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Canonical decomposition of affine motion for visual servoing

We report both the theoretical development and experimental results of a visual servoing technique which makes use of canonical decomposition of the affine motion model in computer vision, to six one-parameter groups (2D translation, dilation, rotation and 2D affine shears). Because the canonical decomposition yields one-parameter basis groups, a localized form of correlation can be used to obtain measures of these 6 image deformations. In addition, since these basis functions obey the rules of quaternion algebra, they form an integrable representation of 2D motion, and are thereby compatible with methods of recursive estimation, such as Kalman filtering. Two principles of visual servoing are featured in the system which was developed to verify this model. The first is, that by nesting the perceptual module within an active robotic system, the act of controlling the motion of the sensor adds important information, without which, the perception of certain observables would not be possible. Secondly, whether computer vision is used as a pre-processing stage before displaying information to a human operator, or whether that information will be used within an automated visual feedback loop, the following principle is common: the system is more efficient if the visual information can be transformed in a way which makes the task-specific information explicit.