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High precision laser scanners deliver virtual surfaces of industrial objects whose accuracy must be evaluated. But this requires the automatic detection of reliable components such as facets, cylindric and spherical parts, etc. The method described here finds automatically parts in the surface to which geometric primitives can be fitted. Knowing certain properties of the input object, this primitive fitting helps quantifying the precision of an acquisition process and of the scanned mires. The method combines mesh segmentation with model fitting. The mesh segmentation method is based on the level set tree of a scalar function defined on the mesh. The method is applied with the simplest available intrinsic scalar function on the mesh, the mean curvature. In a first stage a fast algorithm extracts the level sets of the scalar function. Adapting to meshes a well known method for extracting Maximally Stable Extremal Regions from the level set tree on digital images, the method segments automatically the mesh into smooth parts separated by high curvature regions (the edges). This segmentation is followed by a model selection on each part permitting to fit planes, cylinders and spheres and to quantify the overall accuracy of the acquisition process.