This paper proposes a novel video representation method for videos capturing events held in a wide field. Such events can be captured with high resolution due to the recent development of video capturing technologies. Despite the development of these technologies, representation methods for wide field-of-view (wide-FOV) video are limited in number. Our work aims at simultaneously achieving (1) high visibility for regions of interest (ROIs), (2) easy overviewing, and (3) intuitive comprehension of the relative positions of video objects. Because of these advantages, the proposed method is especially suitable for showing wide-FOV videos on small display devices such as tablets and smartphones. To achieve the abovementioned aims, we propose a convex object surface mapping technique that provides high ROI visibility and easy overviewing. In addition, by using an elliptic cylinder or an oval as a convex object, the convex object surface mapping enables intuitive comprehension of the relative positions of video objects. The efficacy of the proposed method was verified through objective and subjective experiments.