Shape Distinction
for
3D Object Retrieval
Philip Shilane
Shape Matching
Shape matching is important for numerous projects including
constructing 3D models, object recognition, and protein analysis.
Molecular Biology
Protein Databank
H.M. Berman et al. 2000.
Shape Matching
Shape matching is important for numerous projects including
constructing 3D models, object recognition, and protein analysis.
Molecular Biology
Protein Databank
H.M. Berman et al. 2000.
Mechanical CAD
National Design Repository
W. Regli et al. 2001.
Engineering Shape
Benchmark
N. Iyer et al. 2005.
Shape Matching
Shape matching is important for numerous projects including
constructing 3D models, object recognition, and protein analysis.
Molecular Biology
Protein Databank
H.M. Berman et al. 2000.
Tracking
E3D
Mechanical CAD
National Design Repository
W. Regli et al. 2001.
Engineering Shape
Benchmark
N. Iyer et al. 2005.
Shape Matching
Shape matching is important for numerous projects including
constructing 3D models, object recognition, and protein analysis.
Molecular Biology
Protein Databank
H.M. Berman et al. 2000.
Tracking
Computer Graphics
Princeton Shape Benchmark
P. Shilane et al. 2004.
E3D
Mechanical CAD
National Design Repository
W. Regli et al. 2001.
Engineering Shape
Benchmark
N. Iyer et al. 2005.
Min et al.
Min et al.
Shape Retrieval
Find similar shapes in a database using a query shape.
3D
Model
Model Database
Best
Matches
Shape Descriptors
Shape descriptors are feature vector representations for
shapes
3D
Model
Model Database
Best
Matches
Example Shape Descriptors
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Extended Gaussian Image (EGI)
Surface
Normals
Complex Extended Gaussian Image (CEGI)
Shape Histograms (Shells)
Shape Histograms (Sectors)
Shape Histograms (SecShells)
Surface
D2 Shape Distributions
Distribution
Spherical Extent Function (EXT)
Radialized Spherical Extent Function (REXT)
Voxel
Gaussian Euclidean Distance Transform (GEDT)
Morphing
Harmonic Shape Descriptor (HSD)
Distance
Fourier Shape Descriptor (FSD)
Light Field Descriptor (LFD)
ImageDepth Buffer Descriptor (DBD)
Based
Properties of Shape Descriptors
Shape
Descriptor
Size
bytes
Create
seconds
Compare
μ-seconds
EGI
1,032
0.41
14
CEGI
2,056
0.37
27
Shells
136
0.66
2
Sectors
552
0.90
14
32,776
1.38
451
D2
136
1.12
2
EXT
562
1.17
8
REXT
17,416
2.22
229
Voxel
32,776
1.34
450
GEDT
32,776
1.69
450
HSD
2,184
1.69
27
FSD
32,768
1.82
450
LFD
4,700
3.25
1300
DBD
1,752
0.55
18
SecShells
Shape Retrieval with Descriptors
•
•
Which shape descriptors are the best?
How do we evaluate retrieval success?
