Dominique Bechmann

3D distance transform adaptive filtering for smoothing and denoising triangle meshes

In this paper we compute the distance transform of a 3D triangle mesh. A volumetric voxel representation is defined over the mesh to evaluate the distance transform. Optimizations are described to efficiently manipulate the volumetric data structure that represents the mesh. A new method for adaptive filtering of the distance transform is introduced to smooth and reduce the noise on the meshes that were reconstructed from scanned data acquired with a 3D scanner. A modified version of the Marching Cube algorithm is presented to correctly reconstruct the final mesh of the filtered distance transform defined with the voxel representation. The new filtering method is feature preserving and it is more versatile than previous algorithms described in the literature. Results show that this method outperforms previous ones in term of an error metric comparison. Future works are discussed to improve the new method and its computing performances.

A new vector field distance transform and its application to mesh processing from 3D scanned data

In this paper we define a new 3D vector field distance transform to implicitly represent a mesh surface. We show that this new representation is more accurate than the classic scalar field distance transform by comparing both representations with an error metric evaluation. The widely used marching cube triangulation algorithm is adapted to the new vector field distance transform to correctly reconstruct the resulting explicit surface. In the reconstruction process of 3D scanned data, the useful mesh denoising operation is extended to the new vector field representation, which enables adaptive and selective filtering features. Results show that mesh processing with this new vector field representation is more accurate than with the scalar field distance transform and that it outperforms previous mesh filtering algorithms. Future work is discussed to extend this new vector field representation to other mesh useful operations and applications.

Marching triangle polygonization for efficient surface reconstruction from its distance transform

In this paper we propose a new polygonization method based on the classic Marching Triangle algorithm. It is an improved and efficient version of the basic algorithm which produces a complete mesh without any cracks. Our method is useful in the surface reconstruction process of scanned objects. It works over the scalar field distance transform of the object to produce the resulting triangle mesh. First we improve the original algorithm in finding new potential vertices in the mesh growing process. Second we modify the Delaunay sphere test on the new triangles. Third we consider new triangles configuration to obtain a more complete mesh. Finally we introduce an edge processing sequence to improve the overall Marching Triangle algorithm. We use a relevant error metric tool to compare results and show our new method is more accurate than Marching Cube which is the most widely used triangulation algorithm in the surface reconstruction process of scanned objects.

Surface Reconstruction: 3D Mesh Filtering with Feature Preserving Bi-Adaptive Algorithms

In this paper we define two bi-adaptive mesh filtering algorithms for efficient features preserving restoration of noisy models acquired from 3D scanners. The new filters are based on 2D image processing adaptive algorithms extended to 3D mesh processing. We combine two adaptive algorithms to design more efficient bi-adaptive algorithms. The first filter is applied on the mesh triangles normal vector orientation and the second filter is applied on the vertices normal vector orientation. Both filters are applied on adaptively selected local neighborhood based on a threshold angle between normal vectors. Then the algorithm to update the vertices position is also adaptive according to a local variance evaluation compared to a noise variance threshold. We compare our two bi-adaptive algorithms results to other filtering algorithms according to reliable error metrics and show the new filters outperform previous features preserving and adaptive mesh denoising methods.

A New Volumetric Implicit Surface Data Structure and Its Triangulation Algorithm Applied to Mesh Integration

In this paper we propose a new volumetric implicit surface data structure as an alternative representation to perform mesh processing algorithms. We introduce a new triangulation algorithm suitable for our voxel-based volumetric structure which is a vector field distance transform from an explicit mesh. This new representation is an extension of the implicit scalar field distance function of a mesh. We show our new vector field function is more accurate than the classic scalar field function by comparing both representations with an error metric evaluation. We adapt to this new vector representation mesh integration operation in the reconstruction process of 3D objects from scanned data which was previously performed on the implicit scalar field function. Results show that using this new vector field representation, our mesh integration and mesh triangulation algorithm designs outperform the previous processes based on the implicit scalar field function representation.