A convergent mean shift algorithm to select targets for LAMOST

Abstract

This paper firstly finds that the Mean Shift Algorithm used by the Observation Control System (OCS) Research Group of the University of Science and Technology of China in Survey Strategy System 2.10 (SSS2.10) to select targets for the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) is not convergent in theory. By carefully studying the mathematical formulation of the Mean Shift Algorithm, we find that it tries to find a point where some objective function achieves its maximum value; the Mean Shift Vector can be regarded as the ascension direction for the objective function. If we regard the objective function as the numerical description for the imaging quality of all targets covered by the focal panel, then the Mean Shift Algorithm can find the place where the imaging quality is the best. So, the problem of selecting targets is equal to the problem of finding the place where the imaging quality is the best. In addition, we also give some effective heuristics to improve computational speed and propose an effective method to assign point sources to the respective fibers. As a result, our program runs fast, and it costs only several seconds to generate an observation.