Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Exploring Vision-Based Interfaces: How to Use Your Head in Dual Pointing Tasks

The utility of vision-based face tracking for dual pointing tasks is evaluated. We first describe a 3-D face tracking technique based on real-time parametric motion-stereo, which is non-invasive, robust, and self-initialized. The tracker provides a real-time estimate of a ?frontal face ray? whose intersection with the display surface plane is used as a second stream of input for scrolling or pointing, in paral-lel with hand input. We evaluated the performance of com-bined head/hand input on a box selection and coloring task: users selected boxes with one pointer and colors with a second pointer, or performed both tasks with a single pointer. We found that performance with head and one hand was intermediate between single hand performance and dual hand performance. Our results are consistent with previously reported dual hand conflict in symmetric pointing tasks, and suggest that a head-based input stream should be used for asymmetric control.