Princeton Shape Benchmark
Philip Shilane, Patrick Min, Michael Kazhdan, and
Thomas Funkhouser
Princeton Shape Benchmark
• Large shape database
• 1,814 classified models, 161 classes
• Separate training and test sets
• Standardized suite of tests
• Multiple classifications
• Targeted sets of queries
• Standardized evaluation tools
• Visualization software
• Quantitative metrics
Princeton Shape Benchmark (PSB)
Num
Classes
Num
Models
Largest
Class
Osada
25
133
20%
MPEG-7
15
227
15%
Hilaga
32
230
15%
Technion
17
258
10%
Zaharia
23
362
14%
CCCC
54
416
13%
Utrecht
6
512
45%
Taiwan
47
549
12%
Viewpoint
85
1,280
12%
161
1,814
6%
PSB
Princeton Shape Benchmark
51 potted plants
33 faces
15 desk chairs
22 dining chairs
100 humans
28 biplanes
14 flying birds
11 ships
Evaluation Tools
Visualization tools
• Precision/recall plot
• Best matches
• Distance image
• Tier image
Quantitative metrics
• Nearest neighbor
• First and Second tier
• E-Measure
• Discounted Cumulative
Gain (DCG)
Multiple Classifications
• Granularity
• Model Properties
Base Classification
(92)
LFD
Evaluation Tools
Visualization tools
• Precision/recall plot
• Best matches
• Distance image
• Tier image
Quantitative metrics
• Nearest neighbor
• First and Second tier
• E-Measure
• Discounted Cumulative
Gain (DCG)
Multiple Classifications
• Granularity
• Model Properties
EGI
Nearest
Neighbor
LFD
100%
EGI
100%
LFD
Evaluation Tools
Visualization tools
• Precision/recall plot
• Best matches
• Distance image
• Tier image
Quantitative metrics
• Nearest neighbor
• First and Second tier
• E-Measure
• Discounted Cumulative
Gain (DCG)
Multiple Classifications
1 if correct
• Granularity n 0 if incorrect

log 2 (i  1)
• Model
DCGProperties
 i
Max Score
EGI
Nearest
Neighbor
DCG
LFD
100%
88%
EGI
100%
75%
PSB Contributions
• Methodology to compare shape descriptors
• Vary classifications
• Query lists targeted at specific properties
• Unexpected results
• EGI: good at discriminating man-made vs. natural
objects, though poor at fine-grained distinctions
• DBD: good overall performance across tests
• Freely available Princeton Shape Benchmark
• classified polygonal models
• Source code for evaluation tools
• Downloaded ~8,700 times since 2003
• http://shape.cs.princeton.edu/benchmark
Shape Retrieval
Matching the whole shape has drawbacks.
3D
Model
Model Database
Best
Matches
Local Matches for Retrieval
Matching local regions of shapes to improve retrieval.
3D
Model
Model Database
D(A,B) =
∑ ΔFeatureShape
Correspondences
+
Best
Matches
∑ ΔSpatialConsistency
Correspondence
Pairs
Local Matches for Retrieval
Focusing on matching local regions of shapes can improve
retrieval results.
Using many local
descriptors is slow.
3D
Model
Model Database
D(A,B) =
∑ ΔFeatureShape
Correspondences
+
Best
Matches
∑ ΔSpatialConsistency
Correspondence
Pairs
Local Matches for Retrieval
Focusing on matching local regions of shapes can improve
retrieval results.
Using many local
descriptors is slow.
3D
Model
Best
Matches
ModelMany
Database
descriptors
do
D(A,B) =
∑ ΔFeatureShape
Correspondences
represent
∑not
ΔSpatialConsistency
Correspondence
distinguishing
parts.
Pairs
+
Local Matches for Retrieval
Focusing on matching local regions of shapes can improve
retrieval results.
3D
Model
D(A,B) =
Focusing on the
distinctive regions
Best
improves
retrieval
time
Matches
Model Database
and accuracy.
∑ ΔFeatureShape + ∑ ΔSpatialConsistency
Correspondences
Correspondence
Pairs
Outline
•
•
•
•
•
•
•
•
Introduction
Shape Descriptors for Retrieval
Related Work
System Overview
Evaluating Distinction
Computational Improvements
Applications
Conclusion
Related Work
• Random Selection
• Perceptual Criteria
• Eye Tracking
• Saliency
• Shape Matching
• Likelihood
• Stability
Related Work
• Random Selection
• Perceptual Criteria
• Eye Tracking
• Saliency
• Shape Matching
• Likelihood
• Stability
Mori 2001
Frome 2004
Related Work
• Random Selection
• Perceptual Criteria
• Eye Tracking
• Saliency
• Shape Matching
• Likelihood
• Stability
Howlett et al.
Related Work
• Random Selection
• Perceptual Criteria
• Eye Tracking
• Saliency
• Shape Matching
• Likelihood
• Stability
Lee et al.
