04/21/23

Presenter Yunhai@VCC

Co-Segmentation of 3D Shapes via Subspace Clustering

Ruizhen Hu, Lubin Fan, Ligang Liu.Computer Graphics Forum (Proc. SGP), 2012

Background

Single-Shape Segmentation

K-Means

[Shalfman et al. 2002]

Random Walks

[Lai et al. 08]

Fitting Primitives

[Attene et. al 2006]

Normalized Cuts

[Golovinskiy and Funkhouser 08]

Randomized Cuts

[Golovinskiy and Funkhouser 08]

Core Extraction

[Katz et al. 05]

Shape Diameter Function

[Shapira et al. 08]

Supervised Co-Segmentation

Input Mesh

Training Meshes

Labeled Mesh

Head

NeckTorso

LegTailEar

Limitations Prior knowledge of the category Shape variation within each category shall be small

[Kalogerakis et al.10, van Kaick et al. 11]

Unsupervised Co-Segmentation

[Sidi et al.11]

[Huang et al. 11]

Problem

Each feature descriptor generally has its own advantages and limitations.

However, existing methods concatenate all features into a higher dimensional descriptor

AGD SDF

Approach

Pipeline

Over-segmentationwith normalized cuts

Gaussian curvatureShape diameter function

Average geodesic distanceShape contextsConformal factor

Feature descriptors Subspace clustering

Subspace

Let be a given set of points drawn

from an unknown union of linear or affine subspaces of unknown dimensions

The subspaces can be described as

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An example

Subspace Sparse Representation

Each data point in a union of linear subspaces can always be represented as a linear combination of the points belonging to the same linear subspace.

To get a sparse linear combination>>minimizing the number of nonzero

In practice use: 04/21/23

Subspace Sparse Representation

Written in matrix form

To enforce the sparsity of the optimal solution

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Sparse Subspace Clustering

Each entry of the matrix measures the linear correlation between two points in the dataset. We use this matrix to define a directed graph G = (V,E)

To make it balanced, we define the adjacency matrix

Cluster the graph with normalized cut

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Sparse Subspace Clustering

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An example

Data drawn from 3 subspaces Matrix of sparse coefficients Similarity graph

Multi-feature co-segmentation

Multi-feature penalty

Multi-feature co-segmentation

Multi-feature: penalty

W1

W2

Wn

Illustration of W

Clustering

Affinity matrix

Minimal curvature mc

Ncut clustering

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Results

Result

The algorithm vs supervised approach

92.6% vs 96.1%

Result

Too many labels

Result

The algorithm vs unsupervised approach

94.4% vs 88.2%

Compared to Sidi et al.

Do not require the input model to have the same topologies

Can generate the satisfactory co-segmentation results from only a few models ??

Limitation

Only use the geometric properties to distinguish patches and classify them.

Video

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Q&A