Tissue deformation plays an important role in lung physiology, as lung parenchyma largely deforms during spontaneous ventilation. However, excessive regional deformation may lead to lung injury, as observed in patients undergoing mechanical ventilation. Thus, the accurate estimation of regional strain has recently received great attention in the intensive care community. In this work, we assess the accuracy of regional strain maps computed from direct differentiation of B-Spline (BS) interpolations, a popular technique employed in non-rigid registration of lung computed tomography (CT) images. We show that, while BS-based registration methods give excellent results for the deformation transformation, the strain field directly computed from BS derivatives results in predictions that largely oscillate, thus introducing important errors that can even revert the sign of strain. To alleviate such spurious behavior, we present a novel finite-element (FE) method for the regional strain analysis of lung CT images. The method follows from a variational strain recovery formulation, and delivers a continuous approximation to the strain field in arbitrary domains. From analytical benchmarks, we show that the FE method results in errors that are a fraction of those found for the BS method, both in an average and pointwise sense. The application of the proposed FE method to human lung CT images results in 3D strain maps are heterogeneous and smooth, showing high consistency with specific ventilation maps reported in the literature. We envision that the proposed FE method will considerably improve the accuracy of image-based biomechanical analysis, making it reliable enough for routine medical applications.