We propose a method for calculating cohomology operations on finite simplicial complexes. Of course, there exist well–known methods for computing (co)homology groups, for example, the “reduction algorithm” consisting in reducing the matrices corresponding to the differential in each dimension to the Smith normal form, from which one can read off the (co)homology groups of the complex [Mun84], or the “incremental algorithm” for computing Betti numbers [DE93]. Nevertheless, little is known about general methods for computing cohomology operations. For any finite simplicial complex K, we give a procedure including the computation of some primary and secondary cohomology operations. This method is based on the transcription of the reduction algorithm mentioned above, in terms of a special type of algebraic homotopy equivalences, called contractions [McL75], of the (co)chain complex of K to a “minimal” (co)chain complex M(K). More concretely, whenever the ground ring is a field or the (co)homology of K is free, then M(K) is isomorphic to the (co)homology of K. Combining this contraction with the combinatorial formulae for Steenrod reduced pth powers at cochain level developed in [GR99] and [Gon00], these operations at cohomology level can be computed. Finally, a method for calculating Adem secondary cohomology operations Φq : Ker(Sq2Hq (K)) → Hq+3(K)/Sq2Hq (K) is showed

Underwater imaging has been present for many decades due to its relevance in vision and navigation systems. In recent years, advances in robotics have led to the availability of autonomous or unmanned underwater vehicles (AUVs, UUVs). Despite the rapid development of new studies and promising algorithms in this field, there is currently a lack of research toward standardized, general-approach proposals. This issue has been stated in the literature as a limiting factor to be addressed in the future. The key starting point of this work is to identify a synergistic effect between professional photography and scientific fields by analyzing image acquisition issues. Subsequently, we discuss underwater image enhancement and quality assessment, image mosaicking and algorithmic concerns as the last processing step. In this line, statistics about 120 AUV articles fro recent decades have been analyzed, with a special focus on state-of-the-art papers from recent years. Therefore, the aim of this paper is to identify critical issues in autonomous underwater vehicles encompassing the entire process, starting from optical issues in image sensing and ending with some issues related to algorithmic processing. In addition, a global underwater workflow is proposed, extracting future requirements, outcome effects and new perspectives in this context.