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3D Object Modelling 3D Object Modelling and Classificationand Classification
Intelligent Robotics Research Centre (IRRC)
Department of Electrical and Computer Systems Engineering
Monash University, Australia
Visual Perception and Robotic Manipulation
Springer Tracts in Advanced Robotics
Chapter 4Chapter 4
Geoffrey Taylor
Lindsay Kleeman
2Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ContentsContents
• Introduction and motivation.
• Split-and-merge segmentation algorithm
• New method for surface type classification based on Gaussian image and convexity analysis
• Fitting geometric primitives
• Experimental results
• Conclusions
3Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
IntroductionIntroduction
• Motivation: enablea humanoid robotto perform ad hoctasks in a domesticor office environment.
• Flexibility in anunknown environmentrequires data driven segmentation to support object classification.
Metalman: an upper-torsohumanoid robot
4Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
IntroductionIntroduction
• Object modelling in robotic applications:
– CAD models (Kragić, 2001)
– Generalized cylinders (Rao et al, 1989)
– Non-parametric (Müller & Wörn, 2000)
– Geometric primitives (Yang & Kak, 1986)
• Many domestic objects can be adequately modelled with geometric primitives.
• Colour/range data provided by robust stereoscopic light stripe scanner (Taylor et al, 2002).
5Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
SegmentationSegmentation
• Basic techniques:– Region Growing: iteratively grow seed segments.
– Split-and-Merge: find region boundaries.
– Clustering: transform and group points.
• Region growing requires accurate range data for fitting primitives to small seed regions.
• Split-and-Merge maintains large regions that can be robustly fitted to primitives.
6Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
SegmentationSegmentation
• Raw range/colour data from stereoscopic light stripe camera.
• Calculate normal vector and surface type for each range element.
7Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
SegmentationSegmentation
• Remove range discontinuities and creases.
• Fit primitives.
• Compare best model to dominant surface type.
• Split poorly modelled regions by surface type and fit primitives again.
8Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
SegmentationSegmentation
• Iteratively grow regions by adding unlabelled pixels that satisfy model.
• Merge regions using iterative boundary cost minimization to compensate for over-segmentation.
9Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
SegmentationSegmentation
• Extract primitives and add texture using projected colour data.
• Use models for object classification, tracking and task planning
10Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
Surface TypeSurface Type
• Determine local shape of NxN element patch:
11Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
Classification methodsClassification methods
• Conventional method:– Fit surface, calculate mean and Gaussian curvature
– Classify based on curvature sign ( > 0, < 0, = 0) Sensitive to noise (second-order derivatives required) Arbitrary approximating function introduces bias.
• Our novel method:– Based on convexity and principal curvatures.
– Non-parametric (no approximating surface)
– Robust to noise
12Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ClassificationClassification
Number of non-zero principal curvatures
Con
vexi
ty
conv
ex
co
ncav
e
ne
ithe
r
Zero One Two
13Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
Principal CurvaturesPrincipal Curvatures
• Determine number of principal curvatures from Gaussian image of surface patch.
Surface representation Gaussian image
14Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
Principal CurvaturesPrincipal Curvatures
• Spread of normal vectors in Gaussian image of patch indicates non-zero principal curvature.
plane
ridge/valley pit/peak/saddle
15Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
• Align central normal to z-axis.
• Measure spread in direction using MMSE:
• Optimize with respect to • Two solutions:
(, e)max and (, e)min
• Non-zero curvature whenemax > eth or emin > eth
Principal CurvaturesPrincipal Curvatures
2)sincos( ii yxe
min
max
y
x
amin
16Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ConvexityConvexity
Convex Concave
n0
n1
d
n1 x n0
(n1 x n0) x dn1
n0
d
n1 x n0
(n1 x n0) x d
17Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
• For each element in patch, calculate:
• Let S=Ncv/Ncc, ratio of convex to concave elements.
• Global convexity given by dominant local property:
ConvexityConvexity
concave : 0
convex : 0 ])[( 001 ndnn
convex (peak, ridge): S > Sth
concave (pit, valley): S < 1/Sth
neither (plane, saddle): 1/Sth < S < Sth
18Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
Surface Type SummarySurface Type Summary
principal curvatures
convexity
raw 3D scan surface type
19Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
• Planes:– Principal component analysis
• Spheres, cylinders, cones:– Minimize distance to fitted surface:
– Levenberg-Marquardt numerical optimization.
– Initial estimate of parameters required.
• Choose model with minimum error, e < eth.
Fitting PrimitivesFitting Primitives
Ri
i fe 2|)(|)( pmp
20Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
Cylinder EstimationCylinder Estimation
• Estimate cylinder axis from Gaussian image:
min
y
x
a
Cylindrical region and axis
Gaussian image and direction of minimum spread
a
21Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ResultsResults
• Box, ball and cup:
Raw colour/range scan Discontinuities, surface type
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ResultsResults
• Box, ball and cup:
Region growing, merging Extracted object models
23Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ResultsResults
• Bowl, funnel and goblet:
Raw colour/range scan Discontinuities, surface type
24Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ResultsResults
• Bowl, funnel and goblet:
Region growing, merging Extracted object models
25Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ResultsResults
• Comparison with curvature-based method:
Besl and Jain, 1988Non-parametric result
26Taylor and Kleeman, Visual Perception and Robotic Manipulation, Springer Tracts in Advanced Robotics
ConclusionsConclusions
• Split-and-merge segmentation using surface type and geometric primitives is capable of modelling a variety of domestic objects using planes, spheres, cylinders and cones.
• New surface type classifier based on principal curvatures and convexity provides greater robustness than curvature-based methods without additional computational cost.