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M.A. Chapman et al.
Though many interpretations of the epsilon band exist, they can be categorized in two
groups: deterministic and probabilistic. In the deterministic case, the true position of
the line is considered to lie somewhere in the buffer zone. Deterministic interpretation
of the epsilon band sounds counter intuitive, because:
1) it provides no model of error distribution inside the band
and
2) it proposes that the true line is definitely located within this region
In the probabilistic interpretation of the epsilon band, the width of the zone is
assumed to be a function of different variables, and that their uncertainties accumulate
into the final stage. For instance Alai (1993) assumed scale, digitization, slope and
attribute of the polygons adjacent to the lines are the related variables while Blakemore
(1984) simply related the band width to the digitizing error, round off error and
generalization error. The probabilistic interpretation of the epsilon band has been
inconsistent with what analytical procedures suggested (Shi, 1994).
However, in spite of its weaknesses, the epsilon band model has the following
advantages (Carver, 1991):
it involves minimal extra processing time
it uses existing spatial operations for implementation (e.g. buffer zone
operation)
different feature categories can have different epsilon values assigned to them
as attributes
and
the concept is easily understood and can be applied during the execution of
many spatial operations
THE ERROR BAND MODEL
In an effort to further develop the epsilon band model Dutton (1992) proposed the error
band model. In the error band model, the digitized end points of a straight line are
drawn from a random sample of possible positions, having a circular normal
distribution that forms a population of connected line segments. Unlike the epsilon
band that assumes constant width along a line segment, Dutton’s model (Fig. 3)
suggests a narrower band in the middle of the line segment. Shi (1994) computed the
error distribution along the line segments and through analytical derivations
demonstrated the shape of Dutton’s model. Dutton’s simulated model and Shi’s
analytically-derived model are based on the assumption of circular errors at the
endpoints of a line segment. A circular error assumption neglects the correlation
M.A. Chapman et al.
Though many interpretations of the epsilon band exist, they can be categorized in two
groups: deterministic and probabilistic. In the deterministic case, the true position of
the line is considered to lie somewhere in the buffer zone. Deterministic interpretation
of the epsilon band sounds counter intuitive, because:
1) it provides no model of error distribution inside the band
and
2) it proposes that the true line is definitely located within this region
In the probabilistic interpretation of the epsilon band, the width of the zone is
assumed to be a function of different variables, and that their uncertainties accumulate
into the final stage. For instance Alai (1993) assumed scale, digitization, slope and
attribute of the polygons adjacent to the lines are the related variables while Blakemore
(1984) simply related the band width to the digitizing error, round off error and
generalization error. The probabilistic interpretation of the epsilon band has been
inconsistent with what analytical procedures suggested (Shi, 1994).
However, in spite of its weaknesses, the epsilon band model has the following
advantages (Carver, 1991):
it involves minimal extra processing time
it uses existing spatial operations for implementation (e.g. buffer zone
operation)
different feature categories can have different epsilon values assigned to them
as attributes
and
the concept is easily understood and can be applied during the execution of
many spatial operations
THE ERROR BAND MODEL
In an effort to further develop the epsilon band model Dutton (1992) proposed the error
band model. In the error band model, the digitized end points of a straight line are
drawn from a random sample of possible positions, having a circular normal
distribution that forms a population of connected line segments. Unlike the epsilon
band that assumes constant width along a line segment, Dutton’s model (Fig. 3)
suggests a narrower band in the middle of the line segment. Shi (1994) computed the
error distribution along the line segments and through analytical derivations
demonstrated the shape of Dutton’s model. Dutton’s simulated model and Shi’s
analytically-derived model are based on the assumption of circular errors at the
endpoints of a line segment. A circular error assumption neglects the correlation