  We introduce a novel construction of a contour deformation within the
framework of Loop-Tree Duality for the numerical computation of loop integrals
featuring threshold singularities in momentum space. The functional form of our
contour deformation automatically satisfies all constraints without the need
for fine-tuning. We demonstrate that our construction is systematic and
efficient by applying it to more than 100 examples of finite scalar integrals
featuring up to six loops. We also showcase a first step towards handling
non-integrable singularities by applying our work to one-loop infrared
divergent scalar integrals and to the one-loop amplitude for the ordered
production of two and three photons. This requires the combination of our
contour deformation with local counterterms that regulate soft, collinear and
ultraviolet divergences. This work is an important step towards computing
higher-order corrections to relevant scattering cross-sections in a fully
numerical fashion.
