The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

Nanoengineering heterogeneous catalysts for the selective hydrogenation of key agrochemical derivatives

Rapidly rising world populations have sparked growing concerns over global food production to meet this increasing demand. Figures released by The World Bank suggest that a 50 % increase in worldwide cereal production is required by 2030. Primary amines are important intermediates in the synthesis of a wide variety of fine chemicals utilised within the agrochemical industry, and hence new 'greener' routes to their low cost manufacture from sustainable resources would permit significantly enhanced crop yields. Early synthetic pathways to primary amines employed stoichiometric (and often toxic) reagents via multi-step protocols, resulting in a large number of by-products and correspondingly high Environmental factors of 50-100 (compared with 1-5 for typical bulk chemicals syntheses). Alternative catalytic routes to primary amines have proven fruitful, however new issues relating to selectivity and deactivation have slowed commercialisation. The potential of heterogeneous catalysts for nitrile hydrogenation to amines has been demonstrated in a simplified reaction framework under benign conditions, but further work is required to improve the atom economy and energy efficiency through developing fundamental insight into nature of the active species and origin of on-stream deactivation. Supported palladium nanoparticles have been investigated for the hydrogenation of crotononitrile to butylamine (Figure 1) under favourable conditions, and the impact of reaction temperature, hydrogen pressure, support and loading upon activity and selectivity to C=C versus CºN activation assessed.