Ellipsoid Fitting Using Variable Sample Consensus and Two-Ellipsoid-Bounding-Counting for Locating Lingwu Long Jujubes in a Natural Environment

Locating Lingwu Long Jujubes is a key step for the automatic picking of the jujubes which can lower labour costs. In this paper, a method for detecting Lingwu Long Jujubes in a natural environment with a three-dimensional (3D) point cloud is proposed. First, the jujubes are preliminarily extracted in two-dimensional (2D) image. Then, the points are fitted to ellipsoid by least square (LS) in the sample consensus framework. The model scores are different when sample size is changed. The variable sample consensus (VARSAC) is proposed to get higher score than random sample consensus (RANSAC). The normal vector and the distance need to be calculated in score calculation of the RANSAC. However, this score calculation method is complex and time-consuming. Thus, a new method called two-ellipsoid-bounding-counting (TEBC) is proposed. The TEBC produces two auxiliary ellipsoids that are obtained by scaling semiaxis of the model. The points, which is bounded by two auxiliary ellipsoids, are regarded as inliers. The functional value of every candidate point is calculated to select the inliers. The valid ellipsoids are determined by the prior information and the invariants. Finally, the centre, size and the attitude angle of the jujubes are solved using eigenvalues and eigenvectors. Experiments are carried out on synthetic and real datasets. The experimental results show that the proposed method can faster and more accurately detect jujube. The speed of the VARSAC+TEBC is approximately 4 times faster than that of the RANSAC in the real dataset.