1. A Coherent Locomotion Engine Extrapolating Beyond Experimental Data SCA ’ 04 Speaker: Alvin Data: January 3, 2005

2. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data2 Outline Introduction Framework Results Evaluation Form Conclusions Future Works

3. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data3 Introduction Input: MoCap Output: Locomotion Animate characters of any size through high-level parameters. An on-line reactive method. Use PCA to reduce computation cost for Real-time.

4. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data4 Framework Normalize Motion Main PCA Motion Extrapolation Sub-PCA Level 1 Sub-PCA Level 2 Linear Square Fit Motion Generation

5. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data5 Input Data Record 5 subjects. (2 ♀ & 3 ♂ ) Walking speed from 3.0 km/h to 7.0 km/h. (Interval is 0.5 km/h) Running speed from 6.0 km/h to 12.0 km/h. (Interval is 1.0 km/h) Sequences are segmented into cycles. (2 steps, starting from right heel strike), and 4 of them are selected

6. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data6 Normalize Motion All 3D positions of motion vectors are divided by the leg length. [Murray67] Use frequency function to handle time warp. [InmanRT81]

7. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data7 Main PCA A motion can be represented by a set of joint angle vectors measured at regularly sampled intervals. Blending technique can be applied on various α, but not appropriate for motion extrapolation.

8. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data8 Motion Extrapolation Speed Radial Basis FunctionRadial Basis Function No motion get a zero weight. Undesired results due to the influence of other subjects examples. All example motions have to be classified by group of similarities (subject, type of locomotion) Allow a linear least square in a very low dimension.

9. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data9 Motion Extrapolation – Sub-PCA Level 1 Use simple clustering method to separate the different subjects. Coefficient vectors α grouped by subject are used to apply sub-PCA level 1.

10. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data10 Motion Extrapolation – Sub-PCA Level 1

11. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data11 Motion Extrapolation – Sub-PCA Level 2 Coefficient vectors β grouped by type of locomotion are used to apply sub-PCA level 2. Two sub-PCA level 2 are needed to avoid giving too much importance to the neutral posture.

12. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data12 Motion Extrapolation – Linear Square Fit Determine a relationship between a coefficient vector γ and its corresponding speed value. Find the approximation function by minimizing the sum of square distances.

13. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data13 Motion Extrapolation – Linear Square Fit

14. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data14 Motion Generation Speed (S) Type of Locomotion (T) Personification (p) Human Size (H) Transition After motions are normalized, cut into cycles, frame i for walking near frame i for running. Accord to T. Real-time

15. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data15 Results Data compression rate is 25. Preprocess spends 13 sec. New motion (100 frames) generation spends 1.5 ms. CPU 1.8 GHz

16. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data16 Results

17. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data17 Evaluation Form 論文簡報部份 完整性介紹 (4) 系統性介紹 (4) 表達能力 (3) 投影片製作 (3) 論文審閱部分 瞭解論文內容 (4) 結果正確性與完整性 (4) 原創性與重要性 (4) 讀後啟發與應用： We can use PCA to reduce high-dimension motion data and extract the features of motions. Because the hierarchical structure of PCA can help the classification, so I will try to adapt it into my method. Besides, the description about motion represented as motion vector can be referenced in my paper.

18. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data18 Conclusions Experimental data classification Space and time normalization Generate locomotion sequences at each parameter update. Real-time Allow quantitative extrapolation.

19. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data19 Future Works Motion Prediction CD for the foot Jump over an obstacle or walk around it RBF can be added to linear fitting. Apply to other locomotion types.

20. Alivn/GAME Lab./CSIE/NDHU A Coherent Locomotion Engine Extrapolating Beyond Experimental Data20 Radial Basis Function A linear combination of translates of basis functions, the basis functions being invariant with respect to rotations on the underlying space.