  The Convolutional Neural Network (CNN) has been successfully applied in many
fields during recent decades; however it lacks the ability to utilize prior
domain knowledge when dealing with many realistic problems. We present a
framework called Geometric Operator Convolutional Neural Network (GO-CNN) that
uses domain knowledge, wherein the kernel of the first convolutional layer is
replaced with a kernel generated by a geometric operator function. This
framework integrates many conventional geometric operators, which allows it to
adapt to a diverse range of problems. Under certain conditions, we
theoretically analyze the convergence and the bound of the generalization
errors between GO-CNNs and common CNNs. Although the geometric operator
convolution kernels have fewer trainable parameters than common convolution
kernels, the experimental results indicate that GO-CNN performs more accurately
than common CNN on CIFAR-10/100. Furthermore, GO-CNN reduces dependence on the
amount of training examples and enhances adversarial stability. In the
practical task of medically diagnosing bone fractures, GO-CNN obtains 3%
improvement in terms of the recall.
