Geodesic
Introducing the interaction distance in the context of distance geometry for human motions
Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 273-283.

Voir la notice de l'article provenant de la source Math-Net.Ru

The dynamical Distance Geometry Problem (dynDGP) is a recently introduced subclass of the distance geometry where problems have a dynamical component. The graphs $$G=(V \times T,E,\{\delta,\pi\})$$ of dynDGPs have a vertex set that is the set product of two sets: the set $V$, containing the objects to animate, and the set $T$, representing the time. In this article, the focus is given to special instances of the dynDGP that are used to represent human motion adaptation problems, where the set $V$ admits a skeletal structure $(S,\chi)$. The “interaction distance” is introduced as a possible replacement of the Euclidean distance which is able to capture the information about the dynamics of the problem, and some initial properties of this new distance are presented.
Keywords: dynamical distance geometry, interaction distance, human motion adaptation, retargeting, animated skeletal structures, symmetric quasi-distance. 
@article{CHEB_2019_20_2_a20,
     author = {A. Mucherino},
     title = {Introducing the interaction distance in the context of distance geometry for human motions},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {273--283},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a20/}
}
TY  - JOUR
AU  - A. Mucherino
TI  - Introducing the interaction distance in the context of distance geometry for human motions
JO  - Čebyševskij sbornik
PY  - 2019
SP  - 273
EP  - 283
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a20/
LA  - en
ID  - CHEB_2019_20_2_a20
ER  - 
%0 Journal Article
%A A. Mucherino
%T Introducing the interaction distance in the context of distance geometry for human motions
%J Čebyševskij sbornik
%D 2019
%P 273-283
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a20/
%G en
%F CHEB_2019_20_2_a20
A. Mucherino. Introducing the interaction distance in the context of distance geometry for human motions. Čebyševskij sbornik, Tome 20 (2019) no. 2, pp. 273-283. http://geodesic.mathdoc.fr/item/CHEB_2019_20_2_a20/

[1] A. Y. Alfakih, “On Dimensional Rigidity of Bar-and-Joint Frameworks”, Discrete Applied Mathematics, 155:10 (2007), 1244–1253 | MR | Zbl

[2] A. Bernardin, L. Hoyet, A. Mucherino, D. S. Gonçalves, F. Multon, “Normalized Euclidean Distance Matrices for Human Motion Retargeting”, MIG17 (Barcelona, Spain, November 2017), ACM Conference Proceedings, Motion in Games 2017, 2017

[3] K. J. Choi, H. S. Ko, “Online Motion Retargetting”, The Journal of Visualization and Computer Animation, 11:5 (2000), 223–235 | Zbl

[4] G. M. Crippen, “An Alternative Approach to Distance Geometry using $L^\infty$ Distances”, Discrete Applied Mathematics, 197 (2015), 20–26 | MR | Zbl

[5] J. E. Cutting, P. M. Vishton, P. A. Braren, “How We Avoid Collisions With Stationary and Moving Objects”, Psychological Review, 102:4 (1995), 627–651

[6] M. M. Deza, E. Deza, Encyclopedia of Distances, Springer, 2016, 756 pp. | MR | Zbl

[7] B. Erdmann, Reflexionen Kants zur Kritischen Philosophie, v. II, Reflexionen Kants zur Kritik der Reinen Vernunft, aus Kants Handschriftlichen Aufzeichnungen, Fues's Verlag, Leipzig, 1884

[8] M. Gleicher, “Retargetting Motion to New Characters”, ACM Proceedings of the $25^{th}$ annual conference on Computer Graphics and Interactive Techniques, 1998, 33–42

[9] W. Glunt, T. L. Hayden, M. Raydan, “Molecular Conformations from Distance Matrices”, Journal of Computational Chemistry, 14:1 (1993), 114–120

[10] E. S. L Ho, T. Komura, C-L. Tai, “Spatial Relationship Preserving Character Motion Adaptation”, ACM Transactions on Graphics, 29:4, Proceedings of the $37^{th}$ International Conference and Exhibition on Computer Graphics and Interactive Techniques (2010), 8 pp.

[11] G. Laman, “On Graphs and Rigidity of Plane Skeletal Structures”, Journal of Engineering Mathematics, 4:4 (1970), 331–340 | MR | Zbl

[12] L. Liberti, C. Lavor, N. Maculan, A. Mucherino, “Euclidean Distance Geometry and Applications”, SIAM Review, 56:1 (2014), 3–69 | MR | Zbl

[13] L. Liberti, G. Swirszcz, C. Lavor, “Distance Geometry on the Sphere”, Proceedings of the Japanese Conference on Discrete and Computational Geometry and Graphs, JCDCGG15 (Kyoto, Japan, 2015), Lecture Notes in Computer Science, 9943, eds. J. Akiyama, H. Ito, T. Sakai, Y. Uno, 2015, 204–215 | MR

[14] M. Meredith, S. Maddock, Motion Capture File Formats Explained, Technical Report 211, Department of Computer Science, University of Sheffield, 2001, 36 pp.

[15] A. Mucherino, On the Discretization of Distance Geometry: Theory, Algorithms and Applications, HDR Monograph, University of Rennes 1. INRIA Hal archive id: tel-01846262, July 17, 2018

[16] A. Mucherino, D.S. Gonçalves, “An Approach to Dynamical Distance Geometry”, Proceedings of Geometric Science of Information, GSI17 (Paris, France, 2017), Lecture Notes in Computer Science, 10589, eds. F. Nielsen, F. Barbaresco, 2017, 821–829 | MR | Zbl

[17] A. Mucherino, D.S. Gonçalves, A. Bernardin, L. Hoyet, F. Multon, “A Distance-Based Approach for Human Posture Simulations”, Federated Conference on Computer Science and Information Systems (FedCSIS17), Workshop on Computational Optimization (WCO17) (Prague, Czech Republic, 2017), IEEE Conference Proceedings, 2017, 441–444

[18] A. Mucherino, C. Lavor, L. Liberti, “The Discretizable Distance Geometry Problem”, Optimization Letters, 6:8 (2012), 1671–1686 | MR | Zbl

[19] A. Mucherino, C. Lavor, L. Liberti, N. Maculan (eds.), Distance Geometry: Theory, Methods and Applications, Springer, 2013, 410 pages pp. | MR | Zbl

[20] A. Mucherino, J. Omer, L. Hoyet, P. Robuffo Giordano, F. Multon, “An Application-based Characterization of Dynamical Distance Geometry Problems”, Optimization Letters, Springer, 2019 (to appear) | MR

[21] F. Schwarzer, M. Saha, J-C. Latombe, “Exact Collision Checking of Robot Paths”, Algorithmic Foundations of Robotics V, Springer, 2004, 25–41

[22] J. Sivadjian, Le Temps. Étude Philosophique Physiologique et Psychologique, v. III, Le Problème Psychologique, Hermann C$^{\rm le}$, 1938