A methodology for translating A methodology for translating positional error into measures of positional error into measures of attribute error, and combining the attribute error, and combining the two error sources two error sources Yohay Carmel 1 , Curtis Flather 2 and Denis Dean 3 1 The Thechnion, Haifa, Israel 2 USDA, Forest Service 3 Colorado State University
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A methodology for translating positional error into measures of attribute error, and combining the two error sources Yohay Carmel 1, Curtis Flather 2 and.
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A methodology for translating positional A methodology for translating positional error into measures of attribute error, and error into measures of attribute error, and combining the two error sourcescombining the two error sources
Yohay Carmel1, Curtis Flather2 and Denis Dean3
1 The Thechnion, Haifa, Israel2 USDA, Forest Service3 Colorado State University
Part 1: bridging the gap between positional error and classification error
classification error -- difference in pixel class between the map and a reference
Positional error(misregistration, location error)
Is the gap between the true location of an item and its location on the
map / image
Positional error may translate to thematic error
positional error largely affects overall thematic error (often more than classification error)(Townshend et al 1992, Dai and Khorram 1998)
Goal 1: find a common denominator for both error typesGoal 2: combine the two error types to get an overall estimate of error (in the context of temporal change)
THE PROBABILITY THAT AN OBSERVED TRANSITION IS CORRECT
positional error affects thematic error
Expressing positional error in terms of thematic error
Shift = 1, 0Shift = 15, 7
Shift = 2, 3
Forest Shrubs GrassForestShrubsGrassClassified
ReferenceExpressing positional error in terms of thematic error
Map aggregation = image degradationoverlay a grid of cells on the image (cell >>pixel)
and define the larger cell as the basic unit
Impact of positional error is largely reduced when cells are aggregated
ab
c
At the pixel level:
only 55% of the pixels remained unaffected by a minor shift
At the grid cell level:
post-shiftpre-shift0.170.210.340.330.490.46
Impact of positional error is largely reduced when cells are aggregated
This trade-off calls for a model that quantifies the process
to aid decisions on optimal level of aggregation
Aggregation:
Gain in accuracy BUT loss of information
A geometric approach to the impact of positional error
Effective positional error at the grid cell level
2A
eeeAeA yxyx is the proportion of
pixels that transgress into neighboring cells
(RMSE units)
Positional error at the GRID CELL level
p(loc) is the probability that positional error translates into attribute error
pA(loc) is the same probability – in the context of a larger grid cell
)()( locplocp A
The impact of aggregation on thematic accuracy
0.23
A p(loc) cell size error
0.6 m 0.23
6 m 0.14
60 m 0.01
Conclusions
• positional error has a large impact on thematic accuracy, particularly in the context of change
• But can be easily mitigated: increase MMU to >10X[positional error] and do not worry about it.
• Within overall thematic error at the pixel level –classification error component is typically smaller than the positional error component, but is more difficult to get rid of by aggregation.