Abstract:

A nonlinear kernel with a bias is proposed here in the convolutional neural network. Negative square of subtraction between input image pixel numbers and the kernel coefficients are convolved to conform new feature map through the convolution layer in convolutional neural network. The operation is nonlinear from the input pixel point of view, as well as from the kernel weight coefficient point of view. Maximum-pooling may follow the feature map, and the results are finally fully connected to the output nodes of the network. While using gradient descent method to train relevant coefficients and biases, the gradient of the square of subtraction term appears in the whole gradient over each kernel coefficient. The new subtraction kernel is applied to two sets of images, and shows better performance than the existing linear convolution kernel. Each coefficient of the nonlinear subtraction kernel has quite image-equivalent meaning on top of pure mathematical number. The subtraction kernel works equally for a given black and white image set and its reversed version or for a given gray image set and its reversed version. This attribute becomes important when patterns are mixed with light color and dark color, or mixed with background color, and still both sides are equally important.

Keywords: