HyperLS for Parameter Estimation in Geometric Fitting

Abstract

We present a general framework of a special type of least squares (LS) estimator, which we call “HyperLS, ” for parameter estimation that frequently arises in computer vision applications. It minimizes the algebraic distance under a special scale normalization, which is derived by a detailed error analysis in such a way that statistical bias is removed up to second order noise terms. We discuss in detail many theoretical issues involved in its derivation. By numerical experiments, we show that HyperLS is far superior to the standard LS and comparable in accuracy to maximum likelihood (ML), which is known to produce highly accurate results but may fail to converge if poorly initialized. We conclude that HyperLS is a perfect candidate for ML initialization.