Hyper-convolutions via implicit kernels for medical image analysis.

The convolutional neural network (CNN) is one of the most commonly used architectures for computer vision tasks. The key building block of a CNN is the convolutional kernel that aggregates information from the pixel neighborhood and shares weights across all pixels. A standard CNN's capacity, and thus its performance, is directly related to the number of learnable kernel weights, which is determined by the number of channels and the kernel size (support). In this paper, we present the hyper-convolution, a novel building block that implicitly encodes the convolutional kernel using spatial coordinates. Unlike a regular convolutional kernel, whose weights are independently learned, hyper-convolution kernel weights are correlated through an encoder that maps spatial coordinates to their corresponding values. Hyper-convolutions decouple kernel size from the total number of learnable parameters, enabling a more flexible architecture design. We demonstrate in our experiments that replacing regular convolutions with hyper-convolutions can improve performance with less parameters, and increase robustness against noise. We provide our code here: https://github.com/tym002/Hyper-Convolution.