Real-Time Hyperbola Recognition and Fitting in GPR Data

Abstract

The problem of automatically recognizing and fitting hyperbolae from ground-penetrating radar (GPR) images is addressed, and a novel technique computationally suitable for real-time on-site application is proposed. After preprocessing of the input GPR images, a novel thresholding method is applied to separate the regions of interest from background. A novel column-connection clustering (C3) algorithm is then applied to separate the regions of interest from each other. Subsequently, a machine learnt model is applied to identify hyperbolic signatures from outputs of the C3 algorithm, and a hyperbola is fitted to each such signature with an orthogonal-distance hyperbola fitting algorithm. The novel clustering algorithm C3 is a central component of the proposed system, which enables the identification of hyperbolic signatures and hyperbola fitting. Only two features are used in the machine learning algorithm, which is easy to train using a small set of training data. An orthogonal-distance hyperbola fitting algorithm for “south-opening” hyperbolae is introduced in this work, which is more robust and accurate than algebraic hyperbola fitting algorithms. The proposed method can successfully recognize and fit hyperbolic signatures with intersections with others, hyperbolic signatures with distortions, and incomplete hyperbolic signatures with one leg fully or largely missed. As an additional novel contribution, formulas to compute an initial “south-opening” hyperbola directly from a set of given points are derived, which make the system more efficient. The parameters obtained by fitting hyperbolae to hyperbolic signatures are very important features; they can be used to estimate the location and size of the related target objects and the average propagation velocity of the electromagnetic wave in the medium. The effectiveness of the proposed system is tested on both synthetic and real GPR data.