Abstract: Individual identification of dolphins is of much interest to marine mammologists. Natural markings and notches on the trailing edge of the dorsal fin provide an almost unique signature within a study population for individual recognition. Dorsal fin is an almost rigid, planar object, as a result the problem boils down to the planar curve matching. Invariants under three groups of similarity, affine, and projective transformations are examined in this paper. Three families of differential, algebraic, and semi-differential invariants are studied and evaluated for their applicability and performance in dolphin photo-identification. It is observed that under practical conditions, for smooth quasi-rigid curves like trailing edge of the dorsal fin, curvature based matching methods outperform almost all of the other techniques, which offer a higher level of invariance.