three components are involved: the input image, the kernel, and the output feature map.

The heart of a convolutional layer is the kernel, which is a small matrix that slides over the input image to extract features. The kernel is applied to the input image using a convolution operation, which involves element-wise multiplication of the kernel and the input image, followed by summing the results to produce a single output value in the feature map.

Padding

Padding is a technique used to preserve the spatial dimensions of the input image when applying convolutional operations. It involves adding extra rows and columns of zeros around the input image. Padding can be used to control the size of the output feature map and to prevent information loss at the edges of the image.

Stride

Stride is a parameter that determines the step size of the kernel as it slides over the input image. A stride of 1 means the kernel moves one pixel at a time, while a stride of 2 means the kernel moves two pixels at a time.

Calculating Output Size

The output size of a convolutional layer can be calculated using the following formula, assuming the width and height of the input image are the same: