Shape Gradient Domain (V5.0)

Shape Gradient Domain (Version 5.0)

links description executable notes examples changes

LINKS
[Chuang et al. 2009], [Prada et al. 2016], [Chuang et al. 2016]
Windows (x64) Executables
Source Code
GitHub Repository
(Older Versions: V4.5, V4.0, V3.0, V2.0, V1.0)

DESCRIPTION

This code performs gradient domain processing [Chuang et al. 2009, Chuang et al. 2016] on signals defined on a mesh, where the signal can be either a color-field represented as a color per vertex or is the position of the vertices themselves. The code supports both sharpening and smoothing of the signals through the solution of a screened-Poisson equation. Specifically, given an input signal F, it solves for the signal G minimizing:
E(G) = ||F-G||² + β⋅||λ⋅∇F - ∇G||²
where β is the gradient-fitting weight and λ is the gradient scale factor.
The code supports inhomogenous processing by allowing the user to replace the Riemannian metric, g, given by the embedding, with a metric that adjusts to the curvature of the surface. Specifically, given orthonormal principal curvature directions, the (idenity) metric is replaced with:
g ← Id. + ε⋅Κ² where Id. is the identity matrix, Κ² is the diagonal matrix whose entries are the sum of the squares of the principal curature values, and ε is the curvature weight. (When ε=0, this reproduces the Riemannian metric given by the embedding.)
Curvatures are estimated using the surface normals. If none are provided, the vertex normals are estimated as the area-weighted sum of adjacent triangle normals.
For robustness, the implementation supports pre-smoothing the normals before estimating curvatures. Similar to above, this amounts to minimizing an energy of the form:
E(G) = ||F-G||² + γ⋅||∇G||²
where γ is the normal smoothing weight.
In the case that the signal processed describes the vertices' normals, we also support fitting the original geometry to the processed normals using the approach of [Yu et al. 2004].
Given input positions F and a target normal field N This amounts to minimizing:
E(G) = ||F-G||² + δ⋅||(∇F - N⋅⟨∇F,N⟩) - ∇G||²
where δ is the projected gradient fitting weight weight.

EXECUTABLE

--in <input geometry>: This string specifies the name of the input geometry, represented in PLY format.
[--out <ouput geometry>]: This string specifies the name of the output geometry, represented in PLY format.
[--nWeight <normal smoothing time>]: This floating point value gives the normal smoothing weight (γ).
The default value for this parameter is 10^-4.
[--gWeight <gradient interpolation weight>]: This floating point value gives the weight for gradient interpolation (β).
The default value for this parameter is 10^-4.
[--gScale <gradient scale>]: This floating point value gives the scale factor for the target gradient field (λ).
The default value for this parameter is 1.0.
[--kWeight <curvature weight>]: This floating point value gives the curvature weight for adjusting the metric (ε).
The default value for this parameter is 0.0.
[--npWeight <normal projection weight>]: This floating point value gives the normal projection weight (δ).
The default value for this parameter is 10².
[--signal]: This inter value describes which signal is to be processed:

0: Vertex positions
1: Vertex normals (will be assigned if none are give)
2: Vertex colors
3: Vertex normals used to fit the geometry.
The default value for this parameter is 0.
[--verbose]: If this flag is enabled, the code will output processing information.
--in <input geometry>: This string specifies the name of the input geometry, represented in PLY format.
[--out <ouput geometry>]: This string specifies the name of the output geometry, represented in PLY format.
[--nWeight <normal smoothing weight>]: This floating point value gives the normal smoothing weight (γ).
The default value for this parameter is 10^-4.
[--verbose]: If this flag is enabled, the code will output processing information.

NOTES

The code requires Eigen as a numerical solver.
If you are using Eigen and your implementation is backed by Intel's Math Kernel Library (see discussion here), enable the EIGEN_USE_MKL_ALL macro by defining it in the file PreProcessor.h. (The two versions of the Windows executables are compiled with and without MKL support.)
For consistency of parameters, surfaces are rescaled to have unit area prior to processing (and then scaled back after processing).

EXAMPLES

ShapeGradientDomain:

The figure below shows example of both homogenous and inhomogeneous geometry processing.

Top row: Homogeneous sharpening:

     ShapeGradientDomain --in armadillo.ply --out armadillo.sharp.ply --gScale 2 --gWeight <gradient weight>

Middle row: Homogeneous smoothing:

     ShapeGradientDomain --in armadillo.ply --out armadillo.smooth.ply --gScale 0 --gWeight <gradient weight>

Bottom row: Inhomogeneous smoothing:

     ShapeGradientDomain --in armadillo.ply --out armadillo.smooth.ply --gScale 0 --gWeight <gradient weight> --kWeight 0.02

For all three, the value of <gradient weight> is chosen from {1e-3, 1e-4, 1e-5}

ShapeCurvature:
The figure below visualizes the total curvature (square root of the sum of the squares of the principal curvatures) as per-vertex grayscale colors and gives the standard deviations of the estimated total curvature σ_|κ|
```
     ShapeCurvature --in armadillo.ply --out armadillo.curvature.ply --nWeight <normal smoothing weight>
```
The value of <normal smoothing weight> is chosen from {1e-4,1e-5,1e-6}.