Supervised classification methods group images according to their similarity to existing prototypes, often called templates, or references. Correlation averaging of crystals (Frank, 1982; Saxton and Baumeister, 1982) incorporates a supervised classification of some sort: here, a reference is simply picked from the raw crystal image, in the form of a patch that is somewhat larger than a unit cell, or generated by quasi-optical Fourier filtration of the raw image. Its cross-correlation with the full crystal field produces a correlation peak wherever a match occurs. Those lattice repeats for which the correlation coefficient falls below a certain threshold are rejected. Application of such a criterion means that only those repeats that are most similar to the reference are accepted. This practice conforms with the notion that the repeats originate from the same motif, which is slightly rotated or distorted in different ways, and are corrupted by noise. Only those corresponding to the undistorted, unrotated template are picked. The dependency of the result on the choice of the template is strikingly demonstrated by the correlation averaging of an image representing a double layer (front and back) of a bacterial membrane (Kessel et al., 1985). In this example, repeats of the front layer are selected by the template obtained by quasi-optical filtering of the front layer, and those of the back layer by the back-layer template. Sosinski et al. (1990) demonstrated this selectivity by using an artificially created field of periodically repeating patterns (a hand) that differ in the position of a component (the index finger) (figure 4.22).

Supervised classification has become commonplace in reference-based orientation determination (3D projection matching). Here, the experimental data are matched with a large number of 2D templates (a case of multireference classification; see below), each of which is a projection of the same 3D map (the reference map) in a different direction of view. This subject will be treated in the context of 3D reconstruction (chapter 5).

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