Peter G. Anderson

Neural network applications to the color scanner and printer calibrations

In the context of colorimetric matching, the intent of color scanner and printer calibrations is to characterize the device-dependent responses to the device-independent representations such as CIEXYZ or CIE 1976 L*a*b* (CIELAB). Usually, this is accomplished by a two-step process of gray balancing and a matrix transformation, using a transfer matrix obtained from multiple polynomial regression. Color calibrations, printer calibrations in particular, are highly nonlinear. Thus, a new technique, the neural network with the Cascade Correlation learning architecture, is employed for representing the map of device values to CIE standards. Neural networks are known for their capabilities to learn highly nonlinear relationships from presented examples. Excellent results are obtained using this particular neural net; in most training sets, the average color differences are about one ΔE ab . This approach is compared to the polynomial approximations ranging from a 3-term linear fit to a 14-term cubic equation. The results from training sets indicate that the neural net outperforms the polynomial approximation. However, the comparison is not made in the same ground and the generalizations, using the trained neural net to predict relationships it has not been trained with, are sometimes rather poor. Nevertheless, the neural network is a very promising tool for use in color calibrations and other color technologies in general.

Cobordism classes of squares of orientable manifolds

THEOREM 1A. If M is an orientable manifold, then there exists a spin manifold N such that [M x M]2 = [N]2. I would like to express my thanks to my graduate advisor, F. P. Peterson, who suggested these problems to me, and who gave me considerable help and encouragement. If M is an n-dimensional manifold and N is a 2n-dimensional manifold, let R(M, N) denote that there is an isomorphism of Z2-algebras,

Multidimensional Golden Means

The golden mean,

Combinatorial Proofs of Fermat's, Lucas's, and Wilson's Theorems

\tau = \frac{{\sqrt {5} - 1}}{2} = \mathop{{\lim }}\limits_{{n \to \infty }} \;\frac{{{F_{{n - 1}}}}}{{{F_n}}} = \frac{1}{{}} = 0.618033988749

The interpretation of i.r. and Raman spectra using pattern recognition

(1.1)

Genetic Algorithm Selection of Features for Hand-printed Character Identification

1 + \frac{1}{{}} 1 + \frac{1}{{}} 1 + \frac{1}{{}} 1 + \frac{1}{{}} 1 + \frac{1}{{}} 1 + \frac{1}{{}} 1 + \cdots