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Radio-loud AGN typically manifest powerful relativistic jets extending up tomillions of light years and often showing superluminal motions organised in acomplex kinematic pattern. A number of physical models are still competing toexplain the jet structure and kinematics revealed by radio images using theVLBI technique. Robust measurements of longitudinal and transverse velocityfield in the jets would provide crucial information for these models. This is adifficult task, particularly for transversely resolved jets in objects like 3C273 and M87. To address this task, we have developed a new technique foridentifying significant structural patterns (SSP) of smooth, transverselyresolved flows and obtaining a velocity field from cross-correlation of theseregions in multi-epoch observations. Detection of individual SSP is performedusing the wavelet decomposition and multiscale segmentation of the observedstructure. The cross-correlation algorithm combines structural information ondifferent scales of the wavelet decomposition, providing a robust and reliableidentification of related SSP in multi -epoch images. The algorithm enablesrecovering structural evolution on scales down to 0.25 full width at halfmaximum (FWHM) of the image point spread function (PSF). We present hereexamples of applying this algorithm to obtain the first detailed transversevelocity fields and to study the kinematic evolution in the parsec-scale jetsin 3C 273 and M87.

Longitudinal and transverse velocity fields in parsec-scale jets