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We report on the measurement of freeze-out radii for pairs ofidentical-charge pions measured in Pb--Pb collisions at $\sqrt{s_{\rmNN}}=2.76$ TeV as a function of collision centrality and the average transversemomentum of the pair $k_{\rm T}$. Three-dimensional sizes of the system(femtoscopic radii), as well as direction-averaged one-dimensional radii areextracted. The radii decrease with $k_{\rm T}$, following a power-law behavior.This is qualitatively consistent with expectations from a collectivelyexpanding system, produced in hydrodynamic calculations. The radii also scalelinearly with $\left< \mathrm{d}N_{\rm ch}/\mathrm{d}\eta \right>^{1/3}$. Thisbehaviour is compared to world data on femtoscopic radii in heavy-ioncollisions. While the dependence is qualitatively similar to results at smaller$\sqrt{s_{\rm NN}}$, a decrease in the $R_{\rm out}/R_{\rm side}$ ratio isseen, which is in qualitative agreement with specific predictions fromhydrodynamic models. The results provide further evidence for the production ofa collective, strongly coupled system in heavy-ion collisions at the LHC.

Centrality dependence of pion freeze-out radii in Pb-Pb collisions at $\sqrt{\mathbf{s_{NN}}}$=2.76 TeV