Digital Signal Processing Reference
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Figure 5.1.
Order and Mappings: a) in general, mapping between sets (A-E) vs. (V-
Z) can match any two letters from different sets b) if we enforce consistency of order
(the alphabetical order) in our mappings as defined in Eq. 5.1, we disallow mappings
between the two sets that cross each other c) the consistency allows for a divide and
conquer approach for finding a mapping across two ordered sets.
et al., 1990]. As we shall see in section 5., although the topological order
of a DAG is not necessarily unique, this consistency of the topological
order allows us to apply divide and conquer methods to find a mapping
between substructures of DAGs. By using DAG
S
as a robust represen-
tation, we can use the efficient calculation of an ordered mapping to
robustly compare sets of data.
3. PARTITIONING
Our approach for recognition is based on the concept of
partitioning
(to be defined within this section). In speech and on-line cursive hand-
writing, the information is transmitted as
datastrearns,
time-indexed se-
ries of real vectors. Recognition of a datastream as a whole is difficult
unless we use order to decompose the datastream into smaller elements.
This decomposition via partitioning is instrumental to the recognition
process. Our discussion of partitioning in this chapter applies to only
datastreams with l-D order. In the next chapter, we extend these con-
cepts to 2-D data.
We introduce two terms related to datastreams: the
macro-structure
and the
break. Macro-structures
are consecutive series of ordered vec-
tors from the datastream that are related to only one sub-element of
the datastream. For instance, in cursive handwriting word recognition,
loops and lines are a consecutive series of points within a handwrit-
ten letter and can be considered macro-structures of the handwritten
letter. In speech word recognition, syllables are macro-structures and
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