| | <Poster Width="1735" Height="1227"> |
| | <Panel left="20" right="186" width="333" height="181"> |
| | <Text>PROBLEM STATEMENT</Text> |
| | <Text>Given partial 2D or 3D trajectories of the</Text> |
| | <Text>motion of a uniformly colored bouncing</Text> |
| | <Text>ball, that is viewed by a single or multi-</Text> |
| | <Text>ple cameras, estimate its full 3D state,</Text> |
| | <Text>over time, i.e. location, orientation, an-</Text> |
| | <Text>gular and linear velocities.</Text> |
| | </Panel> |
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| | <Panel left="22" right="373" width="330" height="138"> |
| | <Text>MOTIVATION</Text> |
| | <Text>Scene understanding can benefit from</Text> |
| | <Text>exploiting the fact that a dynamic scene</Text> |
| | <Text>and its visual observations are invariably</Text> |
| | <Text>determined by the laws of physics.</Text> |
| | </Panel> |
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| | <Panel left="23" right="512" width="328" height="233"> |
| | <Text>MAIN IDEA</Text> |
| | <Text>• Model the physics of the scene using</Text> |
| | <Text>physics-based simulation</Text> |
| | <Text>• Acquire visual observations</Text> |
| | <Text>• Define an objective function that con-</Text> |
| | <Text>nects the model to the observations</Text> |
| | <Text>• Produce physically plausible interpre-</Text> |
| | <Text>tations of the scene by performing</Text> |
| | <Text>black-box optimization</Text> |
| | </Panel> |
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| | <Panel left="359" right="188" width="673" height="552"> |
| | <Text>PHYSICS BASED SIMULATION</Text> |
| | <Text>(A) Dynamics of a bouncing ball</Text> |
| | <Text>The bouncing ball is affected by gravity</Text> |
| | <Text>and air resistance while in flight and fric-</Text> |
| | <Text>tion while in bounce with a surface.</Text> |
| | <Figure left="374" right="344" width="293" height="133" no="1" OriWidth="0.516744" OriHeight="0.144003 |
| | " /> |
| | <Text>(B) Equations of motion</Text> |
| | <Text>We assume standard equations of mo-</Text> |
| | <Text>tion for the flight phase and add air re-</Text> |
| | <Text>sistance. We derive equations for the</Text> |
| | <Text>bounce phase by extending [1].</Text> |
| | <Text>(C) Simulation of a bouncing ball</Text> |
| | <Text>We define a parameterized ball throwing simulation process S that:</Text> |
| | <Text>• receives a 21-D vector of scene properties and initial conditions</Text> |
| | <Text>• at each point in time, produces a 12-D vector of location, orientation, linear and</Text> |
| | <Text>angular velocities</Text> |
| | <Text>• is implemented by augmenting the Newton Game Dynamics simulator with our</Text> |
| | <Text>physics modeling</Text> |
| | <Text>• performs at 500fps, but is sub-sampled to real acquisition rate (30fps), in order to</Text> |
| | <Text>account for aliasing effects</Text> |
| | </Panel> |
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| | <Panel left="1040" right="188" width="669" height="314"> |
| | <Text>PHYSICALLY PLAUSIBLE SCENE INTERPRETATION</Text> |
| | <Text>We estimate the physically plausible explanation e of the observed scene by formu-</Text> |
| | <Text>lating an optimization problem, where:</Text> |
| | <Text>• the hypothesis space of x is defined over the domain of simulation process S</Text> |
| | <Text>• the observation data o are trajectories of a bouncing ball</Text> |
| | <Text>(potentially partial, 3D or 2D, from single or multiple cameras)</Text> |
| | <Text>• the objective function quantifies the discrepancy between the result of an invocation</Text> |
| | <Text>to S and the observations</Text> |
| | <Text>• the objective function is optimized by means of Differential Evolution [5]</Text> |
| | </Panel> |
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| | <Panel left="1040" right="507" width="668" height="229"> |
