scholarly journals Symmetry and reduction in collectives: cyclic pursuit strategies

2013 ◽  
Vol 469 (2158) ◽  
pp. 20130264 ◽  
Author(s):  
Kevin S. Galloway ◽  
Eric W. Justh ◽  
P. S. Krishnaprasad
Keyword(s):  
Invariant Manifold ◽  
Collective Motion ◽  
Shape Space ◽  
Relative Equilibria ◽  
Loop Dynamics ◽  
Cyclic Pursuit ◽  
Special Solutions ◽  
Feedback Laws ◽  
Low Dimensional ◽  
Joint Shape

We specify and analyse models that capture the geometry of purposeful motion of a collective of mobile agents, with a focus on planar motion, dyadic strategies and attention graphs which are static, directed and cyclic. Strategies are formulated as constraints on joint shape space and are implemented through feedback laws for the actions of individual agents, here modelled as self-steering particles. By reduction to a labelled shape space (using a redundant parametrization to account for cycle closure constraints) and a further reduction through time rescaling, we characterize various special solutions (relative equilibria and pure shape equilibria) for cyclic pursuit with a constant bearing (CB) strategy. This is accomplished by first proving convergence of the (nonlinear) dynamics to an invariant manifold (the CB pursuit manifold), and then analysing the closed-loop dynamics restricted to the invariant manifold. For illustration, we sketch some low-dimensional examples. This formulation—involving strategies, attention graphs and sensor-driven steering laws—and the resulting templates of collective motion, are part of a broader programme to interpret the mechanisms underlying biological collective motion.

scholarly journals Symmetry and reduction in collectives: low-dimensional cyclic pursuit

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160465 ◽  
Author(s):  
Kevin S. Galloway ◽  
Eric W. Justh ◽  
P. S. Krishnaprasad
Keyword(s):  
Closed Loop ◽  
Physical Space ◽  
Relative Equilibria ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Control Schemes ◽  
Loop Dynamics ◽  
Cyclic Pursuit ◽  
Steering Law ◽  
Low Dimensional

We investigate low-dimensional examples of cyclic pursuit in a collective, wherein each agent employs a constant bearing (CB) steering law relative to exactly one other agent. For the case of three agents in the plane, we characterize relative equilibria and pure shape equilibria of associated closed-loop dynamics. Re-scaling time yields a reduction of phase space to two dimensions and effective tools for stability analysis. Study of bifurcation of a family of collinear equilibria dependent on a single CB control parameter reveals the presence of a rich collection of trajectories that are periodic in shape and undergo precession in physical space. For collectives in three dimensions, with an appropriate notion of CB pursuit strategy and corresponding steering law, the two-agent case proves to be explicitly integrable. These results suggest control schemes for small teams of mobile robotic agents engaged in area coverage tasks such as search and rescue, and raise interesting possibilities for behaviour in biological contexts.

scholarly journals Collective motion under beacon-referenced cyclic pursuit

Automatica ◽  
2018 ◽  
Vol 91 ◽  
pp. 17-26 ◽  
Author(s):  
Kevin S. Galloway ◽  
Biswadip Dey
Keyword(s):  
Collective Motion ◽  
Cyclic Pursuit

scholarly journals Adaptive Shape Kernel-Based Mean Shift Tracker in Robot Vision System

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Chunmei Liu ◽  
Yirui Wang ◽  
Shangce Gao
Keyword(s):  
Manifold Learning ◽  
Vision System ◽  
Mean Shift ◽  
Robot Vision ◽  
Shape Space ◽  
Training Data ◽  
Learning Technique ◽  
Adaptive Kernel ◽  
Dimensional Shape ◽  
Low Dimensional

This paper proposes an adaptive shape kernel-based mean shift tracker using a single static camera for the robot vision system. The question that we address in this paper is how to construct such a kernel shape that is adaptive to the object shape. We perform nonlinear manifold learning technique to obtain the low-dimensional shape space which is trained by training data with the same view as the tracking video. The proposed kernel searches the shape in the low-dimensional shape space obtained by nonlinear manifold learning technique and constructs the adaptive kernel shape in the high-dimensional shape space. It can improve mean shift tracker performance to track object position and object contour and avoid the background clutter. In the experimental part, we take the walking human as example to validate that our method is accurate and robust to track human position and describe human contour.

