Nasal Mesh Unfolding – An Approach to Obtaining 2-D Skin Templates from 3-D Nose Models

Nasal reconstruction requires a 2-D template representing the skin area to be taken from the donor site of the patient. We propose a new framework for template design, called nasal mesh unfolding, to obtain 2-D skin templates from 3-D nose models. The proposed nasal mesh unfolding framework takes as input a target digital nose model represented by a 3-D triangle mesh and unfolds the nasal mesh under structure constraints using semidefinite programming. The solution of the unfolding problem is in the form of a Gram matrix from which the 2-D representation of the 3-D model, or embedding, is extracted. The embedding defines a digital template representing the skin requirement for nasal reconstruction, which can in turn be used to produce a physical 2-D template to apply on the donor site for guiding skin incision. Experiments on synthetic data demonstrate the effectiveness of the proposed unfolding approach, and results on real data show the feasibility of generating physical 2-D skin templates from 3-D nose meshes. The proposed approach efficiently converts 3-D nose models to digital 2-D skin templates for fast easy and accurate preparation of physical templates and can be useful for other plastic surgery tasks.