Other Projects:
Li et al.
Novotni et al.
Frintrop et al.
Watanabe et al.
Hoffman et al.
Gal et al.
Related Work
• Random Selection
• Perceptual Criteria
• Eye Tracking
• Saliency
• Shape Matching
• Likelihood
• Stability
Johnson et al.
Chua et al.
Related Work
• Random Selection
• Perceptual Criteria
• Eye Tracking
• Saliency
• Shape Matching
• Likelihood
• Stability
Shan et al.
Distinct Regions
Distinctive regions distinguish an object from other types.
0
Mesh
Mesh Distinction
Distinction
1
Key Idea
Determining which regions are important is based on the
other shapes under consideration.
Mesh
Shape DB
Mesh
Distinction
Key Idea
A classified shape database provides a ground truth to
assess which regions of a shape are distinctive.
Mesh
Classified Shape DB
Mesh
Distinction
Outline
•
•
•
•
•
•
•
•
Introduction
Shape Descriptors for Retrieval
Related Work
System Overview
Evaluating Distinction
Computational Improvements
Applications
Conclusion
System Overview
Mesh
Regions
Shape
Descriptors
Distinct
Regions
Distinctive Regions of 3D Surfaces
Philip Shilane and Thomas Funkhouser
ACM Transactions on Graphics
Vertex
Distinction
Constructing Regions
Consistent segmentation is difficult and unnecessary. Regions could
be disjoint, overlap, or exist at multiple scales.
Segmentation
Katz et al.
Constructing Regions
Randomly selecting points on the surface is a simple solution.
Constructing Regions
Regions are created at multiple scales at each position.
Size of Regions
0.5
0.25
0.5
1.0
1.0
2.0
Describing Shapes
•
•
•
•
•
Quick to compute
Compact to store
Fast to compare
Robust to mesh problems
Discriminating of similar models
Describing Shapes
•
•
•
•
•
Quick to compute
Compact to store
Fast to compare
Robust to mesh problems
Discriminating of similar models
Experimented with several descriptors
• Shells Shape Histogram
• Harmonic Shape Descriptor
• Fourier Shape Descriptor
Measuring Distinction
We would like to calculate distinction scores for each region.
Mesh
Distinction
Measuring Distinction
Our approach is to analyze each region relative to a database to
determine which regions match shapes that are similar.
Distinction
Mesh
Classified Shape DB
Measuring Distinction
We would like to know the distinction of all combinations of
regions.
Distinction
Mesh
Classified Shape DB
Measuring Distinction
We make an independence assumption to calculate distinction for
each region.
Distinction
Mesh
Classified Shape DB
Distinction = Retrieval Performance
The distinction of each local descriptor is based on how well it
retrieves shapes of the correct class.
Query
Descriptors
Retrieval Results
Distinction = Retrieval Performance
The distinct descriptors that distinguish between classes are
classification dependent.
Query
Descriptors
Retrieval Results
Mapping to Vertices
For visualization, mesh simplification, and icon generation, it is
useful to have distinction scores for each vertex.
Mapping to Vertices
We map distinction scores to each vertex using a Gaussian weighted
average.
2
 xv
x D( x) exp[ 2 2 ]
D (v ) 
2
 xv
x exp[ 2 2 ]
v is a vertex
x is a point with distinctio n
σ  0.1 of mesh radius
Outline
•
•
•
•
•
•
•
•
Introduction
Shape Descriptors for Retrieval
Related Work
System Overview
Evaluating Distinction
Computational Improvements
Applications
Conclusion
Evaluating Distinction
1. What regions are distinctive?
2. Does distinction improve retrieval?
Analysis
Distinctive regions of meshes correspond to important regions
that define a class of objects.
Analysis
Compared to a database of flying objects, the helicopter blades
are most distinctive.
Mesh Saliency
Analysis
For human models in this pose, the elbow area is most distinctive.
Analysis
The distinctive regions of a mesh change with the database
under consideration.
