Mariano Rivera

Centro de Investigaciones en Optica, Mathematics Research Center

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About

Mariano Rivera’s research lies at the intersection of computational imaging, inverse problems, and numerical optimization, with a particular focus on gradient field integration and motion estimation. His most influential work, the 1997 paper “Fast algorithm for integrating inconsistent gradient fields,” introduced a discrete Fourier transform (DFT)-based method for solving a quadratic cost functional that regularizes inconsistent gradient fields into consistent ones. This algorithm, which has garnered 20 citations, enables straightforward integration using simple techniques and has become a foundational tool in shape-from-shading, photometric stereo, and image reconstruction. Rivera’s contributions extend to mechanical engineering, as seen in his 2018 study on using fully Cartesian coordinates to calculate support reactions in multi-scale mechanisms, addressing dynamic balancing to reduce vibrations, noise, and wear—a critical advance for machine performance. His 2011 work on variational multi-valued velocity field estimation for transparent sequences further showcases his versatility in handling complex motion analysis. With a career spanning decades, Rivera’s algorithmic innovations continue to influence researchers in computer vision and computational mechanics, demonstrating a unique ability to bridge theoretical rigor with practical engineering challenges.