An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vector field is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. It is shown that spheres are stationary points when the total variation of the normal is minimized under an area constraint. Shape calculus is used to characterize the relevant derivatives. Since the total variation functional is non-differentiable whenever the boundary contains flat regions, an extension of the split Bregman method to manifold valued functions is proposed.

中文翻译：

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作为形状先验的法向矢量场的总变化

介绍了沿 3D 中平滑形状边界的法向矢量场的总变化先验的模拟。法向量场的总变化分析基于微分几何设置，其中单位法向量被视为二维球流形的一个元素。结果表明，当面积约束下法线的总变化最小时，球体是静止点。形状演算用于表征相关导数。由于当边界包含平坦区域时，总变分函数是不可微的，因此建议将分裂 Bregman 方法扩展到流形值函数。