7
C H A P T E R 2
Basics of Feature Design
In order to define channel representations and to describe their properties, some terminology and
concepts need to be introduced, which is the purpose of this chapter. Channel coding is based on
local operators, whose design is guided by statistical properties (accuracy, precision, robustness)
and geometrical properties (mostly invariance or equivariance). Algorithmically, it is a dense
or sparse, grid-based approach, combining histograms and signatures. It is well motivated by
biological observations.
2.1 STATISTICAL PROPERTIES
In practice, the input of any operator has to be considered as noisy and the input noise is prop-
agated to the operator output. us, the operator output has to be considered as an estimator of
the ideal result and potentially suffers from bias, errors, or outliers. More formally, these terms
are defined as follows.
e bias (systematic error) of a visual feature may occur at different levels and often has
severe effects. For instance, structure-tensor based corner detectors such as the Harris detector
[Harris and Stephens, 1988] have a tendency to move the location of the corner toward the
interior, although this can be mitigated by a correction step [Förstner, 1991]. Also, high-level
features such as ellipses are often extracted using algorithms that suffer from bias [Kanatani
et al., 2016]. Note that the bias of a feature reduces its accuracy, i.e., the proximity to the true
values, and has to be distinguished from the variability of the estimator, i.e., its precision.
e variability of a visual feature is a measure of random errors, repeatability, or repro-
ducibility. A feature with high precision shows a small variance of the output in comparison
to the variance of the input, but it still may suffer from low accuracy. Typically, experiments
for assessing the feature extractor confuse the effects of systematic and random errors by using
the root-mean-square error (RMSE), i.e., measuring mean deviations from the ground truth
[Rodehorst and Koschan, 2006]. If no ground truth is available, often only precision is assessed
and systematic errors are neglected [Schmid et al., 2000]. Furthermore, visual feature extrac-
tion might be prone to outliers and including these in the precision measurement might lead to
unbalanced results.
e robustness of a visual feature is a measure of the insensitivity to violations of model
assumptions. If some model assumption is violated, the operator output might become random
and (quadratic) precision measures are dominated by the resulting outliers. However, the op-
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