The emergence of additive manufacturing has enabled the production of complex structures, notably cellular architected structures, also commonly referred to as lattice structures, which offer exceptional performance characteristics, including high stiffness-to-weight ratios, high stretchability, auxeticity, and more. In practice, lattice structures consist of periodically repeating well-designed unit cells, often composed of struts (or beams) interconnected in various ways via nodes. However, the intricacies of the additive manufacturing process, combined with the geometric complexity of lattice structures, often lead to geometric defects, such as variations in strut thickness, strut waviness, and displacements of lattice nodes, which can significantly influence their mechanical behavior. This study focuses on constructing a mechanical digital twin, i.e., a geometric model that (i) incorporates the specimen-specific geometry for each individual tested sample and (ii) can be easily used for numerical simulations. More precisely, we develop a method to extract an analysis-suitable Computer-Aided Design (CAD)-based geometry from 3D CT scan data of lattice structures. A multipatch B-spline surface model is constructed to represent the boundary of the lattice structure, ensuring a compact yet detailed geometric description. A template-fitting technique is developed to move the control points of the initial as-designed B-spline surface so that it fits the as-manufactured geometry, leveraging active contour methods from computer vision. Key innovations within this framework include utilizing a data fitting metric based on the Virtual Image Correlation (VIC) approach, combined with an image learning component, the integration of the membrane strain energy of the surface for regularization, and the enforcement of higher continuity between the patches where appropriate. The approach has been validated through various experiments, including those on a BCC lattice structure, where sub-voxel measurement accuracy has been achieved. Ultimately, the developed method provides a compact representation of the as-manufactured geometry with the same CAD-based discretization support as the initial as-designed structure, which should facilitate the quantitative assessment of defects and allow for efficient mechanical simulations using IsoGeometric Analysis.