If we want to preserve the spatial information typically found in images, then it is convenient to represent each image with a matrix of pixels. Then, a simple way to encode the local structure is to connect a submatrix of adjacent input neurons into one single hidden neuron belonging to the next layer. That single hidden neuron represents one local receptive field. Note that this operation is named Convolution and it provides the name to this type of network.

Of course, we can encode more information by having overlapping submatrices. For instance, let's suppose that the size of every single submatrix is 5 x 5 and that those submatrices are used with MNIST images of 28 x 28 pixels. Then we will be able to generate 23 x 23 local receptive field neurons in the next hidden layer. In fact, it is possible to slide the submatrices by only 23 positions before touching the borders of the images.

Let's define the feature map from one layer to another. Of course, we can have multiple feature maps that learn independently from each hidden layer. For instance, we can start with 28 x 28 input neurons to process MNIST images, and then recall k feature maps of size 23 x 23 neurons each (again with a stride of 5 x 5) in the next hidden layer.