Formulations of the Image Decomposition Problem as a Multicut Problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are hard to solve in practice, and, secondly, due to the lack of long-range terms in the objective function of the MP. We propose a generalization of the MP with long-range terms (LMP). We design and implement two efficient algorithms (primal feasible heuristics) for the MP and LMP which allow us to study instances of both problems w.r.t. the pixel grid graphs of the images in the BSDS-500 benchmark. The decompositions we obtain do not differ significantly from the state of the art, suggesting that the LMP is a competitive formulation of the Image Decomposition Problem. To demonstrate the generality of the LMP, we apply it also to the Mesh Decomposition Problem posed by the Princeton benchmark, obtaining state-of-the-art decompositions.
This paper presents a simple and efficient automatic mesh segmentation algorithm that solely exploits the shape concavity information. The method locates concave creases and seams using a set of concavity-sensitive scalar fields. These fields are computed by solving a Laplacian system with a novel concavity-sensitive weighting scheme. Isolines sampled from the concavity-aware fields naturally gather at concave seams, serving as good cutting boundary candidates. In addition, the fields provide sufficient information allowing efficient evaluation of the candidate cuts. We perform a summarization of all field gradient magnitudes to define a score for each isoline and employ a score-based greedy algorithm to select the best cuts. Extensive experiments and quantitative analysis have shown that the quality of our segmentations are better than or comparable with existing state-of-the-art more complex approaches. This paper presents a 3D-mesh segmentation algorithm based on a learning approach. A large database of manually segmented 3D-meshes is used to learn a boundary edge function. The function is learned using a classifier which automatically selects from a pool of geometric features the most relevant ones to detect candidate boundary edges. We propose a processing pipeline that produces smooth closed boundaries using this edge function. This pipeline successively selects a set of candidate boundary contours, closes them and optimizes them using a snake movement. Our algorithm was evaluated quantitatively using two different segmentation benchmarks and was shown to outperform most recent algorithms from the state-of-the-art. We propose a fast method for 3D shape segmentation and labeling via Extreme Learning Machine (ELM). Given a set of example shapes with labeled segmentation, we train an ELM classifier and use it to produce initial segmentation for test shapes. Based on the initial segmentation, we compute the final smooth segmentation through a graph-cut optimization constrained by the super-face boundaries obtained by over-segmentation and the active contours computed from ELM segmentation. Experimental results show that our method achieves comparable results against the state-of-the-arts, but reduces the training time by approximately two orders of magnitude, both for face-level and super-face-level, making it scale well for large datasets. Based on such notable improvement, we demonstrate the application of our method for fast online sequential learning for 3D shape segmentation at face level, as well as realtime sequential learning at super-face level.  This paper presents a data-driven approach to simultaneous segmentation and labeling of parts in 3D meshes. An objective function is formulated as a Conditional Random Field model, with terms assessing the consistency of faces with labels, and terms between labels of neighboring faces. The objective function is learned from a collection of labeled training meshes. The algorithm uses hundreds of geometric and contextual label features and learns different types of segmentations for different tasks, without requiring manual parameter tuning. Our algorithm achieves a significant improvement in results over the state-of-the-art when evaluated on the Princeton Segmentation Benchmark, often producing segmentations and labelings comparable to those produced by humans. An overview of the state-of-the-art in 3D mesh segmentation.An overview of performance evaluation frameworks for 3D mesh segmentation.New categorization for 3D mesh segmentation methodologies.Pros and cons in performance evaluation frameworks. 3D mesh segmentation has become a crucial part of many applications in 3D shape analysis. In this paper, a comprehensive survey on 3D mesh segmentation methods is presented. Analysis of the existing methodologies is addressed taking into account a new categorization along with the performance evaluation frameworks which aim to support meaningful benchmarks not only qualitatively but also in a quantitative manner. This survey aims to capture the essence of current trends in 3D mesh segmentation.