Abstract Omni-directional cameras have many advantages over conventional cameras in that they have a much wider fieldof-view (FOV). Accordingly, several approaches have been proposed recently to apply convolutional neural networks (CNNs) to omni-directional images for various visual tasks. However, most of them use image representations defined in the Euclidean space after transforming the omni-directional views originally formed in the non-Euclidean space. This transformation leads to shape distortion due to nonuniform spatial resolving power and the loss of continuity. These effects make existing convolution kernels experience diffi- culties in extracting meaningful information. This paper presents a novel method to resolve such problems of applying CNNs to omni-directional images. The proposed method utilizes a spherical polyhedron to represent omni-directional views. This method minimizes the variance of the spatial resolving power on the sphere surface, and includes new convolution and pooling methods for the proposed representation. The proposed method can also be adopted by any existing CNN-based methods. The feasibility of the proposed method is demonstrated through classification, detection, and semantic segmentation tasks with synthetic and real datasets.