Shape Gradient Domain (Version 4.0)

links description executable notes examples changes

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

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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:
Id. + ε⋅Κ² where Id. is the identity matrix, Κ² is the diagonal matrix whose entries are the squares of the principal curature values, and ε is the curvature weight.
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 more robust estimation of normals, the executable also supports harmonic smoothing of normals as described in [Prada et al. 2016]. As with the code above, this amounts to minimizing:


E(G) = ||F-G||² + γ⋅||∇G||²
where γ is the diffusion 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.

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EXECUTABLE

ShapeGradientDomain: Processes either the vertex positions, or per-vertex colors, performing isotropic/anisotropic gradient-domain smoothing and sharpening (with the option of smoothing normals in a pre-processing step)

--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.

[--nIters <normal smoothing iterations>]

This integer value gives the number of iterations of harmonic normal smoothing to be performed before estimating curvatures. (If normal smoothing is desired, we have found that a single iteration suffices.)
The default value for this parameter is 0.


[--nTime <normal diffusion time>]

This floating point value gives the normal diffusion time (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 10^-3.


[--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.

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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.)

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EXAMPLES

The figure below shows example of both isotropic and anisotropic geometry processing.

• Top row: Isotropic sharpening:

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

• Middle row: Isotropic smoothing:

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

• Bottom row: Anisotropic smoothing:

       ShapeGradientDomain --in armadillo.ply --out armadillo.smooth.ply --gScale 0 --gWeight <gradient weight> --kWeight 0.02 --nIters 1 

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

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HISTORY OF CHANGES

Version 2.0:

1. Added options to weight both value and gradient interpolation terms.
2. Changed default values to correspond to diffusion time.

Version 3.0:

1. Integrated normal smoothing within the gradient-domain processing application.

Version 4.0:

1. Fixed default value weight to 1.0.
2. Added support for fitting the geometry to prescribed normals.