Phil Palmer

Detection and Tracking of Very Small Low Contrast Objects

We present a Kalman tracking algorithm that can track a number of very small, low contrast objects through an image sequence taken from a static camera. The issues that we have addressed to achieve this are twofold. Firstly, the detection of small objects comprising a few pixels only, moving slowly in the image, and secondly, tracking of multiple small targets even though they may be lost either through occlusion or in noisy signal. The approach uses a combination of wavelet filtering for detection with an interest operator for testing multiple target hypotheses based within the framework of a Kalman tracker. We demonstrate the robustness of the approach to occlusion and for multiple targets.

A Performance Measure for Boundary Detection Algorithms

In this paper we discuss the issues involved when trying to compare the performance of algorithms which seek to find boundaries and boundary models between regions of differing mean gray-level value. The usefulness of such measures is not confined to comparing different approaches, but provides an important step to building self-optimizing vision systems that automatically adjust algorithm parameters at each level of the system to improve performance. We discuss the issues that such a performance measure should address, and then present a theoretical framework for the performance measure we proposed. We demonstrate the power of the measure by characterizing the performance of a three-stage medium level vision system for detecting straight line boundaries. Both synthetic imagery, for which ground truth is known, and real imagery are used to test the ability of the criterion to characterize the output of the system.

Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite

The challenging problem of controlling the attitude of satellites subject to actuator failures has been the subject of increased attention in recent years. The problem of controlling the attitude of a satellite on all three axes with two reaction wheels is addressed in this paper. This system is controllable in a zero-momentum mode. Three-axis attitude stability is proven by imposing a singular quaternion feedback law to the angular velocity trajectories.Two approaches are proposed and compared to achieve three-axis control: The first one does not require angular velocity measurements and is based on the assumption of a perfect zero momentum, while the second approach consists of tracking the desired angular velocity trajectories. The full-state feedback is a nonlinear singular controller. In-orbit tests of the first approach provide an unprecedented practical proof of three-axis stability with two control torques. The angular velocity tracking approach is shown to be less efficient using the nonlinear singular controller. However, when inverse optimization theory is applied to enhance the nonlinear singular controller, the angular velocity tracking approach is shown to be the most efficient. The resulting switched inverse optimal controller allows for a significant enhancement of settling time, for a prescribed level of the integrated torque.

Optimal Relocation of Satellites Flying in Near-Circular-Orbit Formations

In this paper we present a general analytic formulation for optimal transfer paths for satellites flying in formation based upon the circular Hills problem. Optimization is performed to minimize the transfer energy required from the thruster. We consider the optimization problem as the choice of trajectory the satellite should follow during the maneuver, whereas the time taken is fixed as are the boundary conditions. We show that this optimal control problem has simple analytic solutions that provide a powerful basis from which to develop formation control strategies. In formation flying, maneuvers require low levels of thrust, and we assume that the thruster will be firing throughout the maneuver and the optimization scheme solves for the magnitude and direction of thrust as functions of time. We illustrate how we can exploit these analytic results and present examples of maneuvers using them. We also present a discussion of a docking problem, where we reverse the analysis and solve for initial conditions fixing the thruster characteristics in the optimal solutions found. Finally, we present a discussion of how we might exploit the natural dynamics to gain further propellant savings by adjusting the boundary conditions. This is illustrated by considering a cross-track maneuver for plane change.

An optimizing line finder using a Hough transform algorithm

In this paper we present an optimization algorithm for locating peaks in the accumulator of the Hough algorithm with robust voting kernel. We present a detailed discussion of the accuracy that can be achieved by locating these peaks in the accumulator, and show that the error bounds on the estimates of line parameters are always within those based upon least squares. This arises from the robust nature of the voting kernel. We describe the optimization algorithm in some detail since the shape of the peaks in the standard parameter space for straight lines are sinusoidal ridges. Standard approaches therefore fail, but the method described is shown to be robust from the experimental results presented. Some discussion of post-processing is also made, in which the shortcomings of standard Hough techniques, splitting long lines across parameter bins, can be remedied. We also discuss the use of a confidence measure in the line parameters based upon the value of the accumulator, and show that this is related to the mean squared distance from the line of the edge pixels associated with it. Finally, we present results produced by this optimizing Hough technique on a disparate set of images, with various application areas in mind, to demonstrate the versatility of the method and the accuracy that can be achieved at little computational overhead.

Using focus of attention with the hough transform for accurate line parameter estimation

Abstract In this paper we describe a Hough transform algorithm for finding lines in an image that can have an order of magnitude denser sampling in both parameters of the parameter space without significant increase in required memory or overhead in CPU time. By increasing the sampling density we determine the line parameters for each line segment much more accurately. The method circumvents the problems of requiring large amounts of memory to store the accumulator array, and is not significantly slower than other Hough algorithms by using a focus of attention approach. We illustrate the benefits that can be obtained on a wide variety of images, and quantify the improvements in line parameter estimation by performing statistical tests. We also discuss the benefits that can be obtained by algorithms attempting to locate higher level features in the image, and determining the 3D model of the image scene.

Reconstruction of scene models from sparse 3D structure

In this paper we present a geometric theory for reconstruction of surface models from sparse 3D data captured from N camera views which are consistent with the data visibility. Sparse 3D measurements of real scenes are readily estimated from image sequences using structure-from-motion techniques. Currently there is no general method for reconstruction of 3D models of arbitrary scenes from sparse data. We introduce an algorithm for recursive integration of sparse 3D structure to obtain a consistent model. This algorithm is shown to converge to the real scene structure as the number of views increases and to have a computational cost which is linear in the number of views. Results are presented for real and synthetic image sequences which demonstrate correct reconstruction for scenes containing significant occlusions.

Locating boundaries of textured regions

The authors introduce the concept of free angle to locate boundaries of textured regions in grey-level images. Using this with methods of mathematical morphology, the authors demonstrate that boundaries of all textured regions in remotely sensed images ran be located accurately.

Analytic Model Predictive Controller for Collision-Free Relative Motion Reconfiguration

Large formations of satellites currently require extensive ground-based planning to enable formation-wide collision-free reconfiguration. Allowing satellite formations the flexibility to execute collision-free reconfiguration operations onboard each spacecraft can significantly reduce the ground operations burden and increase the responsiveness of the formation to reconfiguration events. An analytic model predictive controller for fuelminimized, collision-free trajectory following is developed. The controller exploits the natural dynamics for relativemotion path-following using minimal fuel and requires a minimal computational burden. Constraints are handled implicitly and performance provides 423 times the fuel savings compared with traditional proportional-integralderivative-type control at the same computational speed. Through hardware testing and comparison with other approaches, results also show that constraints can also be handled explicitly while still performing significantly faster than similar forms of model predictive control for formation reconfiguration.

Simple derivation of Symplectic Integrators with First Order Correctors

In this paper we consider almost integrable systems for which we show that there is a direct connection between symplectic methods and conventional numerical integration schemes. This enables us to construct several symplectic schemes of varying order. We further show that the symplectic correctors, which formally remove all errors of first order in the perturbation, are directly related to the Euler—McLaurin summation formula. Thus we can construct correctors for these higher order symplectic schemes. Using this formalism we derive the Wisdom—Holman midpoint scheme with corrector and correctors for higher order schemes. We then show that for the same amount of computation we can devise a scheme which is of order O(εh6) + (ε2h2), where ε is the order of perturbation and h the stepsize. Inclusion of a modified potential further reduces the error to O(εh6) + (ε2h4).