An Approach to Dynamical Distance Geometry

Mucherino, Antonio; Gonçalves, Douglas

doi:10.1007/978-3-319-68445-1_94

Cited by 13 publications

(16 citation statements)

References 15 publications

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“…Once an approximated distance matrix is defined, the problem to be solved is a classical one in the context of distance geometry, where an EDM near to the approximated matrix needs to be identified, by revealing in this way the posture for the new skeletal structure. Our computational experiments show that the presented methodology is promising when the corresponding distance geometry problem is solved by using the non-monotone spectral gradient method proposed in [7] in the context of the dynamical distance geometry. Future works will mostly be aimed at improving and at performing a theoretical validation of the procedure detailed in Section II, as well as at extending the entire methodology to the simulation of motions.…”

Section: Discussionmentioning

confidence: 94%

“…This section shows the results obtained by constructing an approximated distance matrix by the method detailed in Section II, and by looking for the corresponding posture by implementing the spectral gradient method with non-monotone line search described in [7]. All codes were written in Matlab 2016b and the experiments were carried out on an Intel Core 2 Duo @ 2.4 GHz with 2GB RAM, running Mac OS X.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…Table I shows the list of short labels for all joints forming the skeletal structure, together with the original distances from the corresponding joint parents (bone lengths). Table II shows some preliminary experiments, where the parameters of the non-monotone spectral gradient method, are the same of the experiments presented in [7]. The distance matrix is generated by applying the procedure detailed in Section II.…”

Section: Computational Experimentsmentioning

confidence: 99%

See 2 more Smart Citations

A Distance-Based Approach for Human Posture Simulations

Mucherino¹,

Gonçalves²,

Bernardin³

et al. 2017

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

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Abstract-Human-like characters can be modeled by suitable skeletal structures, which basically consist in trees where edges represent bones and vertices are joints between two adjacent bones. Motion is then defined as variations of the joints' configuration (i.e., partial rotations) over time, which also influences joint positions. However, this representation does not allow to easily represent the relationship between joints that are not directly connected by a bone. This work is therefore based on the premise that variations of the relative distances between such joints are important to represent complex human motions. While the former representations are currently used in practice for playing and analyzing motions, the latter can help in modeling a new class of problems where the relationships in human motions need to be simulated. Our main interest in this work is in adapting previously captured human postures (one frame of a given motion) with the aim of satisfying a certain number of geometrical constraints, which turn out to be easily definable in terms of distances. We present a novel procedure for approximating the relative inter-joint distances for skeletal structures having arbitrary features and respecting a predefined posture. This set of inter-joint distances defines an instance of the Distance Geometry Problem (DGP), that we tackle with a non-monotone spectral gradient method.

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Section: Discussionmentioning

confidence: 94%

Section: Computational Experimentsmentioning

confidence: 99%

Section: Computational Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

A Distance-Based Approach for Human Posture Simulations

Mucherino¹,

Gonçalves²,

Bernardin³

et al. 2017

Proceedings of the 2017 Federated Conference on Computer Science and Information Systems

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“…Examples are action recognition from dynamic interjoint distance skeleton data [22] and more generally data structures for describing kinetic point sets [14]. Applications in multi-robot coordination, crowd simulations, and motion retargeting are explored in [23], [24], where the authors introduce the dynamical distance geometry problem (dynDGP). 1 Even in applications to proteins and molecules, the atoms move (for example, proteins fold) in specific ways [25].…”

Section: Introductionmentioning

confidence: 99%

Kinetic Euclidean Distance Matrices

Tabaghi

Vetterli

2020

IEEE Trans. Signal Process.

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Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize points from a snapshot of distances. If the objects move, one expects to do better by modeling the motion. In this paper, we introduce Kinetic Euclidean Distance Matrices (KEDMs)-a new kind of time-dependent distance matrices that incorporate motion. The entries of KEDMs become functions of time, the squared time-varying distances. We study two smooth trajectory models-polynomial and bandlimited trajectoriesand show that these trajectories can be reconstructed from incomplete, noisy distance observations, scattered over multiple time instants. Our main contribution is a semidefinite relaxation (SDR), inspired by SDRs for static EDMs. Similarly to the static case, the SDR is followed by a spectral factorization step; however, because spectral factorization of polynomial matrices is more challenging than for constant matrices, we propose a new factorization method that uses anchor measurements.Extensive numerical experiments show that KEDMs and the new semidefinite relaxation accurately reconstruct trajectories from noisy, incomplete distance data and that, in fact, motion improves rather than degrades localization if properly modeled. This makes KEDMs a promising tool for problems in geometry of dynamic points sets.

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“…Finally, given that an EDM is specific to the morphology of a given character, we propose a novel method to normalize EDMs to create a morphology-independent distancebased representation. We then demonstrate that these normalized EDMs can be efficiently combined with a new skeletal morphology to retarget motions using an existing Distance Geometry Problem (DGP) approach [Mucherino and Gonçalves 2017].…”

Section: Introductionmentioning

confidence: 99%

Normalized Euclidean distance matrices for human motion retargeting

Bernardin

Hoyet

Mucherino

et al. 2017

Proceedings of the Tenth International Conference on Motion in Games

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Figure 1: (a) Example pose where the actor's hands come to a close distance. The same pose retargeted on a skeleton with longer forearms by (b) simply transferring joint angles or (c) using our normalized Euclidean distance matrix approach. ABSTRACTIn character animation, it is often the case that motions created or captured on a specific morphology need to be reused on characters having a different morphology while maintaining specific relationships such as body contacts or spatial relationships between body parts. This process, called motion retargeting, requires determining which body part relationships are important in a given animation. This paper presents a novel frame-based approach to motion retargeting which relies on a normalized representation of body joints distances. We propose to abstract postures by computing all the inter-joint distances of each animation frame and store them in Euclidean Distance Matrices (EDMs). They 1) present the benefits of capturing all the subtle relationships between body parts, 2) can be adapted through a normalization process to create a morphologyindependent distance-based representation, and 3) can be used to efficiently compute retargeted joint positions best satisfying newly computed distances. We demonstrate that normalized EDMs can be efficiently applied to a different skeletal morphology by using a Distance Geometry Problem (DGP) approach, and present results on a selection of motions and skeletal morphologies. Our approach opens the door to a new formulation of motion retargeting problems, solely based on a normalized distance representation.ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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An Approach to Dynamical Distance Geometry

Cited by 13 publications

References 15 publications

A Distance-Based Approach for Human Posture Simulations

A Distance-Based Approach for Human Posture Simulations

Kinetic Euclidean Distance Matrices

Normalized Euclidean distance matrices for human motion retargeting

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