Partial retrieval of CAD models based on the gradient flows in Lie group

Based on the gradient flows in Lie group, a partial retrieval approach for CAD models is presented in this paper. First, a representation of the face Attributed Relational Graph (ARG) for a CAD model is created from its B-rep model and thus partial retrieval is converted to a subgraph matching problem. Then, an optimization method is adopted to solve the matching problem, where the optimization variable is the vertex mapping and the objective function is the measurement of compatibility between the mapped vertices and between the mapped edges. Different from most previously proposed methods, a homogeneous transformation matrix is introduced to represent the vertex mapping in subgraph matching, whose translational sub-matrix gives the vertex selection in the larger graph and whose orthogonal sub-matrix presents the vertex permutation for the same-sized mapping from the selected vertices to the smaller graphʹs vertices. Finally, a gradient flow method is developed to search for optimal matching matrix in Special Euclidean group SE(n). Here, a penalty approach is used to handle the constraints on the elements of the matching matrix, which leads its orthogonal part to be a permutation matrix and its translational part to have different integer elements. Experimental results show that it is a promising method to support the partial retrieval of CAD models.