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able to fully capture the concept of image complexity, nor that the fractal image
compression was able to capture the complexity of visual perception. They posited
that JPEG was closer to visual complexity than fractal compression, and that fractal
compression was closer to processing complexity than JPEG, subsequently testing
the possibility of using these measures as rough estimates for these concepts in the
context of a specific, and limited, aesthetic theory.
The following formula was proposed as a way to capture the previously-
mentioned notions (Machado and Cardoso
1998
):
CV
a
(CP(t
1
)
1
CP(t
1
)
−
CP(t
0
)
CP(t
1
)
aesthetic value
=
CP(t
0
))
b
×
c
(11.1)
×
where
a
,
b
and
c
, are parameters used to tune the relevance given to each of the
components. The left side of the formula rewards those images which have high CV
and low CP estimates at the same time, while the right side rewards those images
with a stable CP across time. The division by
CP(t
1
)
is a normalisation operation.
The formula can be expanded in order to encompass further instants in time, but
the limitations of the computational implementation led the authors to use only two
instants in their tests.
The images of the DJT were digitalised, converted to greyscale, and resized to a
standard dimension of 512
×
512 pixels, which may involve changes in the aspect
ratio. The estimates for
CV
,
CP(t
1
)
and
CP(t
0
)
were computed for the resulting
images. Using these estimates, the outcome of formula (
11.1
) was calculated for
each of the images. For each of the 90 pairs or triads of images comprising the DJT,
the system chose the image that yielded a higher value according to formula (
11.1
).
The percentage of correct answers obtained by the AJS depends on the values of
the parameters
a
,
b
and
c
. Considering all combinations of values for these param-
eters ranging in the
[
]
interval with 0.1 increments, the maximum percentage
of correct answers was 73.3 % and the minimum 54.4 %. The average success rate
of the system over the considered parametric interval was 64.9 %.
As previously mentioned, the highest average percentage of correct answers in
human tests in the DJT reported by Eysenck and Castle (
1971
) is 64.4 %, and was
obtained by subjects that were final year fine art graduates, a value that is surpris-
ingly similar to the average success rate of our system (64.9 %).
Although comparing the performance of the system to the performance of hu-
mans is tempting, one should not jump to conclusions! A similar result cannot be
interpreted as a similar ability to perform aesthetic judgements. As previously men-
tioned, humans may follow principles that are not exclusively in aesthetic order to
choose images. Moreover, since the test aims at differentiating between humans,
it may take for granted principles that are consensual between them, and the AJS
would be unable to identify. Finally, the results say nothing regarding the validity of
the test itself (a question that is outside the scope of our research). Thus, what can
be concluded is that the considered formulae and estimates are able to capture some
of the principles required to obtain a result that is statistically different from the one
obtained by answering randomly in the DJT.
0
.
5
,
2
