### Style space: How to compare image sets and follow their evolution (part 2)

This is part 2 of a four-part article. Part 1 is here.

text: Lev Manovich

PATTERNS IN STYLE SPACE

if we visualize all van Gogh paintings according to their brightness
and saturation values, what is the shape of their distribution?
According to the estimates, van Gogh produced approximately 900 paintings.
The following visualization plots images of 776 paintings (%86 of
the total estimated number) which were created between 18881 and 1890.

X-axis = brightness median.
Y-axis = saturation median.

The distribution has two clusters: earlier dark paintings on the left,
and lighter later paintings in the center and on the right. The clusters
are not symmetrical: one side is dense, another is more spread out.

If we only plot the paintings done in Arles in 1887, we get a more symmetrical shape.

Many social and natural processes follow a familiar Bell curve (normal
distribution). What are the shapes of distributions of large cultural
data sets? Because humanists only recently started to work
with big data sets, it is too early to make any generalizations. However,
it would not be surprising if the distributions of features of
very large cultural sets do follow the Bell curve pattern:
a dense cluster containing most of the data, gradually falling off to the side,
and a large very sparse area.

However, if the data has this shape, this does not always mean
that it actually follow this distribution exactly. In the case of
one million manga pages data set we analyzed in our lab, many feature
distributions do look like a normal distribution, but normality tests show
that they are actually not. (See this graph
showing distributions of values of eight visual features for 1,074,625 manga pages.)

With smaller data sets we analyzed, we often see some asymmetry.
Consider this visualization of 587 Google logos (1998-2007). Each logo
version was analyzed to extract a number of visual features.
The visualization uses these features to situate all logos in 2D space
according to their difference from the original logo which would have appear
at X = 0. Horizontal distance from 0 on X-axis indicates the degree of
visual difference; vertical position indicates if modifications are
in the uppper part of the logo, or the bottom part.

At first it may appear that the distribution of the Google logos follows
the familiar Bell curve. However a closer look reveals that the
"cloud" of logos extends to the left more. As Google became one of the most
recognized brands in the world, the designers started taking more
chances with the logo, modifying it more dramatically. The function of
the Google logo changed: from identifying the company to surprising
Google users by how much designers can depart from the original logos.
These "anti-logos," so to speak, started to appear after 2007; in our
visualization they occupy the right most part, breaking the symmetry of the
previously established bell-shaped pattern of graphic variability.

VISUALIZING AN IMAGE SET IN RELATION TO A SPACE OF ALL POSSIBLE IMAGES

If we want to visually compare two or more image sets to each other in
relation to two visual properties, we can project them into a 2D space
defined by these visual properties as we did with Piet Mondrian's and
Mark Rothko's paintings in part 1. Using min and max values of the measured
properties of all images in out sets combined as the boundaries of the
visualization will allow us to use the visualization area most
efficiently.

However, if we want to understand the footprint of each image set in
relation to the absolute mix and max - i.e. lowest and highest
possible values of visual features of all possible images - we need to
map our images differently. Mix and max of X and Y in the
visualization should be set to their lowest and highest absolute
possible values. For example, if we measure brightness on 0-255 scale,
mix should be set to 0, and max should be set to 255.

The following visualizations of Mondrian and Rothko paintings uses
this idea. To make visualizations easier to see, we have added small
white squares in the corners; black text inside each square indicates
X and Y coordinates of a point in the center of a square.

X-axis = brightness mean. Min = 0; Max = 255.
Y-axis = brightness standard deviation. Min = 0; Max = 126.7.

VISUALIZING PARTS OF AN IMAGE SET IN RELATION TO THE WHOLE SET

A related idea is to render parts of an image set over the background showing
the complete set. This allows us to see the footprint of the these parts
in relation to the larger footprint of all images.

In the next example we compare pages of two manga titles from our complete set
of 883 titles comprising 1,074,790 pages. (See Manga.viz for more details
the idea about the shape of manga distribution. We visualize pages of nine most
popular titles on onemanga.com. (The visualization uses transparency, so the pages
rendered first remain visible; the drawback is that the contrast of every page is
diminished. Here is an example of manga pages visualization without transparency).

X-axis = brightness mean;
Y-aixs = brightness standard deviation:

Now lets look at just two titles. The pages of each title are rendered
as color points. All other pages are rendered as grey points. As can be seen,
a few pages of the titles overlap, but the rest form two distinct clusters.

Pink points:
title: Ga on-Bi
artist: Ju Deo
intended audience: Shounen (teenage boys)
genre tags (from onemanga.com): action, supernatural.

Blue points:
title: Aozora Pop.
artist: Ouchi Natsumi.
intended audience: shoujo (teenage girls)

(This work is a part of the larger project to find if Japanese manga aimed at different
audiences has different footprints in the style space; to map this space more
comprehensively, we will use 400 features - as opposed to just two features used