A new morphological operator, namely RORPO (Ranking Orientation Responses of Path Operators), was recently introduced as a semi-global, morphological alternative to the local, Hessian-based operators for thin structure filtering in 3D images. In this context, a previous study has already provided experimental proof of its relevance by comparison to such differential operators. In this article, we present a methodological study of RORPO, which completes the presentation of this new morphological filter. In particular, we expose the motivations of RORPO with respect to previous morphological strategies; we present algo-rithmic developments of this filter and the underlying robust path operator; and we discuss computational issues related to parametricity and time efficiency. We conclude this study by a discussion on the methodological and applicative potentiality of RORPO in various fields of image processing and analysis.