Adaptive locally aligned ant technique and manifold blurring mean shift for manifold detection and denoising

The detection and extraction of noisy manifolds from data have various applications, ranging from dimensionality reduction, computer graphics, signal processing, and robotics to the modelling of astronomical structures. In Astronomy, the detection of faint streams and filaments is challenging due to background contamination, which immerses and hides them in noise. The biologically inspired Locally Aligned Ant Technique (LAAT), followed by Manifold Blurring Mean Shift (MBMS) have been demonstrated as an efficient and flexible algorithm for detecting and denoising versatile structures within noisy backgrounds. Our contribution extends both methods by introducing a dynamic local radius, thereby allowing a flexible configuration and reducing sensitivity to a critical hyper-parameter for both of them. For LAAT we propose additional synergy by introducing also locally variable pheromone deposition. The former avoids highlighting spurious patterns in noisy regions and allows smaller movement in areas with strong alignment. The latter increases pheromone deposition in fainter zones. We demonstrate and analyse the novel extensions in two astronomical datasets, namely a synthetic jellyfish galaxy and an N-body cosmic web simulation. • LAAT and MBMS are enhanced by the use of a local dynamic radius. • Dynamic radius applicable to methods based on local PCA. • Ant colony used to detect hidden structures in noise. • New variable pheromone method in LAAT to improve data denoising. • Improved version of 1-DREAM; better accuracy in filaments detected.