Image interpolation is required in several biomedical applications, such as estimating missing information, simulating a continuously evolving process or for comparative analysis in the same referential (longitudinal studies, patient follow-up, analysis of moving organs). The purpose of this study is to develop a 2D interpolation method that can simultaneously apply as a geometric registration approach of two images. The underlying idea is to estimate the transform between the source and target images based on semantic information available, namely the knowledge of the image regions that have to match during the deformation. Such initial knowledge is available from image segmentation and stored as a Max-Tree atlas. The proposed solution consists of building the deformation field in a higher (3D) dimension space based on the identification of the corresponding points in the source/target atlases. A vector field is initiated at the atlas section by pointing to the corresponding regions in the pair atlas. The diffusion of the initial vector field through the entire 3D space, with constraints associated to each atlas region, allows generating a smooth deformation field consistent with even opposite displacements. The final transformation between the source/target images is defined as the flow computed from the deformation vector field. The proposed approach is demonstrated for two use cases of interstitial lung disease: severity assessment in acute respiratory distress syndrome (ARDS) and investigation of lung compliance in fibrosing idiopathic interstitial pneumonia (fIIP).