We describe a special case of structure from motion where the camera rotates on a sphere. The camera's optical axis lies perpendicular to the sphere's surface. In this case, the camera's pose is minimally represented by three rotation parameters. From analysis of the epipolar geometry we derive a novel and efficient solution for the essential matrix relating two images, requiring only three point correspondences in the minimal case. We apply this solver in a structure-from-motion pipeline that aggregates pairwise relations by rotation averaging followed by bundle adjustment with an inverse depth parameterization. Our methods enable scene modeling with an outward-facing camera and object scanning with an inward-facing camera.
Full panoramic images, covering 360 degrees, can be created either by using panoramic cameras or by mosaicing together many regular images. Creating panoramic views in stereo, where one panorama is generated for the left eye, and another panorama is generated for the right eye is more problematic. Earlier attempts to mosaic images from a rotating pair of stereo cameras faced severe problems of parallax and of scale changes. A new family of multiple viewpoint image projections, the Circular Projections, is developed. Two panoramic images taken using such projections can serve as a panoramic stereo pair. A system is described to generates a stereo panoramic image using circular projections from images or video taken by a single rotating camera. The system works in real-time on a PC. It should be noted that the stereo images are created without computation of 3D structure, and the depth effects are created only in the viewer's brain. As the field of view of a picture is much smaller than our own visual field of view, it is common to paste together several pictures to create a panoramic mosaic having a larger field of view. Images with a wider field of view can be generated by using fish-eye lens, or panoramic mosaics can be created by special devices which rotate around the camera's optical center (Quicktime VR, Surround Video), or by aligning, and pasting, frames in a video sequence to a single reference frame. Existing mosaicing methods have strong limitations on imaging conditions, and distortions are common. Manifold projection enables the creation of panoramic mosaics from video sequences under more general conditions, and in particular the unrestricted motion of a hand-held camera. The panoramic mosaic is a projection of the scene into a virtual manifold whose structure depends on the camera's motion. This manifold is more general than the customary projections onto a single image plane or onto a cylinder. In addition to being more general than traditional mosaics, manifold projection is also computationally efficient, as the only image deformations used are image plane translations and rotations. Real-time, software only, implementation on a Pentium-PC, proves the superior quality and speed of this approach. A new approach to computing a panoramic (360 degrees) depth map is presented in this paper. Our approach uses a large collection of images taken by a camera whose motion has been constrained to planar concentric circles. We resample regular perspective images to produce a set of multiperspective panoramas and then compute depth maps directly from these resampled panoramas. Our panoramas sample uniformly in three dimensions: rotation angle, inverse radial distance, and vertical elevation. The use of multiperspective panoramas eliminates the limited overlap present in the original input images and, thus, problems as in conventional multibaseline stereo can be avoided. Our approach differs from stereo matching of single-perspective panoramic images taken from different locations, where the epipolar constraints are sine curves. For our multiperspective panoramas, the epipolar geometry, to the first order approximation, consists of horizontal lines. Therefore, any traditional stereo algorithm can be applied to multiperspective panoramas with little modification. In this paper, we describe two reconstruction algorithms. The first is a cylinder sweep algorithm that uses a small number of resampled multiperspective panoramas to obtain dense 3D reconstruction. The second algorithm, in contrast, uses a large number of multiperspective panoramas and takes advantage of the approximate horizontal epipolar geometry inherent in multiperspective panoramas. It comprises a novel and efficient 1D multibaseline matching technique, followed by tensor voting to extract the depth surface. Experiments show that our algorithms are capable of producing comparable high quality depth maps which can be used for applications such as view interpolation.