Normalized double-differential cross sections for top quark pair ( $\mathrm{t}\overline{\mathrm{t}}$ ) production are measured in pp collisions at a centre-of-mass energy of 8 $,\text {TeV}$ with the CMS experiment at the LHC. The analyzed data correspond to an integrated luminosity of 19.7 $,\text {fb}^{-1}$ . The measurement is performed in the dilepton $\mathrm {e}^{\pm }\mu ^{\mp }$ final state. The $\mathrm{t}\overline{\mathrm{t}}$ cross section is determined as a function of various pairs of observables characterizing the kinematics of the top quark and $\mathrm{t}\overline{\mathrm{t}}$ system. The data are compared to calculations using perturbative quantum chromodynamics at next-to-leading and approximate next-to-next-to-leading orders. They are also compared to predictions of Monte Carlo event generators that complement fixed-order computations with parton showers, hadronization, and multiple-parton interactions. Overall agreement is observed with the predictions, which is improved when the latest global sets of proton parton distribution functions are used. The inclusion of the measured $\mathrm{t}\overline{\mathrm{t}}$ cross sections in a fit of parametrized parton distribution functions is shown to have significant impact on the gluon distribution.