Digital Culture & AudioVisual Challenges

During the course of centuries mathematics has interacted in many ways with culture and human activities, and among these a place of privilege has been reserved for art and architecture. Numerous artists, architects and historians of mathematics have made these relationships evident, such as Piero della Francesca, Leonardo, Albrecht Dürer, Maurits Cornelis Escher, Felix Klein, G. David Birkhoff, Andreas Speiser and Federigo Enriques, to mention only some of the most celebrated. In this study we will show several examples of the existence of three levels of interaction between mathematics and art: the presence of a mathematical substrate in various artifacts from antiquity, the conscious or unconscious application by artists of mathematical principles whose theories had not yet been fully developed, and finally the relationship established by some mathematicians with artists and art theorists that permitted an awareness and acquisition of mathematical knowledge and rules that were then applied to artistic creations. The development of these three levels of interactions between mathematics and art can be a valid aid to the creation of a unified vision of the history of culture of peoples and civilizations.
Curves detection in digital image data is an important task in vision based systems as shapes of real world objects can often be described by geometric primitives like ellipses or be assembled by them. Hough has proposed an interesting and computationally efficient procedure for detecting curves in pictures. The Hough transform (HT) is a technique which can be used to isolate features of a particular shape within an image. Because it requires that the desired features be specified in some parametric form, the classical Hough transform is most commonly used for the detection of regular curves such as lines, circles, ellipses, etc. The main advantage of the Hough transform technique is that it is tolerant of gaps in feature boundary descriptions and is relatively unaffected by image noise. It also shows how the method can be used for more general curve fitting and gives alternative interpretations that explain the source of its efficiency.
We use HT to detect patterns of mathematical curves in paintings to check the degree to which they deviate from standard curves. This will enhance our goal, based mainly on a literature search, in an attempt to validate the view that mathematics and the art of painting are two directly intertwined fields, focusing research interest on the extent to which the science of mathematics in each period was a source of inspiration for painters without being directly observable. There is an inner mathematician visually expressed in art, and this visual approach can demystify mathematical teaching. The interdisciplinary study of math and science through the filter of art is a creative activity that can align emotional and sensory perspectives for educational purposes.

Key words:
history of mathematics; art history; art-science connections; image processing; pattern recognition; curve detection; Hough transformation

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