Optimal positioning of multiple cameras for object recognition using Cramer-Rao lower bound

Farshidi, F.; Sirouspour, Shahin; Kirubarajan, T.

doi:10.1109/robot.2006.1641829

Cited by 3 publications

(7 citation statements)

References 13 publications

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“…There have also been other algorithms for camera placement, for example a probabilistic approach for general sensor deployment based on the Cramér-Rao bound was proposed in [16], and an application of the idea for cameras was given in [17]. In [18] the authors choose to focus on positioning downward facing cameras, as opposed to arbitrarily oriented cameras.…”

Section: A Related Workmentioning

confidence: 99%

“…The first causes the robot to go up to take in a larger view, while the second causes it to go down to get a better view of what it already sees. The angular component (17) rotate the robot to get more of its field of view into the environment, while also rotating away from other robots whose field of view intersects its own. Computation of the gradient component for the rectangular field of view is of the same complexity as the circular case, and carries the same constraint on the communication topology.…”

Section: Theorem 3 (Rectangular Gradientmentioning

confidence: 99%

“…The robots (and their cameras) have three translational degrees of freedom and can rotate about their yaw axis. The controller equations from Algorithm 1 were computed with the gradient in (15), (16), and (17). The environment in this case is nonconvex.…”

Section: Simulationsmentioning

confidence: 99%

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Eyes in the Sky: Decentralized Control for the Deployment of Robotic Camera Networks

et al. 2011

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This paper presents a decentralized control strategy for positioning and orienting multiple robotic cameras to collectively monitor an environment. The cameras may have various degrees of mobility from six degrees of freedom, to one degree of freedom. The control strategy is proven to locally minimize a novel metric representing information loss over the environment. It can accommodate groups of cameras with heterogeneous degrees of mobility (e.g. some that only translate and some that only rotate), and is adaptive to robotic cameras being added or deleted from the group, and to changing environmental conditions. The robotic cameras share information for their controllers over a wireless network using a specially designed networking algorithm. The control strategy is demonstrated in repeated experiments with three flying quadrotor robots indoors, and with five flying quadrotor robots outdoors. Simulation results for more complex scenarios are also presented.

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Section: A Related Workmentioning

confidence: 99%

Section: Theorem 3 (Rectangular Gradientmentioning

confidence: 99%

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Eyes in the Sky: Decentralized Control for the Deployment of Robotic Camera Networks

et al. 2011

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“…It is important to note that in importance sampling, degeneracy is a common problem; wherein, after a few time instances, the density of the weights in (18) become skewed. The resampling step in (18) is crucial in limiting the effects of degeneracy. Finally using Algorithm 1., the particle representation of p(dx t |y 1:t ) and p(dx t+1 |y 1:t+1 ) are given bỹ…”

Section: B General Non-linear Ssmsmentioning

confidence: 99%

“…Some of the key practical applications of the PCRLB include: comparison of several nonlinear filters for ballistic target tracking [13]; terrain navigation [14]; and design of systems with pre-specified performance bounds [15]. The PCRLB is also widely used in several other areas related to: multi-sensor resource deployment (e.g., radar resource allocation [16], sonobuoy deployment in submarine tracking [17]); sensor positioning [18]; and optimal observer trajectory for bearings-only tracking [19], [20].…”

Section: Introductionmentioning

confidence: 99%

A Particle Filter Approach to Approximate Posterior Cramer-Rao Lower Bound: The Case of Hidden States

Tulsyan¹,

Huang²,

Gopaluni³

et al. 2014

IEEE Trans. Aerosp. Electron. Syst.

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The posterior Cramér-Rao lower bound (PCRLB) derived in [1] provides a bound on the mean square error (MSE) obtained with any non-linear state filter. Computing the PCRLB involves solving complex, multi-dimensional expectations, which do not lend themselves to an easy analytical solution. Furthermore, any attempt to approximate it using numerical or simulation based approaches require a priori access to the true states, which may not be available, except in simulations or in carefully designed experiments. To allow recursive approximation of the PCRLB when the states are hidden or unmeasured, a new approach based on sequential Monte-Carlo (SMC) or particle filters (PF) is proposed. The approach uses SMC methods to estimate the hidden states using a sequence of the available sensor measurements. The developed method is general and can be used to approximate the PCRLB in non-linear systems with non-Gaussian state and sensor noise. The efficacy of the developed method is illustrated on two simulation examples, including a practical problem of ballistic target tracking at re-entry phase.

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Optimal coverage for multiple hovering robots with downward facing cameras

Schwager¹,

Julian²,

Rus³

2009

2009 IEEE International Conference on Robotics and Automation

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This paper presents a distributed control strategy for deploying hovering robots with multiple downward facing cameras to collectively monitor an environment. Information per pixel is proposed as an optimization criterion for multicamera placement problems. This metric is used to derive a specific cost function for multiple downward facing cameras mounted on hovering robot platforms. The cost function leads to a gradient-based distributed controller for positioning the robots. A convergence proof using LaSalle's invariance principle is given to show that the robots converge to locally optimal positions. The controller is demonstrated in experiments with three flying quad-rotor robots.

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Optimal positioning of multiple cameras for object recognition using Cramer-Rao lower bound

Cited by 3 publications

References 13 publications

Eyes in the Sky: Decentralized Control for the Deployment of Robotic Camera Networks

Eyes in the Sky: Decentralized Control for the Deployment of Robotic Camera Networks

A Particle Filter Approach to Approximate Posterior Cramer-Rao Lower Bound: The Case of Hidden States

Optimal coverage for multiple hovering robots with downward facing cameras

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