We propose a randomized-Hough-transform-based method for the detection of great circles on a sphere. We first define transformations from images acquired by central cameras to images on the unit sphere, that is, spherical images. Using the transformations, it is possible to normalize all central-camera images to the spherical image. Therefore, spherical image analysis is a fundamental study for image analysis of central cameras. For geometrical analysis and reconstruction of a three-dimensional space from spherical images, great circles on a sphere are an essential feature since a great circle on a sphere corresponds to a line on a plane in a space. For great-circle detection, we formulate the randomized Hough transform on the basis of the geometric duality of a point and a great circle on a sphere. Finally, as an extension of the randomized Hough transform on a sphere, we propose a method for great-circle detection using a continuous spherical Hough space.