Princeton Shape
Benchmark
Plane DB
Vehicle DB
Mesh Saliency
Evaluating Distinction
1. What regions are distinctive?
2. Does distinction improve retrieval?
Partial Matching of 3D Shapes with Priority-Driven Search
Thomas Funkhouser and Philip Shilane
Symposium on Geometry Processing, Sardinia, Italy, July 2006
Distinction within a Database
Classification
Preprocess
Shape
DB
Local
Descriptors
Retrieval
Evaluation
Distinction
Function
Descriptor
DB
Query
Shape
Local
Descriptors
Match
Retrieval
List
Matching Local Shapes
1. Generate local shape features
2. Find correspondences minimizing distance function
Surface
A
B
Matching Local Shapes
1. Generate local shape features
2. Find correspondences minimizing distance function
Features
Points
A
D(A,B) =
∑ ΔFeatureShape
Correspondences
B
+
∑ ΔSpatialConsistency
Correspondence
Pairs
Matching Local Shapes
1. Generate local shape features
2. Find correspondences minimizing distance function
Feature
Correspondences
Features
A
D(A,B) =
∑ ΔFeatureShape
Correspondences
B
+
∑ ΔSpatialConsistency
Correspondence
Pairs
Matching Local Shapes
1. Generate local shape features
2. Find correspondences minimizing distance function
Feature
Correspondences
Spatial Consistency
(Deformation)
Features
A
D(A,B) =
∑ ΔFeatureShape
Correspondences
B
+
∑ ΔSpatialConsistency
Correspondence
Pairs
Priority-Driven Search
Use a priority queue to perform best-first search for the optimal
set of K correspondences in the database.
B2
A1
A6
A5
C1
B3
C2
C5
B5
A2
A3
A4
B1
Query Object
Feature
Correspondences
_______________
D(match)
(A1,B2)
(A3,B1)
(A5,B3)
0.9
Low Cost
B4
C4
C3
Target Objects
(A2,B1)
1.1
(A1,B2)
(A2,B1)
1.5
(A3,B1)
(A2,B1)
1.8
Priority Queue
(A4,C1)
9.1
(A2,C3)
9.6
High Cost
Matching Local Shapes
Filter the database to the most distinctive regions during
preprocessing
Mesh
Descriptors
Distinction
Scores
4 Selected
Descriptors
Alternative Selection Techniques
The database can be filtered according to various selection
techniques.
Distinction
Likelihood
Saliency
Random
Shape Matching Results
Using the most distinctive descriptors improves matching versus
other techniques.
Shape Matching Results
Using multiple descriptors improves over using a single
descriptor.
Descriptor
Selection
Distinction
Random
Distinction
Random
K
NN%
DCG%
3
3
1
1
74.3%
66.5%
62.4%
55.6%
70.6%
63.4%
65.3%
57.8%
Centroid
Oracle
1
1
53.3%
89.5%
54.4%
79.7%
Shape Matching Results
Using a single descriptor on the surface is better than using a
global descriptor.
Descriptor
Selection
Distinction
Random
Distinction
Random
K
NN%
DCG%
3
3
1
1
74.3%
66.5%
62.4%
55.6%
70.6%
63.4%
65.3%
57.8%
Centroid
Oracle
1
1
53.3%
89.5%
54.4%
79.7%
Shape Matching Results
The oracle case shows an upper bound on matching
performance, suggesting research areas for improvement.
Descriptor
Selection
Distinction
Random
Distinction
Random
K
NN%
DCG%
3
3
1
1
74.3%
66.5%
62.4%
55.6%
70.6%
63.4%
65.3%
57.8%
Centroid
Oracle
1
1
53.3%
89.5%
54.4%
79.7%
Shape Matching Results
Priority-driven search with distinctive regions has better retrieval
performance than previous global techniques.
