Overview of Geometric Data Analysishuangqx/CS395_Lecture_III.pdf · 2017-01-23 · Overview of...
Transcript of Overview of Geometric Data Analysishuangqx/CS395_Lecture_III.pdf · 2017-01-23 · Overview of...
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Overview of Geometric Data Analysis
Qixing Huang
Janurary 23th 2017
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Last Lecture --- Scanning
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Last Lecture --- Registration
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Last Lecture --- Reconstruction
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This Lecture --- Overview of Geometric Data Analysis
• Local analysis
• Global analysis
• Semantic analysis
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Local Analysis
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Normal – Triangular Mesh
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Normal – Pointcloud
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CurvatureMaximum
principal curvatureMinimum
principal curvature
Mean curvature Gaussian curvature
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Application in View Selection
[Lee et al. 05]
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Feature Lines
[Ohtake et al. 04]
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Suggestive Contours
[DeCarlo et al. 03]
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Local Analysis --- Feature Point Extraction
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Local Analysis --- Point Descriptors
[Johnson and Hebert’ 99]
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Structure Analysis
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Reflection Symmetry
[Kazhdan 02]
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Rotational Symmetry
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Voting-Based Detection
[Mitra et al. 06]
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Symmetrization[Mitra et al. 07]
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Primitive Segmentation[Cohen-Steiner et al. 04]
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Primitive Segmentation
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Primitive Segmentation --- Reserve Engineering
[Schnabel et al. 07]
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Stability Analysis --- 3D Printing
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Stability Analysis --- Self Supporting Struct.
[Prevost et al. 13]
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Stability Analysis --- Self Supporting Struct.
[Deuss et al. 14]
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Vision-Related Analysis
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Shape Distributions
Distributions of pair-wise distances Invertible
[Osoda et al. 02]
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Spherical Harmonics
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Light-Field Descriptors
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Shape Organization[Huang et al. 13]
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Shape Exploration[Huang et al. 13]
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Fine-grained Shape Classification[Huang et al. 13]
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Shape Classification
[Hang et al. 15]
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3D Convolutions
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Scene Classification[Su et al. 16]
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Shape Matching
[Kim et al. 11]
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Fuzzy Correspondences[Kim et al. 12]
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Shape Distance Function
[Shapira et al. 08]
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Shape Segmentation
K-Means
[Shalfman et al. 2002]
Core Extraction
[Katz et al. 05]
Random Walks
[Lai et al. 08]
Normalized Cuts
[Golovinskiy and Funkhouser 08]
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Randomized Cuts
Inputmesh
RandomizedCuts
PartitionFunction
[Golovinskiy and Funkhouser’ 08]
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Skeleton Extraction
[Au et al. 08]
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Scene Understanding
[Gupta et al. 14]
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Hierarchical Scene Understanding
[Liu et al. 14]
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Semantics Analysis --- Functional Labeling
[Hu et al. 15]
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More Shape Analysis --- Shape Difference
[Rustamov et al. 13]
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Image Analysis vs Shape Analysis
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Data Representation
Triangular mesh Point cloud
Implicit surface Part-based models
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Triangular Meshes
Discrete Exterior Calculus Subdivision Surfaces
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Point Cloud Representation
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Point Cloud Representation
[Su et al. 16]
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Implicit Surface Representation
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Scene Graph Representation
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Scalability of Training Data
3M models in more than 4K categories
3.5 Trillion Images
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The impact of BigData
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Single Analysis vs Joint Analysis
• Extraneous geometric clues
Structural similarity of segmentations
Single shape segmentation[Chen et al. 09]
Joint shape segmentation[Huang et al. 11]
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Single Analysis vs Joint Analysis
Joint shape segmentation[Huang et al. 11]
Structural similarity of segmentations
• Low saliency
Single shape segmentation[Chen et al. 09]
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Single Analysis vs Joint Analysis
• Articulated structures
Joint shape segmentation[Huang et al. 11]
(Rigid) invariance of segments
Single shape segmentation[Chen et al. 09]
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Blended intrinsic maps[Kim et al. 11]
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Matching through intermediate objects --- map propagation
Blended intrinsic maps[Kim et al. 11]
Composite map
Intermediateobject
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In the data collection, correct maps usually form a connected sub-graph
Network of approximately correct blended intrinsic maps
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The map synchronization problem
Identify correct maps among a (sparse) network of maps
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The Influence of Deep Learning
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ShapeNet3D
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Generative Adversarial Network for 3D Voxel Grid
[Wu et al. 16]
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Sparse Convolutions[Riegler et al. 16]
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Deep Architecture for 3D Point Clouds
Classification
Generative Model
[Su et al. 16a, 16b]
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Scene Graphs?
Triangular Meshes?
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Other Topics
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Topological Data Analysis
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Joint Image and Shape Analysis
[Y. Wang et al. 16]
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Discussion