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.

The Alignment of Objects With Smooth Surfaces: Error Analysis of the Curvature Method

The recognition of objects with smooth bounding surfaces from their contour images is considerably more complicated than that of objects with sharp edges, since in the former case the set of object points that generates the silhouette contours changes from one view to another. The "curvature method", developed by Basri and Ullman [1988], provides a method to approximate the appearance of such objects from different viewpoints. In this paper we analyze the curvature method. We apply the method to ellipsoidal objects and compute analytically the error obtained for different rotations of the objects. The error depends on the exact shape of the ellipsoid (namely, the relative lengths of its axes), and it increases a sthe ellipsoid becomes "deep" (elongated in the Z-direction). We show that the errors are usually small, and that, in general, a small number of models is required to predict the appearance of an ellipsoid from all possible views. Finally, we show experimentally that the curvature method applies as well to objects with hyperbolic surface patches.

Object Recognition By Alignment Using Invariant Projections of Planar Surfaces

In order to recognize an object in an image, we must determine the best transformation from object model to the image. In this paper, we show that for features from coplanar surfaces which undergo linear transformations in space, there exist projections invariant to the surface motions up to rotations in the image field. To use this property, we propose a new alignment approach to object recognition based on centroid alignment of corresponding feature groups. This method uses only a single pair of 2D model and data. Experimental results show the robustness of the proposed method against perturbations of feature positions.

Robust and Efficient 3D Recognition by Alignment

Alignment is a prevalent approach for recognizing 3D objects in 2D images. A major problem with current implementations is how to robustly handle errors that propagate from uncertainties in the locations of image features. This thesis gives a technique for bounding these errors. The technique makes use of a new solution to the problem of recovering 3D pose from three matching point pairs under weak-perspective projection. Furthermore, the error bounds are used to demonstrate that using line segments for features instead of points significantly reduces the false positive rate, to the extent that alignment can remain reliable even in cluttered scenes.

Copper phthalocyanine on InSb(111)A?interface bonding, growth mode and energy band alignment

Copper phthalocyanine on InSb(111)A?interface bonding, growth mode and energy band alignment, D.A. Evans, H.J. Steiner, S. Evans, R. Middleton, T.S. Jones, S. Park, T.U. Kampen, D.R.T. Zahn, G. Cabailh and I.T. McGovern, J. Phys.: Condens. Matter, 15, S2729?S2740, (2003)

Alignment of the genomes of brachypodium distachyon and temperate cereals and grasses using bacterial artificial chromosome landing with fluorescence in situ hybridization

Robert Hasterok, Agnieszka Marasek, Iain S. Donnison, Ian Armstead, Ann Thomas, Ian P. King, Elzbieta Wolny, Dominika Idziak, John Draper and Glyn Jenkins (2006). Alignment of the genomes of brachypodium distachyon and temperate cereals and grasses using bacterial artificial chromosome landing with fluorescence in situ hybridization.Genetics, 73 (1), 349-362. Sponsorship: Royal Society / BBSRC;BBSRC RAE2008

Religion and American adolescent delinquency, risk behaviors and constructive social activities

This report demonstrates that religion among U.S. adolescents is positively related to participation in constructive youth activities. In addition, those who participate in religious activities seem to be less likely to participate in many delinquent and risk behaviors.

A Geometric Approach to Slot Alignment in Wireless Sensor Networks

Traditionally, slotted communication protocols have employed guard times to delineate and align slots. These guard times may expand the slot duration significantly, especially when clocks are allowed to drift for longer time to reduce clock synchronization overhead. Recently, a new class of lightweight protocols for statistical estimation in wireless sensor networks have been proposed. This new class requires very short transmission durations (jam signals), thus the traditional approach of using guard times would impose significant overhead. We propose a new, more efficient algorithm to align slots. Based on geometrical properties of space, we prove that our approach bounds the slot duration by only a constant factor of what is needed. Furthermore, we show by simulation that this bound is loose and an even smaller slot duration is required, making our approach even more efficient.