Three-dimensional (3D) photogrammetry is an emerging imaging modality to study patient morphology, detect pathologic anomalies and track disease progression. It has recently gained special popularity to assess pediatric development because of its non-ionizing, non-invasive and cost-effective nature. However, while spatial registration is an important step to enable longitudinal and/or population-based analyses, most deep learning registration methods are designed for voxel-based image representations and their application to 3D photograms is limited, since they are represented as meshes with unordered points with variable resolutions connected by triangles. Although recent deep learning models to register meshes have been proposed, most require either spatial resampling to compensate for different number of points between input meshes or the prior identification of sparse landmarks, which compromise accuracy and increases inference cost. We present a novel geometric learning architecture that incorporates a new feature homogenization mechanism to transform spatial information from meshes with diverse numbers of points to a uniform dimensionality, using geometric convolutions via Chebyshev polynomials to exploit local structural information. Moreover, our model combines offset- and cross-attention between input meshes for improved registration. We first demonstrated the improvements of our offset cross-attention module in the registration task using the publicly available ModelNet40 dataset with point clouds representing diverse objects. Then, we showed state-of-the-art performance of our model incorporating geometric feature homogenization using a database with 1,744 manually annotated craniofacial 3D photograms of children with pathology. Unlike existing methods, this model does not require spatial sampling or prior landmark identification.