Hassan Bozorgmanesh: Sparse Resultant‑Based Minimal Solvers Using Null Spaces

Abstract.

Solving polynomial systems of equations holds a special place in computer vision, as many camera geometry problems can be modeled using polynomial equations derived from minimal sets of data—commonly referred to as minimal problems. A minimal solver computes solutions to these problems and is typically used within RANSAC (Random Sample Consensus) frameworks. In this context, systems with a particular structure of coefficients must be solved repeatedly.   In this talk, after introducing sparse resultant‑based minimal solvers, a new method that increases the efficiency of this approach by employing null‑space computation is proposed. The main advantages of the proposed method over the original one are the stability of its formulation in the offline stage, the elimination of matrix inversion through null‑space computations, and improved accuracy in the online stage. Additionally, its formulation enables the possibility of shifting more computations to the offline stage by exploiting the sparsity of the coefficient matrices, thereby reducing the computational load during the online stage.   Finally, the possibility of combining the sparse resultant‑based method with homotopy continuation to create a new minimal solver is discussed.