object modelling by registration of multiple range images
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Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Object Modelling by Registration of Multiple Range Images
[Yang Chen and Gérard Medioni, 1991]
Jirapong ManitInstitute for Robotics and Cognitive Systems
University of Lübeck
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Outline
• Introduction• Range Image Registration
– Choosing the Evaluation Function– Line-Surface Intersection– Registration Algorithm
• Integration of Multiple Range Images• Results and Discussion• Conclusion
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Introduction
• Model of physical object is necessary component machine of biological vision modules.
• CAD models are hardly accessed in practices.
• Object from multiple views was proposed, but not always enough.
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Introduction
Object Modelling Procedures1. Data acquisition2. Registration between views3. Integration of views
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Introduction
http://carlos-hernandez.org/research.html
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Introduction
http://carlos-hernandez.org/research.html
Transformation
Correspondence problem
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Introduction
The range images of a Mozart bust
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Range Image Registration
http://blogs.rediff.com/alafearrea1983/2015/04/13/download-point-cloud-registration/
Point cloud registration
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Range Image Registration
• Rigid transformation
∀𝑝𝑖∈𝑃 ,∃𝑞 𝑗∈𝑄∨‖𝑇 𝑝𝑖−𝑞𝑖‖=0
D (𝑃 ,𝑄 )=∬Ω
❑
‖𝑇𝑝(𝑢 ,𝑣 )−𝑞( 𝑓 (𝑢 ,𝑣 ) ,𝑔(𝑢 ,𝑣 ))‖2𝑑𝑢𝑑𝑣=0
or
where and and are correspondence mapping functions
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Range Image Registration
• Transformation Matrix
T=[𝑐𝛼 𝑐 𝛽𝑠𝛼𝑐 𝛽−𝑠 𝛽0
𝑐 𝛼𝑠 𝛽 𝑠𝛾−𝑠𝛼𝑐𝛾𝑠𝛼 𝑠 𝛽𝑠𝛾+𝑐𝛼 𝑐𝛾
𝑐 𝛽𝑠𝛾0
𝑐𝛼𝑠 𝛽𝑐𝛾+𝑠𝛼𝑠 𝛾𝑠𝛼𝑠 𝛽𝑐𝛾−𝑐𝛼 𝑠𝛾
𝑐 𝛽𝑐 𝛾0
𝑡𝑥𝑡𝑦𝑡 𝑧1
]Consist of 6 DOF:
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Range Image Registration
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Choosing the Evaluation Function
Minimise : correspondence points
𝑒=∑𝑖=1
𝑁
‖𝑇 𝑝𝑖−𝑞𝑖‖2
Where and ,
𝑒=∑𝑖=1
𝑁
‖𝑇 𝑝𝑖−𝑞 𝑗‖2,with𝑞 𝑗=𝑞|min
𝑞𝜖𝑄‖𝑇 𝑝𝑖−𝑞‖
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Choosing the Evaluation Function
Minimise : approximate points
𝑒𝑘=∑𝑖=1
𝑁
‖𝑇 𝑘𝑝𝑖−𝑞 𝑗𝑘‖2 ,with𝑞 𝑗
𝑘=𝑞|min𝑞𝜖𝑄
‖𝑇 𝑘−1𝑝𝑖−𝑞‖
*Approximate would be easier
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Choosing the Evaluation Function
Minimise : distance between surfaces, Potmesil [2]
𝑒𝑘=∑𝑖=1
𝑁
‖𝑇 𝑘𝑝𝑖−𝑞 𝑗′ 𝑘‖2 ,with 𝑞 𝑗
′ 𝑘=(𝑇𝑘−1 ℓ 𝑖)∩𝑄
is intersection point of line with surface
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Choosing the Evaluation Function
Minimise : approximate using tangent plane
w here 𝑆 𝑗 is the tangent plane of 𝑄at𝑞 𝑗
𝑒=∑𝑖=1
𝑁
‖𝑇 𝑝𝑖−𝑞 𝑗′ ‖2 ,with𝑞 𝑗
′ =𝑞|min𝑞𝜖𝑆 𝑗
‖𝑇 𝑝𝑖−𝑞‖
𝑒=∑𝑖=1
𝑁
‖𝑇 𝑝𝑖−𝑞𝑖‖2
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Choosing the Evaluation Function
Minimise : approximate using tangent plane
𝑒𝑘=∑𝑖=1
𝑁
𝑑𝑠2 (𝑇𝑘𝑝𝑖 , 𝑆 𝑗
𝑘)
w ith 𝑆 𝑗𝑘={𝑠∨𝑛𝑞𝑗
𝑘 ∙ (𝑞 𝑗′ 𝑘−𝑠 )=0 },𝑞 𝑗
′ 𝑘=(𝑇 𝑘− 1 ℓ𝑖 )∩𝑄
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Choosing the Evaluation Function
Distance measures between and illustrated in the 2D case
𝒬
𝒫
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Choosing the Evaluation Function
Distance measures between and illustrated in the 2D case
𝒬𝑇 𝑘−1𝒫
𝑝𝑖 𝑑𝑠
𝑆 𝑗𝑘
𝑛𝑖
Minimise:
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Line-Surface Intersection
0 x
z
𝑝❑Control Point (start point)𝒫𝒬
Initial:- Let be a point on - is a line normal to at - Projecting orthographically
along -axis- Set and
y
Normal Vector Line
OrthogonalProjections
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Line-Surface Intersection
𝑝❑
Normal Vector Line
