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The construction of a spatio-temporal wavelet and its tuning to speed wasfirst realized in the 90s on the Morlet wavelet by M. Duval-Destin\cite{Duval-Destin91a,Duval-Destin92}. This enabled to demonstrate thecapacities of the speed-tuned Morlet for psychovisual analysis. Thisconstruction was also used very efficiently in a powerful aerial targettracking algorithm by Mujica et al.\cite{Mujica99,Mujica2000}. In the lastdecade, this tool was proposed as an elegant and efficient alternativeframework to the Optical Flow (OF), the Block Matching (BM) or the phasedifference, for the study of motion estimation in image sequences.Nevertheless, the aperture selectivity of the 2D+T Morlet wavelet presents somedifficulties. Here we propose to replace the 2D Morlet wavelet by aGaussian-Conical (GC) wavelet for the spatial part of the spatio-temporalwavelet, since the GC wavelet has a better aperture selectivity and allows avery simple adjustment of the aperture. Therefore we build a new, highlydirectional, speed-tuned wavelet called Gaussian-Conical-Morlet (GCM) wavelet.Like the speed-tuned 2D+T Morlet, the new wavelet presents very goodcharacteristics in motion estimation and tracking, namely long temporaldependence, robustness to noise and to occlusions, and supersedes the OF(Optical Flow) and BM (Block Matching) techniques. However, for apertureselectivity, directional speed-capture and spectral recognition and tracking,GCM easily outperforms Morlet. This paper describes the GCM construction,utilization and aperture performances.

A spatio-temporal Gaussian-Conical wavelet with high aperture selectivity for motion and speed analysis