Statistical Classification
In previous chapters, several distance metrics were presented and used to assess pattern similarity relative to a prototype. In the present chapter, we further explore this way of thought, taking into account the specificity of the pattern distributions.
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1.1 Object Recognition Object recognition is a task performed daily by living beings and is inherent to their ability and necessity to deal with the environment. It is performed in the most varied circumstances - navigation towards food sources, migration, identification of predators, identification of mates, etc. - with remarkable efficiency. Recognizing objects is considered here in a broad cognitive sense and may consist of a very simple task, like when a micro-organism flees from an environment with inadequate pH, or refer to tasks demanding non-trivial qualities of inference, description and interpretation, for instance when a human has to fetch a pair of scissors from the second drawer of a cupboard, counting from below . The development of methods capable of emulating the most varied forms of object recognition has evolved along with the need for building "intelligent" automated systems, the main trend of today's technology in industry and in other fields of activity as well. In these systems objects are represented in a suitable way for the type of processing they are subject to. Such representations are called patterns. In what follows we use the words object and pattern interchangeably with similar meaning . Pattern Recognition (PR) is the scientific discipline dealing with methods for object description and classification. Since the early times of computing the design and implementation of algorithms emulating the human ability to describe and classify objects has been found a most intriguing and challenging task. Pattern recognition is therefore a fertile area of research, with multiple links to many other disciplines, involving professionals from several areas. Applications of pattern recognition systems and techniques are numerous and cover a broad scope of activities . We enumerate only a few examples referring to several professional activities :
Agriculture: Crop analysis Soil evaluation Astronomy: Analysis of telescopic images Automated spectroscopy Biology: Automated cytology Properties of chromosomes Genetic studies J. P. Marques de Sá, Pattern Recognition © Springer-Verlag Berlin Heidelberg 2001
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4 Statistical Classification
As seen in previou s chapters, it seems reasonabl e to take those sample means as class prototypes and assign each cork stopper to its nearest prototype. This is the essence of what is called the minimum distan ce or template matching classification. The classification rule is then: If
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(4-15a)
In the formula (4-l5a), vex) is the so-called likelihood ratio. The decision depends on how this ratio compares with the inverse prevalence ratio or prevalence threshold, P(C0.)IP(wI).
Let us assume for the cork stoppers problem that we only used feature N, x=[N], and that a cork was presented with x=[65]. Figure 4.12 shows the histograms of both classes with superimposed normal curve.
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4 Statistical Classification
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