Application of CNN convolutional filter to 2D image. The input image (shown as a colored matrix) contains 3 × 5 pixels, while the convolutional filter (in gray) is a 3 × 3 matrix. The filter moves across the input image and each time a dot product between the filter and the sub 3 × 3 portion of the image is performed. The result of the product is stored in the output. In this example the filter is not applied to all the possible 3 × 3 partitions of the input image but jumps one pixel at every move (the way the filter moves across the image is controlled by the stride parameter, which in this case is equal to 2 as the filter is translated by two pixels at every move). The filter elements w_ij represent the weights of the network which are optimized during training, and do not change while the filter moves. In this example, the value of each pixel in the output layer is the result of the dot product between the filter and the image pixels in the two squares centered on (2, 2) and (2, 4).