Solutions of Quadratic First-Order ODEs applied to Computer Vision Problems.

摘要: This article is a study about the existence and uniqueness of solutions specific quadratic first-order ODE that frequently appears in multiple reconstruction problems. It called \emph{planar-perspective equation} due to duality with geometric problem planar-perspective curves from their modulus. Solutions are related planar parametrized perspective parametrization this interpretation. The proves only two local \emph{initial value problem} \emph{regular initial conditions} maximum analytic \emph{critical conditions}. also gives theorems extend definition domain where both guaranteed. introduces \emph{maximal depth function} as function upper-bound all possible contains its points}. Finally, describes \emph{maximal-depth solution consists finding referred equation has uniqueness. an important it does not need conditions obtain unique frequent practical algorithms state-of-the-art give.