Geoscience Reference
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List of
id TF
Cumulated binary
frequency (TF//tile)
Cumulated proportional frequency
id t
T 1
T 2
[TF #6 ]
T 3 [TF #2 ; TF #6 ]
T 4 [TF #3 ; TF #6 ]
Table 3.1. Example of a temporal tile-based index -
taken and then adapted from [PAL 10d]
These indexing strategies allow us to propose several indexes based on spatial and
calendar tilings: spatial indexes whose segmentations are of district, city, township,
of day, week, month, season, year and century level. In a GIR context, these indexes
range of the query. Standardization by tiling: formalization of the approach
This type of standardization consists of using a tiling to describe the spatial or
temporal representations stored in the first-level indexes generated by the PIV
process flows. This approach is a form of discretization, for example it associates a
temporal object of the calendar domain with a temporal tile corresponding to a
particular segmentation of the same space.
In a more formal way (equation [3.1]), a domain T included in the space R n
corresponds to the domain 1 O included in the space R n 2 . The domain O is composed
of a set of objects O 1 ,...,O p (the features of the first-level index), and the domain
T is composed of the union of m subspaces (the tiles of the standardized index). For
each subspace (T i ) of T in intersection with one or more objects (O j ) of O, we retain
the number of intersections (N T i ).
O ⊆ R n −→ T ⊆ R n
O = { O 1 ,O 2 ,O 3 ,...,O p }
T= i=1 T i
N T i = Card({T i | T i ∩ O j = ∅,∀j =1,...,p})
with Card(x)the cardinality of x
1 Adomainisafiniteorinfinitesetofvalues.Itisrepresentedbyalistofelementsoranecessary
andsufficientconditionofbelonging-thedomainofBooleans: {0,1},thedomainofthefingers
of the hand: {thumb, index finger, middle finger, ring finger, pinky}, the calendar domain.
2 This superset refers to spaces of dimension 1, 2 or more.
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