Outline
•
•
•
•
•
•
•
•
Introduction
Shape Descriptors for Retrieval
Related Work
System Overview
Evaluating Distinction
Computational Improvements
Applications
Conclusion
Computational Bottlenecks
• Computing distinction requires a full retrieval list
[2.4 minutes]
• Computing 128 descriptors at 4 scales
[3 minutes]
Times are per model
Computational Bottlenecks
• Computing distinction requires a full retrieval list
[2.4 minutes]
• Computing 128 descriptors at 4 scales
[3 minutes]
Times are per model
Calculating Distinction
Discounted cumulative gain requires a full retrieval list of n
results.
1 if correct
n
0 if incorrect

log 2 (i  1)
i
DCG 
Max Score
Calculating Distinction
Approximate distinction with a short retrieval list of length k < n.
1 if correct
k
0 if incorrect

log 2 (i  1)
i
DCG 
Max Score
Calculating Distinction
Cover tree index is a spatial structure for efficiently finding
neighbors in high dimensional space.
Query
descriptor
Image adapted from Qin Lv
Calculating Distinction
64 neighbors can be found in a fraction of the time of searching
the whole database, with similar retrieval accuracy.
Updating Distinction
A cover tree index can also be used for updating distinction
1. Build cover tree for DB
descriptors
2. Record R distances in
red-black tree
3. Find K neighbors for
new descriptor, K > R
Rth
Neighbor
Kth
Neighbor
K>R
4. Update distinction for K
neighbors and DB
descriptors with R
distance > K distance
Updating Distinction
A fraction of the DB must be updated depending on K neighbor
search and R-distinction
Computational Bottlenecks
• Computing distinction requires a full retrieval list
[2.4 minutes]
• Computing 128 descriptors at 4 scales
[3 minutes]
Times are per model
Predicting Distinction
We want a predicted distinction score for each position on
the model.
Descriptors
Distinction
Predict
Selecting Distinctive 3D Shape Descriptors for Similarity Retrieval
Philip Shilane and Thomas Funkhouser
Shape Modeling International, Matsushima, Japan, June 2006
Predicting Distinction
We map descriptors into a compact space where we learn
distinction from a training set.
Descriptors
Distinction
Prediction Overview
Training
Shape
DB
Local
Descriptors
Classification
Likelihood
Distinction
Function
Descriptor
DB
Retrieval
Evaluation
Query
Shape
Local
Descriptors
Likelihood
Evaluate
Distinction
Select
Descriptors
Match
Retrieval
List
Likelihood of Descriptors
Multi-dimensional normal density [Johnson 2000]

density ( x ) 

1
2
2 
d
2
 1   t 1   
exp  ( x   )  ( x   )
 2


x
d dimensiona l feature vector



mean feature vector
d x d covariance matrix
Build Predicted Distinction Function
Measure likelihood and retrieval performance of each descriptor.
Build Predicted Distinction Function
Measure likelihood and retrieval performance of each descriptor.
Build Predicted Distinction Function
Measure likelihood and retrieval performance of each descriptor.
Build Predicted Distinction Function
Retrieval performance is averaged within each likelihood bin.
Predicted Distinction Function
A likelihood mapping separates descriptors with different
retrieval performance.
Less Likely
More Likely
Predicted Distinction Function
The most common features are the worst for retrieval.
Less Likely
More Likely
Mapping Descriptors to Distinction
During the query phase, we predict distinction as we generate
descriptors
Descriptors
Distinction
Likelihood Mapping
Local Matches for Retrieval
Y
X
3D
Model
Model Database
Cost
Function

 C( X ,Y )
i
i
Best
Matches
Matching with Distinctive Descriptors
Y
X
3D
Model
Model
Database
Cost
Function
k

 C( X ,Y )
i
i
Best
Matches
Alternative Prediction Methods
Distinction improves retrieval more than other techniques.
