Interactive Topology-aware Surface Reconstruction (Patent pending)
Thomas Lewiner, Gil Shklarski, Sivan
Interactive reconstruction of the riding monk. The finite-element field formulation incorporates the user’s interactive scribbles at automatically-detected weak-topology regions to obtain the expected shape.
The reconstruction of a complete watertight model from scan data is still a difficult process. In particular, since scanned data is often incomplete, the reconstruction of the expected shape is an illposed problem. Techniques that reconstruct poorly-sampled areas without any user intervention fail in many cases to faithfully reconstruct the topology of the model. The method that we introduce in this paper is topology-aware: it uses minimal user input to make correct decisions at regions where the topology of the model cannot be automatically induced with a reasonable degree of confidence. We first construct a continuous function over a three dimensional domain. This function is constructed by minimizing a penalty function combining the data points, user constraints, and a regularization term. The optimization problem is formulated in a mesh-independent manner, and mapped onto a specific mesh using the finite-element method. The zero level-set of this function is a first approximation of the reconstructed surface. At complex undersampled regions, the constraints might be insufficient. Hence, we analyze the local topological stability of the zero level-set to detect weak regions of the surface. These regions are suggested to the user for adding local inside/outside constraints by merely scribbling over a 2D tablet. Each new user constraint modifies the minimization problem, which is solved incrementally. The process is repeated, converging to a topology-stable reconstruction. Reconstructions of models acquired by a structured-light scanner with a small number of scribbles demonstrate the effectiveness of the method.
The smoothness penalty discards outliers and completes smoothly missing parts, as can be seen in the tiger’s head.
Due to the statue’s base (left), the camel’s legs cannot be covered (center-left). Scribble constraints drawn on automatically generated 2D tablets (center-right) can be used to generate a coherent geometry (right).
The topological analysis detects weak regions (center-right) in the presence of noise. Weak regions are typically located where two parts of the shape are close and the topology is ambiguous, such as the arm-leg contacts in the sitting woman.