Control Point (start point)𝒫𝒬
𝑞0
Tangents Each iteration :- Compute - Find intersection of
with tangent plane to at
0 x
𝒫y
z
𝑞1
OrthogonalProjections
The process stop when ,
Approximate Intersection
True Intersection
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
The Registration Algorithm
Rewrite:
• Approximating very small value of in , the lease square algorithm can be converted to linear problem.
is the tangent plane to at
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
The Registration Algorithm
1. Select a set of and compute the surface normal at those points. Let
=2. At each iteration
a) For each control point • Apply to and to get and • Find the intersection of surface • Compute the tangent plane of at
b) Find the transformation that minimises with least square method, let
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
The Registration Algorithm
• The convergence of the procedure is tested by checking
where is a threshold set via experiment
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Test Cases With Range Image Registration
= 0.046, s = 0.6523, min = -39.3, max = 20.2 (in mm)
1st Example
Histogram of the error image
Actual angle: -15.00 degree
Detected angle: -15.06 degree
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Test Cases With Range Image Registration
= 0.0115, s = 0.3219, min = -7.63, max = 9.741 (in mm)
2nd Example
Actual angle: -20.00 degree
Detected angle: -19.75 degree
Histogram of the error image
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Outline
• Introduction• Range Image Registration• Integration of Multiple Range Images• Results and Discussion• Conclusion
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Integration of Multiple Range Images
• Multiple range images from different vantage points are needed
• Surface is not completely covered by using turn table.
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Integration of Multiple Range Images
• Modelling process:1. Take 4 – 8 side view range images from different poses on a turn
table2. Take images on each top and bottom views3. Estimate rotation angles of top and bottom views images
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Transformation from
Registration Process
Object –Centred Representation
Original range image
Cylindrical or
Spherical coordinateMerged Data
Select coordinate frame
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Global Registration
• Register an image with the merged data.• Possible error accumulation can be avoided
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Outline
• Introduction• Range Image Registration• Integration of Multiple Range Images• Results and Discussion• Conclusion
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Results and Discussion
The wood blob, the plaster tooth and the derived models for them
Intensity
Wire frame
Rendered
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Conclusion
• A new surface model constructing method, based on registering range images from multiple views.
• Image registration is achieved by minimising a distance measure function.
• The representation scheme may not be powerful enough to directly accommodate more complex object.
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
References
1. Chen, Y.; Medioni, G., "Object modeling by registration of multiple range images," Robotics and Automation, 1991. Proceedings., 1991 IEEE International Conference on , vol., no., pp.2724,2729 vol.3, 9-11 Apr 1991
2. Michael Potmesil, “Generating Models for Solid Objects by Matching 3D surface Segments”. In Proceedings of the International Joint Conference on Artificial Intelligence, page 1089-1093, Karlsuche, West Germany, August 1983
Institut für Robotik und Kognitive Systeme | Jirapong Manit
Chen Y. and Medioni G., Object Modeling by Registration of Multiple Range Images
Thank you
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