seepa / curvest

Multi-Scale Curvature Estimation of Triangle Meshes

Multi-Scale Curvature Estimation

This project implements a novel algorithm for computing multi-scale mean curvature fields of triangle meshes.

For the mean curvature computation at a given vertex and radius, integral invariants with the ball neighborhood from Yang et al. are used.

The algorithm automatically detects a suitable radius for each vertex corresponding to its scale and deals with local noise to generate a robust curvature estimate.

Note: This is research code and not really optimized for runtime / cross-platform usage.

Building

$ git clone https://github.com/seepa/curvest
$ cd curvest
$ mkdir build && cd $_
$ cmake .. && make

Requirements

• Linux, gcc (never tested on windows)
• cmake >= 3.0
• gnuplot (optional)

The code depends on MVE, which will be automatically downloaded to the build directory.

Example

Using the example mesh example/lionhead_small.ply,

computing its mean curvature field is as simple as issuing the following command (assuming you are in the root of this repository):

$ build/curvestimate example/lionhead_small.ply lionhead_result

The resulting curvature field is saved as vertex values in the output .ply file and can be colorized using the mesh_colorize tool (see further down). The result looks like this:

Included Tools

Curvature Estimation

This is the main application to compute a multi-scale curvature field given a triangle mesh.

$ ./curvestimate IN-PLY OUT

For a complete list of arguments, run:

$ ./curvestimate

Multi-Scale Mean Curvature Estimation

Usage: ./curvestimate [ OPTIONS ] IN-PLY OUT
Available options:
  --subdiv=ARG          Number of subdivision iterations for refining the sphere [2]
  --factor-initial=ARG  Initial radius factor [1]
  --factor-inc=ARG      Radius factor increment [1.3]
  --factor-max=ARG      Max radius factor [10]
  --radius-smooth=ARG   Initial radius smoothing iterations [5]
  -e, --edge-smooth=ARG  Edge smoothing factor (0: no smooth, 1.0: full smooth) [0.2]
  -p, --planar-thres=ARG  Planar threshold [0.2]
  -d, --debug-verts=ARG  (Debug) Comma separated list of vertices to debug
  --save-graphs         (Debug) Save a graph for each vertex
  --save-volume-all     (Debug) Save volume at each radius
  --save-patch-all      (Debug) Save patch at each radius
  --save-patch-final    (Debug) Save patch at final radius
  --fixed-radius=ARG    Compute curvature field with a fixed ball radius.
  --use-confidences     Use mesh confidences as final radii.

Useful arguments:

• -p : increase this, if your model is very noisy and you want more smoothing
• -e : increase this, if you want to smooth edges more
• --factor-initial : increase this, if you want more global smoothing (the start radius at each vertex will be bigger)

Mesh Colorize

A small helper application which uses libcolormap, an implementation of diverging colormaps, to colorize a mesh from its vertex values/confidences.

Colorize a mesh from its vertex values/confidences using diverging colormaps.

Usage: ./mesh_colorize [ OPTIONS ] IN-PLY OUT
Available options:
  -c, --confidences     Use vertex confidences.
  --range=ARG           Range of the colormap (comma-separated)
  --colors=ARG          RGB colors for low and high ends of the colormap (e.g. 1.0,0.0,0.0,0.0,0.0,1.0 for red-blue)
  --colorbar            Save the colorbar as a PNG.

By default vertex values and the red-blue, aka RdBu, colormap are used.

Density Field

Creates a density field from the curvature field by remapping the mean curvature values suitable for mesh simplification.

Possible Applications

Once computed, the curvature field can be used for, e.g.:

• Mesh simplification or
• Mesh smoothing

In both cases, the curvature field may guide the algorithm in a way which preserves features of the model while smoothing (noisy) planar regions.

About

This project resulted from my Bachelor's Thesis Multi-Scale Curvature Field of Triangle Meshes which I handed in and defended in January 2016 at TU Darmstadt.

A paper submission to Vision, Modeling, and Visualization (2016) was created around July 2016, but ultimately rejected (mainly because of incomplete evaluation of your method). The paper can still be found here.

License

The source code is licensed under the BSD 3-Clause, see LICENSE.txt.