Title: Geometry aware convolutional filters for omnidirectional images representation. Abstract: Due to their wide field of view, omnidirectional cameras are frequently used by autonomous vehicles, drones and robots for navigation and other computer vision tasks. The images captured by such cameras, are often analysed and classified with techniques designed for planar images that unfortunately fail to properly handle the native geometry of such images. That results in suboptimal performance, and lack of truly meaningful visual features. In this paper we aim at improving popular deep convolutional neural networks so that they can properly take into account the specific properties of omnidirectional data. In particular we propose an algorithm that adapts convolutional layers, which often serve as a core building block of a CNN, to the properties of omnidirectional images. Thus, our filters have a shape and size that adapts with the location on the omnidirectional image. We show that our method is not limited to spherical surfaces and is able to incorporate the knowledge about any kind of omnidirectional  geometry inside the deep learning network. As depicted by our experiments, our method outperforms the existing deep neural network techniques for omnidirectional image classification and compression tasks.