title: Circular motion geometry using minimal data.
abstract: Circular motion or single axis motion is widely used in computer vision and graphics for 3D model acquisition. This paper describes a new and simple method for recovering the geometry of uncalibrated circular motion from a minimal set of only two points in four images. This problem has been previously solved using nonminimal data either by computing the fundamental matrix and trifocal tensor in three images or by fitting conics to tracked points in five or more images. It is first established that two sets of tracked points in different images under circular motion for two distinct space points are related by a homography. Then, we compute a plane homography from a minimal two points in four images. After that, we show that the unique pair of complex conjugate eigenvectors of this homography are the image of the circular points of the parallel planes of the circular motion. Subsequently, all other motion and structure parameters are computed from this homography in a straighforward manner. The experiments on real image sequences demonstrate the simplicity, accuracy, and robustness of the new method.
authors.affiliation: Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong. gjiang@ee.cuhk.edu.hk
authors.forename: Guang
authors.initials: G
authors.lastname: Jiang
authors.forename: Long
authors.initials: L
authors.lastname: Quan
authors.forename: Hung-Tat
authors.initials: HT
authors.lastname: Tsui
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016208:Databases, Factual; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D012399:Rotation