Current computer graphic tools allow design and visualization of more and more realistic and precise 3D models. These models are numerical representations of both the real and imaginary worlds. Acquisition and design techniques of 3D models (modeler, scanner, sensor, etc.) usually produce huge data sets containing geometrical and appearance attributes. Geometrical attributes describe shape and dimensions of the object and include data relative to a point set on the object surface. Appearence attributes describe object surface properties such as colors, texture coordinates, normal vectors, etc. High quality meshes usually contain a high number of vertices and faces that cause non interactive rendering or high storage space. In recent years results have been presented in order to reduce the mesh complexity either by merging/collasping elements or by re-sampling vertices. Mesh simplification algorithms use different error criteria to measure the fitness of the approximated surfaces. Usually, these algorithms do not return measures of the error introduced while simplifying the mesh. Therefore, a mesh comparison tool would be useful to characterize mesh simplification algorithms.

(a) Original mesh with attributes (18 050 faces)	(b) Simplified with attribute management (1 000 faces)	(c) Simplified without attribute management (1 000 faces)
Figure 1: Mesh simplification example. The simplification algorithm used in (b) manages appearance attributes, and the algorithm used in (c) does not.

Some algorithms simplify the geometry and ignore the distortion caused to other surface attributes (colors, texture, normals, etc.). Figure 1 shows results of an example of mesh simplification algorithms. Figure 1(a) shows the original mesh. The algorithm used in Figure 1(b) manages appearance attributes, while the algorithm used in Figure 1(c) does not. We see clearly in the last figure that the mesh aspect is highly deteriorated.

We present a mesh comparison method based on the attribute deviation metric. This assessment allows one to compute local differences between the attributes of two meshes. The primary advantages of our method are:

• Generality: the method manages meshes containing geometric features as well as other surface attributes such as material colors, texture, temperature, radiation, etc. Moreover the measurements are independent of the viewpoint and the attribute type.


• Locality: assessments are done for given points on the mesh surface. Assessment resolution can be increased by a surface sampling method.


• Applications: the method is suitable for numerical models from real scenes and for synthetic models. This mesh comparison method can be used for many applications: mesh simplification, reverse engineering (comparison between a CAD model and a numerical model of the real object), mesh segmentation, mesh processing algorithm characterization, etc.

Figure 2: Attribute deviation metric scheme.

The proposed mesh comparison method is based on the difference assessment between mesh attributes. The attribute deviation between a point and a surface is the distance from the attribute of the point to the attribute of the nearest point to on the surface. In the case of several points on the surface having the same distance to the point , the attribute deviation is the minimum distance between the attribute of the given point to the attributes of the nearest points on the surface. The attribute deviation metric scheme is presented in Figure 2.

(a) Garland simplification	(b) Jade simplification	(c) ProgMesh simplification
Figure 3: Example of geometric deviation assessment for three different simplification algorithms.

(a) Garland simplification.	(b) Jade simplification.	(c) ProgMesh simplification.
Figure 4: Example of normal deviation assessment for three different simplification algorithms.

All results are obtained with our mesh comparison software called MeshDev. This software is free and can be downloaded on the following website http://meshdev.sf.net.

• Generic Attribute Deviation Metric for Assessing Mesh Simplification Algorithm Quality, Michaël ROY, Sebti FOUFOU, and Frédéric TRUCHETET, In Proceedings of IEEE International Conference on Image Processing, pp. 817-820, September 2002, Rochester, USA.

  Paper:	Roy-Icip02.pdf
  Poster:	Roy-Icip02-Poster.pdf

  
  
• Assessment of Mesh Simplification Algorithm Quality, Michaël ROY, Frédéric NICOLIER, Sebti FOUFOU, Frédéric TRUCHETET, Andreas KOSCHAN, and Mongi ABIDI, In Proceedings of SPIE Electronic Imaging, Vol. 4661, pp. 128-137, January 2002, San Jose, USA.

  Paper:	Roy-Ei02.pdf
  Presentation:	Roy-Ei02.ppt

  
  
• Mesure de la qualité des algorithmes de simplifiation de maillages, Michaël ROY, Frédéric NICOLIER, Sebti FOUFOU, and Frédéric TRUCHETET, In Proceedings of 17èmes Journées de l'AFIG, pp. 175-184, November 2001, Limoges, France.

  Paper:	Roy-Afig01.pdf
  Presentation:	Roy-Afig01.ppt

  
  
• Qualité d'un modèle 3D simplifié, Michaël ROY, Mémoire de DEA Instrumentation et Informatique de l'Image, Université de Bourgogne, June 2001, Dijon, France.

  Paper:

  Roy-Dea01.pdf

This research is being conducted at the IRIS Lab and Le2i by Michaël ROY under the supervision of Dr. Mongi A. ABIDI., Pr. Frédéric TRUCHETET, and Dr. Sebti FOUFOU.