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"The most exotic journey would not be to see a thousand different
places, but to see a single place through a thousand person's
Presented on this page is a
rather unorthodox computer graphics characterization of data that I have used
in applications ranging from sounds to DNA sequences. Please forgive me if the page
is sluggish -- it's doing a massive amount of real-time computation on your machine!
In particular, you
can use a computer-controlled face to represent data. These cartoon faces can be used to represent the values
of as many as 10 variables, each variable corresponding to a facial
feature. You can read all about the method and my applications in my book
Computers, Pattern, Chaos and Beauty. (For example, I've used the
faces to examine cancer gene sequences, for presenting sounds to deaf children,
background, computer graphics has become increasingly useful in the
representation and interpretation of multidimensional data with complex
relationships. Pseudo-color, animation, three-dimensional figures, and a
variety of shading schemes are among the techniques used to reveal
relationships not easily visible from simple correlations based on
two-dimensional linear theories.
Showing correlations between two or
three variables is easy: simply plot a two-dimensional or
graph. But what if
one is trying to present four or five or even ten different
variables at once? The face method of representing multivariate data
was first presented in 1973 by Chernoff, a
Harvard statistician. Using gradations of various facial features, such
as the degree of eyebrow slant or pupil size, a single face can convey
the value of many different variables at the same time.
Such faces have been
shown to be more reliable and more memorable than other tested icons (or
symbols), and allow the human analyst to grasp many of the essential
regularities and irregularities in the data. In general, n
data parameters are mapped into a figure with n
features, each feature varying in size or shape according to the point's
coordinate in that dimension. The data sample variables are mapped to
facial characteristics; thus, each multivariate observation is
visualized as a computer-drawn face. This aspect of the graphical point
displays capitalizes on the feature integration abilities of the human
visual system and is
particularly useful for higher levels of cognitive processing.
The drawing on this page
shows the range of faces produced when random numbers
are mapped. This shows you the diversity of computer-generated faces.
The settings for each of the ten facial parameters were
computed using a random number generator.
(Code for creating the faces is given in the book. This Java applet for
displaying the faces on this page was written by the wonderful AI programmer
In my applications
ten facial parameters,
F(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
are used, and each facial characteristic has ten
settings, S(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),
providing for 10 billion possible
different faces. The controlled features are: head eccentricity, eye
eccentricity, pupil size, eyebrow slant, nose size, mouth shape, eye
spacing, eye size, mouth length, and degree of mouth opening.
Head eccentricity, for example, controls how elongated the head is
in either the horizontal or vertical direction.
is constructed using parabolic interpolation routines, and the other
features are derived from circles, lines, and ellipses.
In my studies, faces computed from speech sounds
(i.e. "speech-faces") could provide useful biofeedback targets for helping deaf
and severely hearing-impaired individuals to modify their vocalizations
in selective ways -- especially since they may provide simple
and memorable features to which children could relate. The
traditional speech spectrogram displays are not the same as pictures,
since pictures have numerous visual features that can be readily
identified, labeled, and integrated into a coherent whole. To compare
SDPs (previous section) and faces: note that unlike faces, SDPs do not
elicit an emotional reaction. Emotion does confer a mnemonic advantage
for the faces, but can sometimes obscure the association, e.g. a smiling
face representing cancer statistics.
A number of recreational
and educational uses for the faces are suggested
in the following sections. As
background, research has demonstrated the potential value that
visualization and iconic systems play in learning and instruction.
Popular educational software for home computers is becoming available
(e.g., the "FaceMaker"
by Spinnaker (see references)) which allows
children to create faces from sets of eyes, ears, and noses. Programs
such as these help children become comfortable with computer
fundamentals such as menus and cursors. The computer-drawn faces
presented in the current section have particular value in that they are
created under parametric control and can provide immediate visual
feedback to the user. In addition, any face can easily be
regenerated at a later time from its control-data.
