Aesthetical issues with stochastic evaluation.

Abstract

<p>This research uses a stochastic computational tool (2D-C) for characterizing images in order to examine similarities and differences among artworks. 2D-C is measures the degree of variability (change in variability vs. scale) in images using stochastic analysis.</p><p>Apparently, beauty is not easy to quantify, even with stochastic measures. The meaning of beauty is linked to the evolution of human civilization and the analysis of the connection between the observer and the beauty (art, nature) has always been of high interest in both philosophy and science. Even though this analysis has mostly been considered part of the so-called social studies and humanities, mathematicians have also been involved. Mathematicians are generally not specialized to contribute, through their expertise, in sociopolitical analysis of messages and motivations of art but have been consistently applying mathematical knowledge, which is their expertise, in trying to explain aesthetics. In most of these analyses, the question at hand is if what is pleasing to the eye or not can be explained though mathematics.</p><p>Historically, it is known that from the time of the ancient Egyptian civilization a mathematic rule of the analogies of human body as models of beauty had been developed, and later in ancient Greece, the mathematicians Pythagoras and Euclid were the first known to have searched for a common rule (canon) existing in shapes that are perceived as beautiful. Euclid's Elements (c. 300 BC), for example, contains the first known definition of the “golden ratio”.</p><p>The opinions of later philosophers on this pursuit of mathematicians in the analysis of aesthetics were more varied. Leibniz, for example, believed that there is a norm behind every aesthetic feeling which we simply don’t know how to measure. On the contrary, Descartes supports that instead of regarding the aesthetic quality as an inherent quality of a physical object, the distinction of mind and nature have allowed humans to incorporate their own subjective feelings in determining their aesthetic preferences.</p><p>Thus many artists knew and apply math and geometry in their artwork, many philosophers tried to connect math and arts. Hence, it might be interesting to examine art work through a stochastic view. Stochastic analyses of the examined artworks are presented using climacograms and through stochastic evaluation with 2D-C we try to quantify some aspects of the artists’ expression. </p>

A Stochastic View of Varying Styles in Art Paintings

“…Α stochastic computational tool called 2D-C [52][53][54][55][56][57][58] is used to analyze images of art paintings quantifying the variability of the brightness vs. scale in a specific image and in a group of images as well. Here, we refer to spatial (not time) scale, defined as the ratio of the area of k × k adjacent cells (i.e., scale k) that are averaged to form the (scaled) spatial field, over the spatial resolution of the original field (i.e., at scale 1).…”

“…The most common stochastic attribute in natural processes is the long-term persistence behavior or HK-behavior, which is identified in global-scale analyses including billions of records, and in over-centennial timeseries of the most important hydrometeorological processes (i.e., temperature, humidity, wind, solar radiation, river discharge, atmospheric pressure, and precipitation), [58,59], and expressed through the climacogram for large scales as shown in Equation 2. Remarkably, the shape of the dependence structure, as visualized through the climacogram, exhibits similarities among natural processes, having a Markov-type behavior at small scales and a long-term persistence behavior (i.e., a power-law function of scale) at large scales, described by the expression 1 / , where q is now a scale-parameter indicative of the transition point between the short-term (roughness) and long-term (persistence) behaviours in the climacogram ( Figure 4).…”