We apply the recently developed HEPTA (Hyperbolic and Elliptic Point Tracking Algorithm) method to track stationary points within altimetric velocity fields and compare its performance with the well-established AMEDA (Angular Momentum Eddy Detection and Tracking Algorithm) algorithm in the Lofoten Basin (2019–2023). HEPTA simultaneously identifies elliptic (eddy centers) and hyperbolic points, whereas AMEDA focuses on closed eddy contours. The comparison reveals that, while both algorithms detect a similar number of long-lived eddies, AMEDA systematically produces longer trajectories and higher translation speeds (by a factor of about two) due to its ability to bridge temporal gaps in eddy tracking. However, the net linear displacements over an eddy’s lifetime do not differ statistically. HEPTA also identifies hyperbolic points whose stable and unstable manifolds can act simultaneously as transport barriers and stretching channels. These points may persist for tens of days, influencing the separation and mixing of water masses in the vicinity of mesoscale eddies. In a case study of a rapid topological reorganisation of the Lofoten Vortex, HEPTA captures the emergence of a hyperbolic point and the formation of a new eddy center, whereas AMEDA tends to artificially prolong the life of the original eddy by interpolating across a gap in tracking. The results indicate that AMEDA and HEPTA are complementary: AMEDA is suited for climatological eddy censuses, whereas HEPTA provides deeper insight into local mixing, eddy interactions, and the topological skeleton of the flow.