Henrik Aanaes | Search PubMed

PubMed2007

Variational surface interpolation from sparse point and normal data.

Many visual cues for surface reconstruction from known views are sparse in nature, e.g., specularities, surface silhouettes, and salient features in an otherwise textureless region. Often, these cues are the only information available to an observer. To allow these constraints to be used either in conjunction with dense constraints such as pixel-wise similarity, or alone, we formulate such constraints in a variational framework. We propose a sparse variational constraint in the level set framework, enforcing a surface to pass through a specific point, and a sparse variational constraint on the surface normal along the observed viewing direction, as is the nature of, e.g., specularities. These constraints are capable of reconstructing surfaces from extremely sparse data. The approach has been applied and validated on the shape from specularities problem.

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Signed distance computation using the angle weighted pseudonormal.

The normals of closed, smooth surfaces have long been used to determine whether a point is inside or outside such a surface. It is tempting to also use this method for polyhedra represented as triangle meshes. Unfortunately, this is not possible since, at the vertices and edges of a triangle mesh, the surface is not C1 continuous, hence, the normal is undefined at these loci. In this paper, we undertake to show that the angle weighted pseudonormal (originally proposed by Thürmer and Wüthrich and independently by Séquin) has the important property that it allows us to discriminate between points that are inside and points that are outside a mesh, regardless of whether a mesh vertex, edge, or face is the closest feature. This inside-outside information is usually represented as the sign in the signed distance to the mesh. In effect, our result shows that this sign can be computed as an integral part of the distance computation. Moreover, it provides an additional argument in favor of the angle weighted pseudonormals being the natural extension of the face normals. Apart from the theoretical results, we also propose a simple and efficient algorithm for computing the signed distance to a closed C0 mesh. Experiments indicate that the sign computation overhead when running this algorithm is almost negligible.

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