A Non-Rigid Three-Dimensional Image Reconstruction Algorithm Based on Deformable Shape Reliability

Most reconstruction algorithms for non-rigid three-dimensional (3D) images assume that non-rigidity can be represented as a linear combination of a fixed number of rigid bases. However, this assumption struggles to establish reliable shape functions and initial values for nonlinear and non-rigid motions, decreasing reconstruction reliability. This paper introduces an enhanced-reliability reconstruction algorithm for non-rigid 3D images. Our algorithm models the dynamic non-rigid shape basis as a low-rank matrix composed of image points and depth factors, improving the restoration of non-rigid shape base changes and providing accurate parameters for constructing objective functions. By leveraging manifold alignment and physical continuity constraints, our method optimizes the function structures. Assuming minimal reconstruction error and shape change, we solve for the motion structure parameters and select the key initial shape basis value by minimizing the objective function with the L-M nonlinear optimization method. Our experimental results on 3D image sequence reconstructions demonstrate significant error reduction, underscoring our model's credibility, robust reliability, and minimal re-projection error.