Statistical Approach to Shape from Shading: Reconstruction of Three-Dimensional Face Surfaces from Single Two-Dimensional Images

1996 ◽  
Vol 8 (6) ◽  
pp. 1321-1340 ◽  
Author(s):  
Joseph J. Atick ◽  
Paul A. Griffin ◽  
A. Norman Redlich
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Practical Interest ◽  
Principal Component ◽  
Shape From Shading ◽  
Shape Space ◽  
Two Dimensional ◽  
Two Dimensional Image ◽  
Low Dimensional ◽  
Dimensional Object

The human visual system is proficient in perceiving three-dimensional shape from the shading patterns in a two-dimensional image. How it does this is not well understood and continues to be a question of fundamental and practical interest. In this paper we present a new quantitative approach to shape-from-shading that may provide some answers. We suggest that the brain, through evolution or prior experience, has discovered that objects can be classified into lower-dimensional object-classes as to their shape. Extraction of shape from shading is then equivalent to the much simpler problem of parameter estimation in a low-dimensional space. We carry out this proposal for an important class of three-dimensional (3D) objects: human heads. From an ensemble of several hundred laser-scanned 3D heads, we use principal component analysis to derive a low-dimensional parameterization of head shape space. An algorithm for solving shape-from-shading using this representation is presented. It works well even on real images where it is able to recover the 3D surface for a given person, maintaining facial detail and identity, from a single 2D image of his face. This algorithm has applications in face recognition and animation.

scholarly journals Optimality, reduction and collective motion

2015 ◽  
Vol 471 (2177) ◽  
pp. 20140606 ◽  
Author(s):  
Eric W. Justh ◽  
P. S. Krishnaprasad
Keyword(s):  
Collective Motion ◽  
Optimal Control Problems ◽  
Coupling Parameter ◽  
Rigid Motion ◽  
Particle Model ◽  
Explicit Integration ◽  
Hidden Symmetry ◽  
Necessary Conditions For Optimality ◽  
Special Solutions ◽  
Optimality Principles

The planar self-steering particle model of agents in a collective gives rise to dynamics on the N -fold direct product of SE (2), the rigid motion group in the plane. Assuming a connected, undirected graph of interaction between agents, we pose a family of symmetric optimal control problems with a coupling parameter capturing the strength of interactions. The Hamiltonian system associated with the necessary conditions for optimality is reducible to a Lie–Poisson dynamical system possessing interesting structure. In particular, the strong coupling limit reveals additional (hidden) symmetry, beyond the manifest one used in reduction: this enables explicit integration of the dynamics, and demonstrates the presence of a ‘master clock’ that governs all agents to steer identically. For finite coupling strength, we show that special solutions exist with steering controls proportional across the collective. These results suggest that optimality principles may provide a framework for understanding imitative behaviours observed in certain animal aggregations.

scholarly journals An effective model for quantification of cell 3Dshape in early embryogenesis

2021 ◽  
Author(s):  
Zelin Li ◽  
Jianfeng Cao ◽  
Zhongying Zhao ◽  
Hong Yan
Keyword(s):  
Cell Fate ◽  
Cell Shape ◽  
Developmental Process ◽  
Morphological Changes ◽  
Shape Space ◽  
Effective Model ◽  
Cell Stage ◽  
Cell Shapes ◽  
Dimensional Shape ◽  
Low Dimensional

Abstract Background: The developmental process is featured by fabulous morphogenesis in multicellular organisms. Describing morphological changes quantitatively concretes the way to investigating both intra and inter cell regulations on cell fate. While Caenorhabditis elegans has been used as a model for cell and development studies for a long time, the exploration of how cell shape is precisely controlled keeps obscured by the lack of methods to model morphological features. Currently, in order to characterize the features of cell shape involved in cell migration and differentiation, there is an increasing demand in analyzing cell shape systematically, especially when many works have contributed to cell reconstruction. Results: In this work, Spherical harmonics and Principal component analysis integrated Cell Shape quantification Models (SPCSMs) is proposed to represent cell shapes in a low-dimensional shape space. SPCSMs incorporates a complete pipeline to quantify cell shapes and analyze their morphological phenotypes in three dimensional (3D) reconstructions. Based on the framework, we extract biological patterns in the lineage of C. elegans embryo before 350-cell stage, during which all hypodermis cells deformed like a funnel and can be recognized by this shape pattern. Finally, SPCSMs is compared with two cell shape representation methods, which substantiates the effectiveness and robustness of our method. Conclusion: SPCSMs provides a general method to decribe shapes in low-dimensional shape space with compact parameters. It can quantify the shapes of cells from single-cell resolution images obtained over one-minute intervals, making it possible for the recognition of developmental patterns in cell lineages. SPCSMs is expected to be an effective model for biologists to explore the relationships between the shapes of cells and their fates.

