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ICPR August 23-26, 2004 University of Cambridge, UK. Sparse Point-Sets Matching with underlying non-rigidity. Baihua Li, Qinggiang Meng, Horst Holstein (speaker) bal@aber.ac.uk, qqm@aber.ac.uk, hoh@aber.ac.uk. University of Wales, Aberystwyth, UK. Where we are.

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## Sparse Point-Sets Matching with underlying non-rigidity

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**ICPR August 23-26, 2004**University of Cambridge, UK Sparse Point-Sets Matching with underlying non-rigidity Baihua Li, Qinggiang Meng, Horst Holstein (speaker) bal@aber.ac.uk, qqm@aber.ac.uk, hoh@aber.ac.uk**University of Wales, Aberystwyth,**UK Where we are**Robust one-to-one correspondence through binary space**partition trees: An application to interpret real-world human motion capture data H Holstein and B Li (University of Wales, Aberystwyth, UK)Speaker: Horst Holstein Abstract Commercial optical motion capture (MoCap) systems successfully achieve real-time motion capture through simplified image acquisition. They employ reflective markers attached to the subject, and track only these feature points in multiple cameras. There remains, however, the problem of establishing the identity of each feature point, so that motion capture can be displayed as an animated joined-up stick figure. Feature point identification is currently a manual process. In this talk, I describe a successful approach towards automated labelling. We set up a feature-point correspondence between a known generic model and one frame of capture data of the subject in a design pose. Pose differences and scaling make this a problem of robust correspondence generation. In the talk, I will include an overview an optical motion system (the Vicon 512), and of k-d trees. A new form of these leads to an elegant approach to the robust correspondence problem.**MLDs as sparse point sets**Moving Light Displays – Gait perception in Psychology: • Activity recognition. [Johansson, 1975] • Friends Recognition. [Cutting et al. 1977] • Gender recognition. [Barclay et al. 1978]**Research with MLDs**• Computer vision recognize and classify human activities; lip reading recognition; identify individual subjects. • Biomedical studies, e.g. gait analysis • Motion analysis and synthesis, (game/animation) • Kinematics studies, e.g. sportsscience • Humanoid robot design [Hill et al, 2000]**Example in animation**• Facial capture and transformation**Z**X Marker-based Optical MoCap Vicon 512 (3D MLD)**Individual Camera Views**camera 1 camera 3 camera 4 camera 2**Our Problem -identify 3D sparse feature points**3D Moving Light Displays (3D-MLDs) - An extension of Johansson’s 2D-MLDs [1975]**Current Practice (Vicon)**• Capture ONE frame of the subject in a design pose • Using a GUI, manually attach labels to screen marker points**head**upper arm Marker Labelling rfh lfh lsh lel**Transfer to Dynamic Marker Labelling/Segment ID**3D Moving Light Displays (3D-MLDs) - An extension of Johansson’s 2D-MLDs [1975]**A common situation**Given marker distribution for • Transverse study (different individuals) • Longitudinal study (same individual) Currently • manually identify markers in each case**Remedy ?