Digital Image Processing of Electron Micrographs

Image processing refers to any technique which alters and displays in a more tangi- ble form, the information contained in images. In the case of electron microscopy, it extends the scientist’s ability to study images of biological structures because details that may be invisible to the naked eye can be clearly revealed. Noise appears in all micro- graphs to varying extents and can arise from a variety of sources [BAKE95], such as vari- ability in the specimen support film, impurities in the sample, irregularities at the atomic, molecular, or macromolecular level, defocus level, etc. Image processing methods identify and separate signal and noise components in the image. The main benefit of the clearer images is an enhanced understanding of biological structure-function relationships. Corre- lation with X-ray diffraction, biochemical, genetic, immunological, and model building studies makes image processing a powerful tool for investigating the basis of molecular events in living systems.

Since 1963 several techniques have been developed and are now routinely used in biological structure studies. Optical and computer diffraction and filtering, three-dimen- sional reconstruction, rotational and translational optical superposition, real-space itera- tion and back-projection, correlation and convolution averaging, and holographic methods are among the many that are available. Image processing techniques are classified as either real-space (direct) or reciprocal-space (Fourier), depending on whether the micrograph or electron image itself is processed, or an intermediate step, involving the Fourier transform of the micrograph is required for processing. The emphasis of this section is on Fourier image processing, since the algorithms and techniques described in this chapter are intended for this type of processing.

Fourier image processing, based on the principles of X-ray diffraction and X-ray crystallography, was primarily developed in the 1960s and 1970s by A. Klug and his col- leagues at the Medical Research Council Laboratory in Cambridge, England [KLUG69], and it has been used in a majority of structural studies of biological macromolecular assemblies. Fourier techniques are most effective for the study of crystalline specimens, although, in principle, they can be applied to the study of any non-crystalline specimen. Fortunately, a wide range of biological specimens occur naturally or can be isolated in

vitro as regular arrays and are amenable to this type of analysis. Viruses, muscle proteins, membranes, ribosomes, enzymes, etc., have been successfully examined by Fourier image processing techniques [BAKE95].

A typical digital processing procedure includes the following steps: (a) image selec- tion, (b) densitometry, (c) boxing and floating, (d) Fourier transformation, (e) indexing two-dimensional lattices (for objects with translational symmetry), and (f) two-dimen- sional filtering and/or three-dimensional reconstruction.

After an initial screening by eye (to discard obviously bad images), several micro- graphs are examined by optical diffraction and a small subset of the best images (in terms of optical quality and specimen preservation) is selected. The images in this subset are fur- ther processed by digital processing methods. In the case of biological specimens believed to possess rotational symmetry, optical diffraction is unsuitable and it is replaced by an analysis of the rotational power spectrum [CROW71].

Densitometry is the step in which the micrograph is digitized by converting optical densities on the photographic emulsion into a numerical array. The devices that have com- monly been used for densitometry are called densitometers. However, the use of CCD (charge coupled device) cameras for microndensitometry has gained popularity over the past few years as they have become more affordable.

The entire digital image, or selected (boxed) areas may be used for subsequent pro- cessing steps. Regions of the image outside the area of interest are zeroed and the numeri- cal image is floated by subtracting the average image intensity around the perimeter of the boxed area from all image intensities within the masked area. The role of floating is to suppress the intense diffraction spots generated by the edges of the boxed area.

The Fourier transform of the image results in an array of complex structure factors (see section 2.1 on page 5). The successful application of image analysis procedures largely depends on correctly indexing the diffraction pattern. For two-dimensional crystal- line biological specimens, the diffraction pattern consists of a series of discrete spots (Bragg reflections) that lie on a reciprocal lattice. Indexing consists of defining the recip- rocal lattice parameters and assigning Miller indices to each reflection. Correct indexing

allows one to decide which regions of the Fourier transform are attributed to noise and which regions are attributed to signal.

Filtering the diffraction pattern means zeroing the amplitudes of all structure factors except at the reciprocal lattice points. The filtered diffraction pattern is then back-trans- formed to reconstruct an averaged image. If the three-dimensional structure of a particle is to be reconstructed, structure factor phases and amplitudes must be determined in three dimensions, to fill in a complete three-dimensional Fourier transform. This is accom- plished by combining data from several two-dimensional diffraction patterns of indepen- dent views of the specimen. The extent of the three-dimensional transform and the resolution that can be computed depend on the number and uniqueness of the specimen images included in the data set. The reconstruction method is based on the Projection The- orem (see section 2.3 on page 12). Figure 4.10 depicts the overall scheme for three-dimen- sional reconstruction [DERO68].