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.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Association Behavior of Biotinylated and Non-Biotinylated PolyEthylene Oxide-b-Poly(2-(Diethylamino)Ethyl Methacrylate)

Biotinylated and non-biotinylated copolymers of ethylene oxide (EO) and 2-(diethylamino)ethyl methacrylate (DEAEMA) were synthesized by the atom transfer radical polymerization technique (ATRP). The chemical compositions of the copolymers as determined by NMR are represented by PEO₁₁₃PDEAEMA₇₀ and biotin-PEO₁₀₄PDEAEMA₉₃ respectively. The aggregation behavior of these polymers in aqueous solutions at different pHs and ionic strengths was studied using a combination of potentiometric titration, dynamic light scattering (DLS), static light scattering (SLS), and transmission electron microscopy (TEM). Both PEO-b-PDEAEMA and biotin-PEO-b-PDEAEMA diblock copolymers form micelles at high pH with hydrodynamic radii (Rh) of about 19 and 23 nm, respectively. At low pH, the copolymers are dispersed as unimers in solution with Rh of about 6-7 nm. However, at a physiological salt concentration (cs) of about 0.16M NaCl and a pH of 7-8, the copolymers form large loosely packed Guassian chains, which were not present at the low cs of 0.001M NaCl. The critical micelle concentrations (CMC) and the cytotoxicity of the copolymers were investigated to determine a suitable polymer concentration range for future biological applications. Both PEO-b-PDEAEMA and biotin-PEO-b-PDEAEMA diblock copolymers possess identical CMC values of about 0.0023 mg/g, while the cytotoxicity test indicated that the copolymers are not toxic up to 0.05mg/g (> 83% cell survival at this concentration).