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This thesis lays the groundwork for the automatic supervision of the laser incision process, which aims to complement surgeons' perception of the state of tissues and enhance their control over laser incisions. The research problem is formulated as the estimation of variables that are representative of the state of tissues during laser cutting. Prior research in this area leveraged numerical computation methods that bear a high computational cost and are not straightforward to use in a surgical setting. This book proposes a novel solution to this problem, using models inspired by the ability of experienced surgeons to perform precise and clean laser cutting. It shows that these new models, which were extracted from experimental data using statistical learning techniques, are straightforward to use in a surgical setup, allowing greater precision in laser-based surgical procedures.