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© IRL Press at Oxford University Press

POLCA, a library running in a modern environment, implements a protocol for averaging randomly oriented images

Pier Luigi Bellon and Salvatore Lanzavecchia

Istituto di Chimica Struttristica Inorganica, Universita' degli Studi via G.Venezian 21. 20133 Milano. Italy

The library POLCA implements the averaging of biological structures whose images are recorded in digital form from electron micrographs. The averaging protocol is based upon a method developed about ten years ago, which allows one to operate on a sequence of objects oriented and displaced at random within their frame; the relative rotations and the displacements of the structures are detected with the use of correlation algorithms and modified to make all objects appear the same, apart from their noisy components. The average image is then obtained by a simple addition and the signal-to-noise ratio is improved by a factor equal to the square root of the number of objects used to calculate the average. With respect to the original implementation of the method, two novel features characterize the library: the first one deals with the functions that are cross-correlated to determine the relative rotations of the structures; the functions used here are the inverse transforms of the amplitude spectra (IAS functions), which give rise to sharp maxima when they are cross-correlated. The second peculiarity is the systematic adoption, in the transformations of coordinates and in other circumstances, of an interpolation technique based upon the Fourier series kernel. POLCA is written in C and runs on a VME machine under the UNIX V/68 operating system. A programming style has been adopted to exploit fully the machine resources.

Received on December 8, 1989; accepted on January 31, 1990

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