What is representation in optical character recognition? I am learning OCR and reading this book 

The authors define 8 processes to implement OCR that follow one by one (2 after 1, 3 after 2 etc):


Optical scanning
Location segmentation
Pre-processing
Segmentation
Representation
Feature extraction
Recognition
Post-processing


This is what they write about representation (#5)


  The fifth OCR component is representation. The image representation
  plays one of the most important roles in any recognition system. In
  the simplest case, gray level or binary images are fed to a
  recognizer. However, in most of the recognition systems in order to
  avoid extra complexity and to increase the accuracy of the algorithms,
  a more compact and characteristic representation is required. For this
  purpose, a set of features is extracted for each class that helps
  distinguish it from other classes while remaining invariant to
  characteristic differences within the class.The character image 
  representation methods are generally categorized into three major
  groups: (a) global transformation and series expansion (b) statistical
  representation and (c) geometrical and topological representation.


This is what they write about feature extraction (#6)


  The sixth OCR component is feature extraction. The objective of
  feature extraction is to capture essential characteristics of symbols.
  Feature extraction is accepted as one of the most difficult problems
  of pattern recognition. The most straight forward way of describing
  character is by actual raster image. Another approach is to extract
  certain features that characterize symbols but leaves the unimportant
  attributes. The techniques for extraction of such features are divided
  into three groups’ viz. (a) distribution of points (b) transformations
  and series expansions and (c) structural analysis.


I am totally confused. I don't understand what is representation. As I understand after segmentation we must take from image some features, for example topological structure like Freeman chain code and must match to some saved at the learning stage model - i.e. to do recognition. By other words - segmentation - feature extraction - recognition. I don't understand what must be done on representation stage. Please, explain.
The representation step is before the feature extraction step for exactly the reasons that they state. 

If you take the full image representation and go right to feature extraction, you have much more data to extract features from (added complexity) and the features you do extract will be much more noisy. This is why one at least reduces the representation to grey level (as the authors suggest). 

Feature extraction is choosing properties of the image which you will then perform recognition on. It is important to already have thrown out unimportant details of the image before doing this. That is why the authors, and people in general, reduce to a proper representation before performing feature extraction.