My statement:
Generally, the specification of accuracy measures is based on the assumption that the errors follow a Gaussian distribution without any outlier. But most of the times, this is not the case as objects above the terrain, such as vegetation, buildings, etc. is present which gets ignored during the filtering program.
Peers comment on my statement:
Elevation errors MUST be distributed normally, otherwise many (probably all) the methods to determining the accuracy of the measurements are wrong.
I would provide a simple counter example to the Peer reviewer's assertion. For example an image of elevation beneath the golden gate bridge....
Normality of errors in measurements is really a standard assumption. However, it should be revised carefully. The historical idea was that errors are additive and near to be independent from measurement to measurement. In this context the Central Limit theorem and its generalizations suggest that the normal model can be adequate. At least, there are two conditions for this model for errors to be conceptually valid. The first one is that the variable which is measured should be real (all real values should be valid measurements, including negative values). This is shown by the fact that the normal distribution is supported on the whole real line. A second point is that the superposition of error sources should be additive thus recalling that the measurements are in an absolute scale, i.e. the differences are computed by subtraction. There are cases in which these conditions are not fulfilled but the normal model still work as an approximation.
At this point, we can realise that most measurements are not real and the errors are not additive. Positive measurements are likely to be in a relative scale with multiplicative errors that, when log-transformed, become to be in a real absolute scale. When measuring small concentrations, which can be considered in a logistic scale, considering normal errors is an error itself: in the literature, you can find intervals on concentrations like 3ppm plus minus 5ppm, intervals spanning impossible negative concentrations.
The problem of outliers or atypical measurements claims for robust statistics. The example cited by J.W. Kern is a good example of this: the error in height will not be repeated with a probability predicted by any reasonable normal distribution of errors.
Definitively, errors may be modelled using distributions dominated by the central limit theorem (normal, log-normal, logistic-normal), but this is not necessarily so and robust statistical methods should be used to avoid the influence of atypical or even erroneous measurements.
https://www.researchgate.net/publication/233968571_Variations_in_multiscale_curvature_distribution_and_signatures_of_LiDAR_DTM_errors
in my practical experience with the above paper, i found some errors that are not necessarily gaussian. on the introduction of the paper as well ther'es a review about researchers finding not gaussian errors...
Article Variations in multiscale curvature distribution and signatur...
You are getting these vegetation-induced outliers or "vegetation" bias because you compare a DSM versus a DTM. In that case you will always get a bi-modal histogram which may be considered as a sum of two Gaussian bells: one representing the white noise over bare ground and the other the same over vegetated areas.
I suggest that you rephrase your statement, first. In the first sentence: 'Generally, the specification of accuracy measures is based on the assumption that the errors follow a Gaussian distribution without any outlier' I do not understand this: 'without any outlier'. Maybe contrary to your statement: There is a place on the Gaussian curve for outliers... Just drop this part: 'without any outlier'.
The second sentence is provided without a context. What are you refereeing to? Perhaps, you are mixing outliers with bias or the other way around?
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