Semi-metric Formal 3D Reconstruction from Perspective Sketches

We present a new approach for accurate and fast reconstruction of 3D models from hand-drawn perspective sketches and imposed geometric constraints. A distinctive feature of the approach is the decomposition of the reconstruction process into the stages of correction of the 2D sketch and elevation of the 3D model. All 3D constraints that describe the spatial structure of the model are strictly satisfied, while preferences that describe the model projection are treated in relaxed manner. The constraints are subdivided into the projective, affine and metric ones and expressed in algebraic form by using the Grassmann-Cayley algebra. The constraints are resolved one by another following the order of their types by using the local propagation methods. The preferences allow to apply linear approximations and to systematically use formal methods.