**• Manually identify one “model” • Automate transfer of marker identities from model to each new “subject”**Robust Correspondence**Problem: • Two point sets (model and subject) • Same cardinality • Differently scaled • Similar but non-identical poses How do the sets correspond? Can’t use rigid transformation foralignment**Robust Correspondence**Idea: • Bottom to top ordering • Left to right ordering Formalise: • Binary space partition tree • partition strategy**The k-d tree**• 1975 J. L. Bentley. Multidimensional binary search trees used for associative searching. Communications of the ACM, 18:509–517. Reference:**The similarity k-d tree**• partition (dynamically) at biggest projected gap • gives robustness • record partition cardinality • deals with translation and scaling Focus on two aspects for tree of model:**A 2D walk through**• Step 1 • construct the k-d tree for the manually identified model • once only**Z-projection**1 3 2 4 5 6 7 X-projection**Z-projection**1 1 3 2 4 5 6 7 X-projection 1**Z-projection**1 1 3 2 4 2 5 6 7 X-projection 2 1**Z-projection**1 1 3 2 3 4 2 5 6 7 X-projection 2 3 1**Z-projection**1 1 3 2 3 4 2 4 5 6 7 X-projection 2 3 1 4**Z-projection**1 1 3 2 3 4 2 4 5 5 6 7 X-projection 2 3 1 4 5**Z-projection**1 1 1 3 2 3 4 2 4 5 5 6 7 6 X-projection 2 6 3 1 4 5**Z-projection**1 1 1 3 2 3 4 2 4 5 5 6 7 6 7 X-projection 2 6 3 1 7 4 5**{1, 2, 3, 4, 5, 6, 7}**(z, 2) Z-projection 1 1 {6, 7} {1, 2, 3, 4, 5} 3 2 3 4 2 4 5 5 6 7 6 7 X-projection 2 6 3 1 7 4 5**(z, 2)**(z, 2) Z-projection 1 1 (x, 1) {6, 7} {1, 2, 3, 4, 5} {1, 2, 3, 4, 5} 3 2 3 4 2 4 6 7 5 5 6 7 6 7 X-projection 2 6 3 1 7 4 5**(z, 2)**(z, 2) Z-projection 1 1 (x, 1) (x, 1) {1, 2, 3, 4, 5} (x, 1) 3 2 3 4 2 4 6 6 7 7 2 {1, 3, 4, 5} 5 5 6 7 6 7 X-projection 2 6 3 1 7 4 5**(z, 2)**(z, 2) Z-projection 1 (x, 1) (x, 1) (x, 1) (x, 1) 3 2 4 6 6 7 7 2 2 {1, 3, 4, 5} (x, 3) 5 {1, 3, 5} 4 6 7 1 3 2 4 5 6 7 X-projection 2 6 3 1 7 4 5**(z, 2)**(z, 2) Z-projection 1 1 (x, 1) (x, 1) (x, 1) (x, 1) 3 2 3 4 2 4 6 6 7 7 2 2 (x, 3) (x, 3) 5 5 {1, 3, 5} (z, 1) 4 4 6 7 6 7 5 {1, 3} X-projection 2 6 3 1 7 4 5**(z, 2)**(z, 2) Z-projection 1 1 (x, 1) (x, 1) (x, 1) (x, 1) 3 2 3 4 2 4 6 6 7 7 2 2 (x, 3) (x, 3) 5 5 (z, 1) (z, 1) 4 4 6 7 6 7 5 5 {1, 3} (z, 1) X-projection 2 6 3 1 7 4 5 3 1**A 2D walk through**• Step 2 • Use the model k-d tree to set up the 1-1 correspondence between the model and a new subject (in a similar pose). • Same cardinality for model and subject**Given a new subject**similar pose to model, same marker protocol, what are the labels? Step 2**What is the correspondence between the labels in model and**new subject? 1 3 2 4 5 E D 6 7 F C B G A Step 2**The model tree contains “navigation” rules**Follow these to partition the subject of a similar pose Assign the labels from terminal partitions (z, 2) (x, 1) (x, 1) 6 7 2 (x, 3) (z, 1) 4 5 (z, 1) 3 1 Step 2**(z, 2)**(x, 1) (x, 1) E 6 7 2 (x, 3) D F (z, 1) 4 C B 5 (z, 1) 3 1 6 G 7 A**(z, 2)**(x, 1) (x, 1) E 6 7 2 (x, 3) D (z, 1) 4 C B 5 (z, 1) 6 7 3 1 2 F G A**(z, 2)**(x, 1) (x, 1) E 6 7 2 (x, 3) D 2 (z, 1) 4 C 5 (z, 1) 6 7 3 1 F 4 B G A**(z, 2)**(x, 1) (x, 1) E 6 7 2 (x, 3) D 2 (z, 1) 4 4 5 (z, 1) 6 7 3 1 F 5 C B G**(z, 2)**(x, 1) (x, 1) E 6 7 2 (x, 3) 2 (z, 1) 4 5 4 5 (z, 1) 6 7 3 1 1 D 3 F C B G A**(z, 2)**(x, 1) (x, 1) 1 E 6 7 2 (x, 3) D 3 2 F (z, 1) 4 5 C 4 B 5 (z, 1) 6 G 7 A 3 1**1**3 2 4 1 E 5 D 3 2 F 6 7 5 C 4 B 6 G 7 A Robust Correspondence**100 Points:**median

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