Selection Techniques
% Improvement Precision
20%
Distinction
15%
Likelihood
10%
Random
5%
0%
10%
30%
50%
-5%
Recall
70%
90%
Outline
•
•
•
•
•
•
•
•
Introduction
Shape Descriptors for Retrieval
Related Work
System Overview
Evaluating Distinction
Computational Improvements
Applications
Conclusion
Applications
Importance scores on the surface of a mesh are useful for
numerous graphics and geometric processing
applications:
•
•
•
•
•
•
•
Shape Matching
Mesh Simplification
Icon Generation
Alignment
Rendering
Morphing
Segmentation
Mesh Simplification
Garland
1,700 tri
300 tri
Mesh
Saliency
Distinct
Regions
Mesh Simplification
97K tri
Mesh Saliency
Distinct Regions
2K tri
2K tri zoom
Icon Generation
Icon Generation
Focusing on the most distinctive regions often (but not always)
highlights important features.
Outline
•
•
•
•
•
•
•
•
Introduction
Shape Descriptors for Retrieval
Related Work
System Overview
Evaluating Distinction
Computational Improvements
Applications
Conclusion
Conclusion
•
•
•
•
•
•
•
•
PSB: data set and tools for evaluating retrieval methods
Defined distinctive regions based on retrieval performance
Analyzed properties of distinction
Focused shape-matching on distinctive regions
Calculate/update distinction efficiently
Predict distinctive regions from training set
Apps of distinction: icons and mesh simplification
Focus on generic methods, independent of shape descriptor
Future Work
•
•
•
•
Efficiency of shape retrieval
Distinction for an unclassified database
Scalability of updating distinction
Predict distinction with improved likelihood model or
other mapping
• Apply distinction analysis to image retrieval and other
applications
Acknowledgements
• Committee: Thomas Funkhouser, Szymon Rusinkiewicz,
Adam Finkelstein, David Dobkin, Andrea LaPaugh,
and Kai Li
• Graphics Group and entire CS Department
• Family and friends
• Funding Sources: Princeton University Departmental Award
National Science Foundation Grants IIS-0612231, CCR-0093343,
CNS 0406415, and 11S-0121446
Air Force Research Laboratory Grant FA8650-04-1-1718
Google Research Grant
Extra Slides
Constructing Regions
Selecting the vertices biases the sampling to the underlying
polygon representation.
Vertices
Applications: Shape Matching
•General strategy:
• Sample set of points
on surface of object
• Build shape descriptor
centered at every point
at multiple scales
• Find matches with
high descriptor similarity &
low geometric deformation
Mesh Simplification
Simplifying a complex mesh is important for improving
rendering time.
Many polygons
Fewer polygons
(quadric error shown)
Garland et al.
Icon Generation
Recent work selects the viewpoint that maximizes the amount
of salient surfaces or that minimizes the symmetric surfaces.
Lee et al.
Podolak et al.
Alternative Prediction Methods
Distinction improves retrieval more than other techniques.
Selection Techniques
20%
% Improvement Precision
Distinctive
15%
Johnson 2000
(Model)
Johnson 2000 (DB)
10%
Random
5%
0%
10%
30%
50%
-5%
Recall
70%
90%
Typical Shape Databases
Osada
MPEG-7
Hilaga
Technion
Zaharia
CCCC
Utrecht
Taiwan
Viewpoint
Num
Models
133
1,300
230
1,068
1,300
1,841
684
1,833
1,890
Num
Num
Classes Classified
25
133
15
227
32
230
17
258
Letter ‘C’ 23
362
54
416
6
512
47
549
85
1,280
Largest
Class
20%
15%
15%
10%
14%
13%
45%
12%
12%
Typical Shape Databases
Osada
MPEG-7
Hilaga
Technion
Zaharia
CCCC
Utrecht
Taiwan
Viewpoint
Num
Models
133
1,300
230
1,068
1,300
1,841
684
1,833
1,890
Num
Num
Classes Classified
25
133
15
227
32
230
17
258
23
362
54
416
6
512
47
549
85
1,280
Largest
Class
20%
15%
15%
10%
14%
13%
45%
12%
12%
Typical Shape Databases
Osada
MPEG-7
Hilaga
Technion
Zaharia
CCCC
Utrecht
Taiwan
Viewpoint
Num
Num
Num
Models
Classes Classified
133
25
133
1,300
15
227
230
32
230
1,068
17
258
Aerodynamic 23
1,300
362
1,841
54
416
684
6
512
1,833
47
549
1,890
85
1,280
Largest
Class
20%
15%
15%
10%
14%
13%
45%
12%
12%
Evaluation Tools
Visualization tools
• Precision/recall plot
• Best matches
• Distance image
• Tier image
Quantitative metrics
• Nearest neighbor
• First and Second tier
• E-Measure
• Discounted Cumulative
Gain (DCG)
Multiple Classifications
• Granularity
• Model Properties
Evaluation Tools
Visualization tools
• Precision/recall plot
• Best matches
• Distance image
• Tier image
Quantitative metrics
• Nearest neighbor
• First and Second tier
• E-Measure
• Discounted Cumulative
Gain (DCG)
Dining Chair
Multiple Classifications
• Granularity
• Model Properties Desk Chair
Related Work
• Random Selection
• Perceptual Criteria
• Eye Tracking
• Saliency
• Shape Matching
• Likelihood
• Stability
Lee et al.
