Hierarchical mesh segmentation based on fitting primitives

Abstract

In this paper we describe a hierarchical face clustering algorithm for triangle meshes based on fitting primitives belonging to an arbitrary set. The method proposed is completely automatic, and generates a binary tree of clusters, each of which fitted by one of the primitives employed. Initially, each triangle represents a single cluster; at every iteration, all the pairs of adjacent clusters are considered, and the one that can be better approximated by one of the primitives forms a new single cluster. The approximation error is evaluated using the same metric for all the primitives, so that it makes sense to choose which is the most suitable primitive to approximate the set of triangles in a cluster. Based on this approach, we implemented a prototype which uses planes, spheres and cylinders, and have experimented that for meshes made of 100k faces, the whole binary tree of clusters can be built in about 8 seconds on a standard PC. The framework here described has natural application in reverse engineering processes, but it has been also tested for surface de-nosing, feature recovery and character skinning.

A graph-based technique for semi-supervised segmentation of 3D surfaces

“…3), that allows for different refinement directions in different parts of the same object (refer to (Chen et al, 2009) for more details about these metrics). The compared method were Randomized and Normalized Cuts (Golovinskiy and Funkhouser, 2008), Shape Diameter Functions (Shapira et al, 2008), Core Extraction (Katz et al, 2005), Random Walks (Lai et al, 2008), Fitting Primitives (Attene et al, 2006a) and K-Means (Shlafman et al, 2002).…”

“…6 we compare the fully supervised ground truth segmentation (first column) with the result obtained by our method setting just 2 hint seeds for each segment. We tried to replicate this result using the interactive Fitting Primitive tool available from Attene et al (2006a), however were not able to obtain a proper segmentation with only 5 clusters (third column), while adding more clusters led the method to oversegmentation (fourth column).…”

“…In the second step the segmentation is refined using the alpha expansion graphcut algorithm, which is used to minimize an energy function that combines the vectors obtained in the first phase along with boundary smoothness and concaveness. Attene et al (2006a) introduce the use of geometric primitives to drive a hierarchical segmentation. Specifically, at an initial stage each surface triangle represents a singleton cluster associated to the primitive that best fits it.…”

“…Golovinskiy and Funkhouser (2008) use both normalized cuts and randomized cuts. In a similar manner to Attene et al (2006a), normalized cut segmentation happens by first assigning each face of the mesh to its own cluster and then by merging them hierarchically in an order determined by the area-normalized cut cost, i.e. the sum of each segment perimeter (weighted by concavity) divided by its area.…”

Semi-supervised Segmentation of 3D Surfaces Using a Weighted Graph Representation

“…Attene et al [17] introduce the use of geometric primitives to drive a hierarchical segmentation. Specifically, at an initial stage each surface triangle represents a singleton cluster associated to the primitive that best fits it.…”