Circular motion geometry by minimal 2 points in 4 images

We describe a new and simple method of recovering the geometry of uncalibrated circular motion or single axis motion using a minimal data set of 2 points in 4 images. This problem has been solved using nonminimal data either by computing the fundamental matrix and trifocal tensor in 3 images, or by fitting conics to tracked points in 5 images. Our new method first computes a planar homography from a minimum of 2 points in 4 images. It is shown that two eigenvectors of this homography are the images of the circular points. Then, other fixed image entities and rotation angles can be straightforwardly computed. The crux of the method lies in relating this planar homography from two different points to a homology naturally induced by corresponding points on different conic loci from a circular motion. The experiments on real image sequences demonstrate the simplicity, accuracy and robustness of the new method.