SURFACE SIMPLIFICATION:

Measuring error on simplified surfaces


Metro is a tool designed to evaluate the difference between two triangular meshes. Metro adopts an approximated approach based on surface sampling and point-to-surface distance computation. 

The new version for the Windows platform, returns only numerical results (maximum and mean error, volume difference, surface difference, etc.).  

Three different surface sampling methods are implemented:

Subdivision sampling

Similar Triangles sampling

Note that the three methods described above are used to sample only the interior of each face. A different scheme is used to sample vertices and edges: vertices are sampled in the straightforward manner, while edges are sampled by uniformly interleaving samples along each edge.

The Metro Software

Metro is a command-line tool which allows the user to select among different sampling schemes. A list of the command-line parameters accepted by the tool is shown in the following.

Usage: Metro file1 file2 [opt]

where "file1" and "file2" are the input meshes in PLY or SMF format, and opt can be:

-V  disable vertex sampling
-E  disable edge sampling
-F  disable face sampling
-Sx set the face sampling mode
    where x can be:
    M  montecarlo sampling (default)
    S  subdivision sampling
    T  similar triangles sampling
-N# set the required number of samples (overrides -A, default: 10 x #faces)
-A# set the required number of samples per area unit (overrides -N)
-Hxxx.yyy save histogram of error values in the file xxx.yyy

By default vertex, edge and face sampling are enabled.


Example:     Metro mesh1.ply mesh2.smf -SS -N50000 -E 

compares the two input meshes using the subdivision method for face sampling with a sampling step of 12.5 samples/area_unit; edge sampling is disabled.

The numerical results retuned are as follows:

-------------------------------
Metro
release date: Nov 26 2002
-------------------------------

reading the mesh 'mesh1.ply'...done
reading the mesh 'mesh2.smf'...done
Mesh info:
M1: 'mesh1.ply'
vertices 5052
faces 10000
area 790329.3211
bbox (-256.5977 -399.9384 -1732.1525)-(210.8112 101.2027 -1472.8544)
bbox diagonal 732.699854
M2: 'mesh2.smf'
vertices 2031
faces 3999
area 789830.8269
bbox (-256.7550 -399.2310 -1732.2300)-(210.8110 101.1740 -1473.0200)
bbox diagonal 732.265616

Forward distance (M1 -> M2):
target # samples : 50000
target # samples/area : 0.063265
Vertex sampling
Subdivision face sampling
distance:
max : 3.160912 (0.004042 with respect to bounding box diagonal)
mean : 0.138594
RMS : 0.204879
# vertex samples 5052
# area samples 44947
# total samples 49999
samples per area unit: 0.063264


Backward distance (M2 -> M1):
target # samples : 50000
target # samples/area : 0.063305
Vertex sampling
Subdivision face sampling
distance:
max : 2.159845 (0.002762 with respect to bounding box diagonal)
mean : 0.129528
RMS : 0.188315
# vertex samples 2031
# area samples 47967
# total samples 49998
samples per area unit: 0.063302


Hausdorff distance: 3.160912 (0.004042 with respect to bounding box diagonal)
Computation time : 3174 ms
# samples/second : 31504.725898

Download

You can now download the PC version of the Metro software from our downloading page:

Download Metro v3.1 for Windows

Linux version (coming soon!)

For any problem, please contact  P. Cignoni.


 

The previous Metro version (v.2.5) was released in public domain on Oct. '98 and was running just on the SGI Irix platform.

Download Metro 2.5 Download the paper describing Metro

A snapshot of Metro v2.5 output window is in the image below  (graphic output is provided only by Metro v2.5 running on SGI platform!).


Papers

Metro: measuring error on simplified surfaces
P. Cignoni, C. Rocchini and R. Scopigno
Computer Graphics Forum, Blackwell Publishers, vol. 17(2), June 1998, pp 167-174

Abstract
This paper presents a new tool, Metro, designed to compensate for a deficiency in many simplification methods proposed in literature. Metro allows one to compare the difference between a pair of surfaces (e.g. a triangulated mesh and its simplified representation) by adopting a surface sampling approach. It has been designed as a highly general tool, and it does no assuption on the particular approach used to build the simplified representation. It returns both numerical results (meshes areas and volumes, maximum and mean error, etc.) and visual results, by coloring the input surface according to the approximation error.

Images