Joint shape segmentation with linear programming

We consider the problem of transporting shape descriptors across shapes in a collection in a modular fashion, in order to establish correspondences between them. A common goal when mapping between multiple shapes is consistency, namely that compositions of maps along a cycle of shapes should be approximately an identity map. Existing attempts to enforce consistency typically require recomputing correspondences whenever a new shape is added to the collection, which can quickly become intractable. Instead, we propose an approach that is fully modular, where the bulk of the computation is done on each shape independently. To achieve this, we use intermediate nonlinear embedding spaces, computed individually on every shape; the embedding functions use ideas from diffusion geometry and capture how different descriptors on the same shape inter‐relate. We then establish linear mappings between the different embedding spaces, via a shared latent space. The introduction of nonlinear embeddings allows for more nuanced correspondences, while the modularity of the construction allows for parallelizable calculation and efficient addition of new shapes. We compare the performance of our framework to standard functional correspondence techniques and showcase the use of this framework to simple interpolation and extrapolation tasks.

Section: Applicationsmentioning

confidence: 99%

Modular Latent Spaces for Shape Correspondences

Ganapathi-Subramanian

Diamanti

Guibas

2018

“…Each segmentation on the left was produced by the top-performing algorithm in the benchmark for that shape. The segmentations on the right were produced by [HKG11], which jointly optimized segmentations and correspondences across the entire data set.…”

Section: Figurementioning

confidence: 99%

Data‐Driven Shape Analysis and Processing

Kim

Huang

et al. 2016

Self Cite

Data‐driven methods serve an increasingly important role in discovering geometric, structural and semantic relationships between shapes. In contrast to traditional approaches that process shapes in isolation of each other, data‐driven methods aggregate information from 3D model collections to improve the analysis, modelling and editing of shapes. Data‐driven methods are also able to learn computational models that reason about properties and relationships of shapes without relying on hard‐coded rules or explicitly programmed instructions. Through reviewing the literature, we provide an overview of the main concepts and components of these methods, as well as discuss their application to classification, segmentation, matching, reconstruction, modelling and exploration, as well as scene analysis and synthesis. We conclude our report with ideas that can inspire future research in data‐driven shape analysis and processing.

“…Kraevoy et al [KJS07] perform an initial segmentation of each model into parts and then create a consistent segmentation by matching the parts and finding their correspondences. Huang et al [HKG11] present a linear programming based approach for jointly segmenting a heterogenous database of shapes, which significantly outperforms single-shape segmentation techniques. However, these two methods provide only mutually consistent segmentation but cannot guarantee the consistency of the final segmentations across the set.…”

Section: Related Workmentioning

confidence: 99%

Co‐Segmentation of 3D Shapes via Subspace Clustering

Fan

Liu

2012

144

107

Figure 1: The co-segmentation result of the Candelabra set by our algorithm. Starting from the over-segmented patches of the shapes (left), our algorithm automatically obtains the consistent segmentations among these objects by grouping the patches using subspace clustering in multiple feature spaces. Corresponding parts are shown in the same colors (right). AbstractWe present a novel algorithm for automatically co-segmenting a set of shapes from a common family into consistent parts. Starting from over-segmentations of shapes, our approach generates the segmentations by grouping the primitive patches of the shapes directly and obtains their correspondences simultaneously. The core of the algorithm is to compute an affinity matrix where each entry encodes the similarity between two patches, which is measured based on the geometric features of patches. Instead of concatenating the different features into one feature descriptor, we formulate co-segmentation into a subspace clustering problem in multiple feature spaces. Specifically, to fuse multiple features, we propose a new formulation of optimization with a consistent penalty, which facilitates both the identification of most similar patches and selection of master features for two similar patches. Therefore the affinity matrices for various features are sparsity-consistent and the similarity between a pair of patches may be determined by part of (instead of all) features. Experimental results have shown how our algorithm jointly extracts consistent parts across the collection in a good manner.