Path operators are powerful tools for the enhancement of thin and elongated objects in an image. In order to cope with noisy acquisition a variant of the path operators was recently proposed. However, both approaches cannot properly handle thin objects with tortuous shapes since strong variations of an object curvature produce disconnections in the paths. In order to address this issue, we propose a novel operator able to properly handle paths in tortuous shapes. It relies on the coupling of attribute filters based on the geodesic tortuosity and conventional path operators. Analogously to the complete version of the path operators, by allowing disconnections within paths it is possible also to define a path operator that is both robust and selective. The effectiveness of the proposed operators in filtering thin and tortuous image objects is proved on a 2D and 3D biomedical image.