•Water diffusivity behavior in dried foods is estimated by the method of slopes (MoS).•The MoS is generalized to shrinking solids with complex-shaped geometries.•Mushroom pilei drying was analyzed by a 2D model in oblate spheroidal coordinates.•Shrinkage characteristics of product were obtained by point set registration method.•MoS surpassed piecewise regression for describing the experimental drying curves. Water diffusivity is an important parameter for designing convective drying processes, as it is instrumental for determining the rate at which moisture is removed from solid foodstuffs. Most estimation methods for water diffusivity estimation rely in simple geometries and are based on analytical solutions for mass transfer under constant diffusivity in a rigid solid, assumptions that most often leads to unreliable estimations. In this study, the method of slopes is generalized to complex-shaped geometries lacking analytical solutions, allowing the estimation of variable diffusivities in shrinking solids. The method is validated with experimental drying data for fresh and osmodehydrated mushroom pilei and implemented by using the numerical solution to an unsteady state 2D drying model formulated in the oblate spheroidal coordinate system. Shrinkage descriptors of drying product were determined using the point set registration algorithm. Water diffusivities were further compared to those estimated by using a piecewise regression approach. Drying kinetics simulations using diffusivities obtained with the method of slopes showed an excellent agreement with experimental data, achieving moisture-averaged relative deviation values lower than 2.4%.