Global Parametrization of Range Image Sets

Nico Pietroni, Marco Tarini, Olga Sorkine, Denis Zorin

Goal• Assign UV texture coordinate (parameterization) to 3d

scanned model that consists of multiple range images

Previous work• Reconstruct 3D, then parameterize

Proposed method• Parameterize in each range image domain,

considering constraints in overlapping area

Results

Previous Proposed

Algorithms overview

Expressed as least square optimization (in the form of Poisson equation) with boundary conditions

How to compute w is very briefly written in section 7

Descretization and consider linearity etc. yields the following term to minimize

Parameterization

TargetTriangle area

For all triangle

3D

Range

UV

Boundary condition in overrapping area

p_

Discretize, consider symmetry and linearity

Optimization

• There are some techniques to solve this optimization (please refer to the paper)

Fusion of Depth Maps with Multiple Scenes

Simon Fuhrmann / Michael Goesele

Goal

• Combine registered depth maps with dramatically varying sampling rate.

Solution

• They introduce “scale” parameter to hierarchical signed distance octree to avoid averaging across different sampling rate.

Problem statement

Their data structure

• 3D hierarchical signed distance field in octree + scale parameter

• Vote triangles one by one• Also consider confidence of votes (depends on

slant angle)

Equation to determine the octree level Rule to update voxel valuesW : weight (confidence)D : distance value

Carefully mix different scales

Surface extraction

• They use marching tetrahedra.

Reconstruction of 3D objects from arbitrary cross-section data

We describe a simple algorithm to reconstruct the surface of smooth three-dimensional multi-labeled objects from sampled planar cross-sections of arbitrary orientation. The algorithm has the unique ability to handle cross-sections in which regions are classified as being inside the object, outside the object, or unknown. This is achieved by constructing a scalar function on R^3, whose zero set is the desired surface. The function is constructed independently inside every cell of the arrangement of the cross-section planes using transfinite interpolation techniques based on barycentric coordinates that guarantee that the function is smooth, and its zero set interpolates the cross-sections.

Currently only abstract is available