Common cameras with a dynamic range of two orders cannot reproduce typical outdoor scenes with a radiance range of over five orders. Most high dynamic range (HDR) imaging techniques reconstruct the whole dynamic range from exposure bracketed low dynamic range (LDR) images. But the camera must be kept steady with no or small motion, which is not practical in many cases. Thus, we develop a more efficient framework for omnidirectional HDR imaging with a moving camera. The proposed framework is composed of three major stages: geometric calibration and rotational alignment, multi-view stereo correspondence and HDR composition. First, camera poses are determined and omnidirectional images are rotationally aligned. Second, the aligned images are fed into a spherical vision toolkit to find disparity maps. Third, enhanced disparity maps are used to warp differently exposed neighboring images to a target view and an HDR radiance map is obtained by fusing the registered images in radiance. We develop disparity-based forward and backward image warping algorithms for spherical stereo vision and implement them in GPU. We also explore some techniques for disparity map enhancement including a superpixel technique and a color model for outdoor scenes. We examine different factors such as exposure increment step size, sequence ordering, and the baseline between views. We demonstrate the success with indoor and outdoor scenes and compare our results with two state-of-the-art HDR imaging methods. The proposed HDR framework allows us to capture HDR radiance maps, disparity maps and an omnidirectional field of view, which has many applications such as HDR view synthesis and virtual navigation.