How an image is represented as the input of a convolutional neural network (CNN) is important because this input directly influences the performance of the CNN. In this paper, we investigate the representation of spherical images by focusing on the inclination estimation of a spherical camera. Unlike other approaches to CNN-based inclination estimation, a spherical image is represented as a geodesicdivision-based discrete spherical image (DSI) that is obtained by sampling a sphere as uniformly as possible. The input of the CNN is a single image that consists of five parallelograms flattened from a regular icosahedron. To demonstrate the advantage of the proposed method, comparative experiments are conducted with two other spherical image representations, namely, equirectangular projection (ERP) and cubemap projection (CMP). The experimental results show that the proposed method using a geodesic-division-based discrete spherical image as the CNN input obtains the best performance-better than that of the cubemap and far superior to that of the equirectangular image. The effect of the image representations used becomes more significant as the relative inclination decreases. Moreover, comparative experiments are conducted using the state-of-the-art methods for spherical camera inclination compensation to further illustrate the superiority of the DSI representation. Consequently, the proposed method provides an important reference for the development of CNNs intended for spherical images.

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