Representation is representation of similarities

1998 ◽  
Vol 21 (4) ◽  
pp. 449-467 ◽  
Author(s):  
Shimon Edelman
Keyword(s):  
Internal Representation ◽  
Shape Space ◽  
Perceived Similarity ◽  
Unified Approach ◽  
Reference Shape ◽  
Order Isomorphisms ◽  
The World ◽  
Low Dimensional ◽  
Perceptual Systems ◽  
Basic Level

Advanced perceptual systems are faced with the problem of securing a principled (ideally, veridical) relationship between the world and its internal representation. I propose a unified approach to visual representation, addressing the need for superordinate and basic-level categorization and for the identification of specific instances of familiar categories. According to the proposed theory, a shape is represented internally by the responses of a small number of tuned modules, each broadly selective for some reference shape, whose similarity to the stimulus it measures. This amounts to embedding the stimulus in a low-dimensional proximal shape space spanned by the outputs of the active modules. This shape space supports representations of distal shape similarities that are veridical as Shepard's (1968) second-order isomorphisms (i.e., correspondence between distal and proximal similarities among shapes, rather than between distal shapes and their proximal representations). Representation in terms of similarities to reference shapes supports processing (e.g., discrimination) of shapes that are radically different from the reference ones, without the need for the computationally problematic decomposition into parts required by other theories. Furthermore, a general expression for similarity between two stimuli, based on comparisons to reference shapes, can be used to derive models of perceived similarity ranging from continuous, symmetric, and hierarchical ones, as in multidimensional scaling (Shepard 1980), to discrete and nonhierarchical ones, as in the general contrast models (Shepard & Arabie 1979; Tversky 1977).

scholarly journals A collective motion description of tubulin βT7 loop dynamics

2019 ◽  
Vol 16 (0) ◽  
pp. 264-273
Author(s):  
Sarbani Chattopadhyaya ◽  
Debamitra Chakravorty ◽  
Gautam Basu
Keyword(s):  
Collective Motion ◽  
Loop Dynamics

scholarly journals Joint modeling of cell and nuclear shape variation

2015 ◽  
Vol 26 (22) ◽  
pp. 4046-4056 ◽  
Author(s):  
Gregory R. Johnson ◽  
Taraz E. Buck ◽  
Devin P. Sullivan ◽  
Gustavo K. Rohde ◽  
Robert F. Murphy
Keyword(s):  
Cell Biology ◽  
Cell Shape ◽  
Computational Cost ◽  
Three Dimensional ◽  
Joint Modeling ◽  
Shape Space ◽  
Nuclear Shape ◽  
Shape Variation ◽  
Shape Spaces ◽  
Low Dimensional

Modeling cell shape variation is critical to our understanding of cell biology. Previous work has demonstrated the utility of nonrigid image registration methods for the construction of nonparametric nuclear shape models in which pairwise deformation distances are measured between all shapes and are embedded into a low-dimensional shape space. Using these methods, we explore the relationship between cell shape and nuclear shape. We find that these are frequently dependent on each other and use this as the motivation for the development of combined cell and nuclear shape space models, extending nonparametric cell representations to multiple-component three-dimensional cellular shapes and identifying modes of joint shape variation. We learn a first-order dynamics model to predict cell and nuclear shapes, given shapes at a previous time point. We use this to determine the effects of endogenous protein tags or drugs on the shape dynamics of cell lines and show that tagged C1QBP reduces the correlation between cell and nuclear shape. To reduce the computational cost of learning these models, we demonstrate the ability to reconstruct shape spaces using a fraction of computed pairwise distances. The open-source tools provide a powerful basis for future studies of the molecular basis of cell organization.

scholarly journals Automatic Sex Determination of Skulls Based on a Statistical Shape Model

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Li Luo ◽  
Mengyang Wang ◽  
Yun Tian ◽  
Fuqing Duan ◽  
Zhongke Wu ◽  
...  
Keyword(s):  
Sex Determination ◽  
Visual Analysis ◽  
Shape Space ◽  
Statistical Shape Model ◽  
Fisher Discriminant Analysis ◽  
Shape Model ◽  
Discriminant Model ◽  
Statistical Shape ◽  
Low Dimensional ◽  
Leave One Out

Sex determination from skeletons is an important research subject in forensic medicine. Previous skeletal sex assessments are through subjective visual analysis by anthropologists or metric analysis of sexually dimorphic features. In this work, we present an automatic sex determination method for 3D digital skulls, in which a statistical shape model for skulls is constructed, which projects the high-dimensional skull data into a low-dimensional shape space, and Fisher discriminant analysis is used to classify skulls in the shape space. This method combines the advantages of metrical and morphological methods. It is easy to use without professional qualification and tedious manual measurement. With a group of Chinese skulls including 127 males and 81 females, we choose 92 males and 58 females to establish the discriminant model and validate the model with the other skulls. The correct rate is 95.7% and 91.4% for females and males, respectively. Leave-one-out test also shows that the method has a high accuracy.

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