| | <Text>CONTRIBUTIONS</Text> |
| | <Text>• First method to consider attributes of state that can only be estimated through</Text> |
| | <Text>physics-based simulation</Text> |
| | <Text>• Extension to existing work [2–4] in exploiting physics based simulation in vision</Text> |
| | <Text>• Proposal of an effective method that is clear, generic, top-down, simulation based</Text> |
| | <Text>• Incorporation of realistic physics</Text> |
| | <Text>• Selected generic and modular components allow for extension to other broader or</Text> |
| | <Text>different contexts</Text> |
| | </Panel> |
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| | <Panel left="20" right="752" width="1348" height="376"> |
| | <Text>EXPERIMENTAL RESULTS</Text> |
| | <Text>(A) Multiview estimation of 3D trajectories</Text> |
| | <Text>(synthetic/real)</Text> |
| | <Figure left="29" right="859" width="385" height="255" no="2" OriWidth="0.605658" OriHeight="0.156226 |
| | " /> |
| | <Text>(B) Single view estimation of 3D trajectories</Text> |
| | <Text>Finding ball throwing simulations that optimally repro-</Text> |
| | <Text>duce 2D observations.</Text> |
| | <Figure left="492" right="895" width="204" height="154" no="3" OriWidth="0.251155" OriHeight="0.124905 |
| | " /> |
| | <Figure left="701" right="876" width="199" height="173" no="4" OriWidth="0.277136" OriHeight="0.166921 |
| | " /> |
| | <Text>(C) Seeing the “invisible”</Text> |
| | <Text>Implicit information, like the state of the ball while</Text> |
| | <Text>occluded (left) and the angular components of its 3D</Text> |
| | <Text>state (right), are computer based on a single camera.</Text> |
| | <Figure left="955" right="921" width="199" height="151" no="5" OriWidth="0.256351" OriHeight="0.127578 |
| | " /> |
| | <Figure left="1161" right="929" width="202" height="142" no="6" OriWidth="0.301963" OriHeight="0.139801 |
| | " /> |
| | </Panel> |
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| | <Panel left="1377" right="753" width="333" height="369"> |
| | <Text>KEY REFERENCES</Text> |
| | <Text>[1] P.J. Aston and R. Shail. The Dynamics of a Bouncing</Text> |
| | <Text>Superball with Spin. Dynamical Systems, 22(3):291–</Text> |
| | <Text>322, 2007.</Text> |
| | <Text>[2] K. Bhat, S. Seitz, J. Popovi´c, and P. Khosla. Com-</Text> |
| | <Text>puting the Physical Parameters of Rigid-body Motion</Text> |
| | <Text>from Video. In ECCV 2002, pages 551–565. Springer,</Text> |
| | <Text>2002.</Text> |
| | <Text>[3] D.J. Duff, J. Wyatt, and R. Stolkin. Motion Estimation</Text> |
| | <Text>using Physical Simulation. In IEEE International Con-</Text> |
| | <Text>ference on Robotics and Automation (ICRA), pages</Text> |
| | <Text>1511–1517. IEEE, 2010.</Text> |
| | <Text>[4] D. Metaxas and D. Terzopoulos. Shape and Nonrigid</Text> |
| | <Text>Motion Estimation through Physics-based Synthesis.</Text> |
| | <Text>IEEE Transactions on Pattern Analysis and Machine</Text> |
| | <Text>Intelligence, 15(6):580–591, 1993.</Text> |
| | <Text>[5] R. Storn and K. Price. Differential Evolution–A Sim-</Text> |
| | <Text>ple and Efficient Heuristic for Global Optimization over</Text> |
| | <Text>Continuous Spaces. Journal of Global Optimization,</Text> |
| | <Text>11(4):341–359, 1997.</Text> |
| | </Panel> |
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| | <Panel left="22" right="1129" width="1686" height="86"> |
| | <Text>MORE INFORMATION</Text> |
| | <Text>For more information, visit http://www.ics.forth.gr/ kyriazis/?e=1 or contact {kyriazis,oikonom,argyros}@ics.forth.gr</Text> |
| | <Text>This work was partially supported by the</Text> |
| | <Text>IST-FP7-IP-215821 project GRASP</Text> |
| | <Figure left="1602" right="1172" width="78" height="44" no="7" OriWidth="0" OriHeight="0 |
| | " /> |
| | </Panel> |
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| | </Poster> |
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