Other Projects:
Li et al.
Novotni et al.
Frintrop et al.
Watanabe et al.
Hoffman et al.
Gal et al.
Analysis
We investigated whether alternative, faster techniques for
calculating importance are correlated with distinction.
• Distance: from center of mass
• Surface Area: percentage of
mesh enclosed within a region
• Likelihood: consider each
shape descriptor as a feature
vector
• Saliency: change in curvature
as calculated by saliency.exe
Analysis
We investigated whether alternative, faster techniques for
calculating importance are correlated with distinction.
• Distance: from center of mass
• Surface Area: percentage of
Correlation
Coefficient
mesh enclosed within
a region
n
1
• Likelihood: consider each
r as a feature
( xi  x)( yi
shape descriptor
(
n

1
)


x
y i 1
vector
• Saliency: change in curvature
as calculated by saliency.exe

 y)
Analysis
We investigated whether alternative, faster techniques for
calculating importance are correlated with distinction.
• Distance: from center of mass
• Surface Area: percentage of
mesh enclosed within a region
• Likelihood: consider each
shape descriptor as a feature
vector
• Saliency: change in curvature
as calculated by saliency.exe
r = -0.04
r = 0.07
r = 0.04
r = 0.03
Shape Matching Results
Priority-driven search with distinctive regions has better retrieval
performance than previous global techniques.
Mesh Simplification
When simplifying a mesh, important regions should be
preserved while less important regions are simplified.
69K tri
Garland et al.
1K tri
Mesh Simplification
Quadric Error is related to the
distance each vertex has
moved during simplification.
Ee  Qv1  Qv 2
Garland et al.
Mesh Simplification
We modified the standard error metric to include distinction
scores for each vertex.
We augment quadric error
with distinction scores.
Dv1
Ee  Dv1Qv1  Dv 2Qv 2
Garland et al.
After an edge collapse, the
remaining vertex is given the
maximum distinction score of
the two vertices involved.
Icon Generation
Selecting the best view point is important for creating icons
that are quickly recognizable.
Blanz et al.
Icon Generation
Important surfaces should be visible when creating icons
for a catalog of shapes.
Good View
Lee et al.
Poor View
Good View
Poor View
Podolak et al.
Evaluation Tools
Man-made vs. Natural
(2)
LFD
REXT
SHD
GEDT
Precision
Visualization tools
• Precision/recall plot
• Best matches
1
• Distance image
0.8
• Tier image
Quantitative metrics
0.6
• Nearest neighbor
• First and Second tier 0.4
• E-Measure
0.2
• Discounted Cumulative
Gain (DCG)
0
Multiple Classifications 0
• Granularity
• Model Properties
EXT
SecShells
Voxel
Sectors
CEGI
EGI
0.2
0.6
0.4
Recall
0.8
1
D2
Shells