Shape Gradient Domain (V2.0)

Shape Gradient Domain (Version 2.0)

links description executables examples notes changes

LINKS
SGP 2009 Paper, SIGGRAPH 2016 Paper, JCGT 2016 Paper
Windows (x64) Executables
Source Code
GitHub Repository
(Older Versions: V1.0)

DESCRIPTION
The code is comprised of two executables.

ShapeGradientDomain: [SGP 2009]
This code performs gradient domain processing 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) = α⋅||F-G||² + β⋅||λ⋅∇F - ∇G||²
where α is the value-fitting weight, 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 and 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.
Normal Smooth: [SIGGRAPH 2016]
This code performs multiple iterations of harmonic smoothing of the surface normals. As with the code above, this amounts to minimizing:

E(G) = ||F-G||² + γ⋅||∇G||²
where γ is the diffusion weight (time).
If no normals are provided, the vertex normals are estimated as the area-weighted sum of adjacent triangle normals.

Note that when β is set to zero the two executables differ in that the first emaulates harmonic flow from the input geometry to Euclidean three-space (allowing the variation at a vertex to occur in any direction) while the second emulates harmonic flow from the input geometry to the two-sphere (constrainting the variation at a vertex to occur in the tangent space of the associated normal).

EXECUTABLES

--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.
[--vWeight <value interpolation weight>]: This floating point value gives the weight for value interpolation (α).
The default value for this parameter is 1.
[--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.
[--useColors]: If this flag is enabled, the signal to be processed is the per-vertex color field. Otherwise, it is the vertex positions.
If the flag is enabled and the input file does not contain per-vertex colors, colors will be assigned from the normals.
[--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.
[--iters <iterations>]: This integer value specifies the number of smoothing iterations that are to be performed..
The default value for this parameter is 1.
[--dTime <gradient interpolation weight / diffusion time>]: This floating point value gives the weight for gradient interpolation / diffusion time (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 similarly compiled with and without MKL support.)

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

Geometric effects are obtained by either amplifying (λ=2 in the top row) or dampening (λ=0 in the bottom two rows) gradients.
From left to right, the gradient weight is successively decreased (β=10^-3, β=10^-4, and β=10^-5) corresponding to successively more loacalized edits.
The processing is isotropic in the top two rows (ε=0 and γ is irrelevent) and isotropic in the bottom one (ε=0.02 and γ=10^-4).

HISTORY OF CHANGES

Version 2.0:

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

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