Frequency-selective trajectory analysis for pulsating visual marker detection under one-dimensional image motion

Visual markers emitting pulsating light can act as reference points in camera-based localization systems.Their identification is possible based on the frequency of changes in the intensity of the detected light.In the localization system concept developed by the authors, frequency information is intended to facilitate the detection and differentiation of markers whose spatial position is known.However, a significant problem that arises during camera movement is the movement of the marker projection between successive frames.In such a situation, analysis of the signal from a single stationary pixel utilizes only a portion of the pulsation information and can lead to degraded detection.This paper proposes a frequency-selective analysis of image-time trajectories, designated FSTRT.The method samples the image intensity along candidate trajectories, and for each of them determines the amplitude of the component corresponding to the known marker pulsation frequency.This allows for simultaneous detection of pulsation and estimation of the initial coordinate and slope of the apparent movement of the marker projection within the analyzed window.A search across the entire adopted parameter range and a local variant using trajectory prediction were considered.Simulation studies showed that for rotational and complex motion, FSTRT recovers approximately 98-100% of the amplitude available for the reference trajectory, while analysis of stationary pixels retains approximately 23-25%.Under high noise conditions, using the local variant of FSTRT increased the detection probability from 0.218 (for the baseline STATIC/STF method) to 0.950 with a comparable false alarm probability.The effects of exposure time, frequency mistuning, and trajectory prediction errors were also analyzed.The presented results concern a single marker, one-dimensional motion of its projection, and block analysis of a single image window.They do not include continuous tracking or estimation of the camera position.Instead, they represent a step towards developing a localization system based on pulsating markers capable of operating during camera motion.