Variational mesh decomposition

Abstract

The problem of decomposing a 3D mesh into meaningful segments (or parts) is of great practical importance in computer graphics. This article presents a variational mesh decomposition algorithm that can efficiently partition a mesh into a prescribed number of segments. The algorithm extends the Mumford-Shah model to 3D meshes that contains a data term measuring the variation within a segment using eigenvectors of a dual Laplacian matrix whose weights are related to the dihedral angle between adjacent triangles and a regularization term measuring the length of the boundary between segments. Such a formulation simultaneously handles segmentation and boundary smoothing, which are usually two separate processes in most previous work. The efficiency is achieved by solving the Mumford-Shah model through a saddle-point problem that is solved by a fast primal-dual method. A preprocess step is also proposed to determine the number of segments that the mesh should be decomposed into. By incorporating this preprocessing step, the proposed algorithm can automatically segment a mesh into meaningful parts. Furthermore, user interaction is allowed by incorporating the user's inputs into the variational model to reflect the user's special intention. Experimental results show that the proposed algorithm outperforms competitive segmentation methods when evaluated on the Princeton Segmentation Benchmark.

New evaluation metrics for mesh segmentation

“…Recent progress in discovering geometric properties includes diffusion distance [17], heat kernel [3], intrinsic primitive decomposition [13], heat walk [10], concavity-sensitive scalar fields [12], and minimum slice perimeter [14]. These geometric features are clustered in a descriptor space using clustering techniques such as recent Gaussian mixture models [18], greedy algorithm [10], and the Mumford-Shah model [15].…”

“…Although many methods are evaluated on the four metrics simultaneously, we consider that they cannot help to generate consistent evaluation Table 1 Summary of recent papers adopting four metrics. [14] CD, HD, RI, CE Zhang et al (2012) [15] RI, CE results. There are two reasons: (1) CD measures segmentation boundaries while HD, RI, and CE are based on region differences of segmented surfaces.…”

Continuous semantic description of 3D meshes

“…We consider an input 3D model Q with m unlabeled segments that may come from any segmentation algorithms [47,48]. By using a database of segmented and labeled models, we infer the labels of Q .…”

Shape segmentation by hierarchical splat clustering

“…Many existing mesh segmentation methods leverage the surface concavity information as a key measure for the underlying algorithms, such as, K-mean clustering [15], graph cut-based fuzzy clustering [16], random walk algorithm [17] and spectral clustering methods [18,19]. There are also some algorithms incorporating some forms of the minima rule to segment the surface of models, such as the approaches based on randomized cuts [20], variational decomposition [21] and concavity-aware fields [22].…”