Cognitive Association of Coordinates with Facial Features
There have been several studies in the literature which have
explored the child'ss ability to organize and represent body location
a simple face-drawing system was developed where
children can type numbers at the terminal keyboard and immediately view
the results on an adjacent graphics screen. For example, faces were
constructed from the control-data entered by Lisa, a 6-year-old girl
with no prior experience with computers. One face in particular was her
favorite, because she found the shape of the mouth amusing. She worked
on the figure for several minutes, developing the mouth to her
specifications, and subsequently she recorded the final control-data on
a piece of paper. This indicated that she understood the concept of
number-to-face parameter mapping.
Target-Pictures for Children
In my book, drawings made by children in an attempt to reproduce
the four computer-drawn targets at top. From top to bottom,
the ages of the children
were 6 , 6, 8, and 10.
The faces can be used to illustrate the concept of similarity,
sameness, and difference. Since the facial parameters are
accurately controlled, the degree of difficulty of the task can
The faces may also
serve as target-pictures for children to draw.
computer faces are created from control-data, the resultant faces can
easily be regenerated at a later time, or altered slightly, in order to
test hand-eye coordination and development.
includes four computer-drawn faces and
children's attempts to reproduce them. The drawing task can be made
much more difficult if the child is asked to view the face first and
then required to draw it as well as possible from memory. Computer
software, and hardware such as digitization tablets, make an analytic
comparison between computer- and child-generated faces easy. Simple
parameters such as center of gravity, and radius of gyration
can be computed to characterize the drawings in an objective way.
For years psychologists have tried to determine when infants
first realize how the features of the human face are naturally arranged
and when an infant's ability to perceive facial expressions begins.
Computer-generated faces might be ideal for the study of infant's
perception of natural and distorted arrangements of a schematic face.
In the study of Maurer and Barrera (1981), it was shown that
2-month-old infants show a preference for a natural arrangement of
facial features on a cartoon face, as opposed to scrambled features.
Though their cartoon faces were not computer-generated, computers could
be used in the placement (random or otherwise) of the facial features on
the head, giving the researcher rigorous control of the resultant
Learning by Means of Analogy
The faces can be used to illustrate the concept of similarity, sameness,
and difference. Since the facial parameters are accurately
controlled, the degree of difficulty of the task can be specified.
Possible tasks include: Which two are
the same? and Which one is different? The faces can be used to explore
memory abilities: initially, one face is shown, then erased, and
the user can subsequently be asked to choose the face from a small
group, somewhat like picking from a police line-up.
Educational Aid for the Presentation of Statistical Concepts
The faces may be suitable as visual supplements in the presentation of
statistical concepts, particularly distribution theory, to individuals
inexperienced in mathematics and with no prior knowledge of the methods
of statistical evaluation. In this work, faces were used to
illustrate the concept of white noise (totally random distribution) such
as that shown on this page in contrast to Gaussian noise (normal error
theories usually not introduced to individuals
prior to the high-school level due to the mathematical complexity of the
For the case of white noise,
one hundred faces were generated, each facial characteristic
having a setting determined from a random number generator.
young students, the faces could be used, in addition to standard
techniques, for visualizing simpler concepts such as the mean, median,
mode, and other measures of central tendency.
Commercial and Military Air Traffic Control
One may speculate about
potentially useful applications of the computer-drawn
faces in the cockpit of airplanes. The growing complexity of
aircraft controls and readouts are making aircraft almost too complex to
fly. The faces can accommodate analog or digital input from a multitude
of readouts, each facial parameter receiving input from one or more
gauges. Deviations in the controls from their expected values would
give rise to excursions of the facial parameters from their middle
settings. While it is true that the more standard concept of having a
gauge blink or beep when a parameter has gone beyond a critical value is
valuable, the faces would be especially useful in alerting the pilot of
conditions where several readings are not themselves at critical stages,
but where the combined effect may be dangerous.
Other faces links:
Faces for pain representation:
Cliff Pickover's home page which includes computer art, educational
puzzles, higher dimensions, fractals, virtual caverns, JAVA/VRML, alien
creatures, black hole artwork, and animations. Click here
for a complete list of over 20 Cliff Pickover books.