Image and pattern analysis for the determination of the method of drawing celebrated thera wall-paintings circa 1650 B.C.

In this article, an integrated conjecture about the method of drawing of monumental prehistoric wall-paintings is presented and supported. Specifically, the article deals with paintings that initially decorated the internal walls of the highest floor of a building, called “Xeste 3”, at Akrotiri of the Greek island of Thera circa. 1650 B.C. It is argued that these wall-paintings could had been drawn while the brush was guided by an apparatus, which corresponds to advanced for the era of geometric prototypes with impressive precision. A set of assumptions concerning the actions the artists might have taken in order to create the spiral themes is stated and supported. These assumptions refer to the existence of a draft plan, the sequence of brush strokes, the placement of the brush on the wall, as well as the possible form of the apparatus. These conjectures are evaluated and tested by means of curve fitting and image analysis methods developed by the authors. The results indicate that all drawn contour parts optimally fit along a single prototype linear spiral with fitting error of less than 0.4mm, supporting existence of a very advanced culture for the era of geometric guide. It is statistically rejected that this guide could have the form of a stamp. Moreover, there is strong evidence that the painter might have used a draft plan of the spiral themes to prepare the final drawing and that the linear spiral guide has been used by alternating its placements in order to form the internal and external spiral contour.

[1]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[2]  Josef Kittler,et al.  A survey of the hough transform , 1988, Comput. Vis. Graph. Image Process..

[3]  Teuvo Kohonen,et al.  Self-organization and associative memory: 3rd edition , 1989 .

[4]  Hon Fung Li,et al.  Shapes Recognition Using the Straight Line Hough Transform: Theory and Generalization , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[6]  Andrew W. Fitzgibbon,et al.  An Experimental Comparison of Range Image Segmentation Algorithms , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Daeryong Lee,et al.  Modified K-means algorithm for vector quantizer design , 1997, IEEE Signal Processing Letters.

[8]  Myung Jin Bae,et al.  An Improvement of Modified K-Means Algorithm for Vector Quantizer Design , 1997 .

[9]  Herbert Süße,et al.  Invariant Fitting of Planar Objects by Primitives , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Didier Zugaj,et al.  A new approach of color images segmentation based on fusing region and edge segmentations outputs , 1998, Pattern Recognit..

[11]  Paul L. Rosin Ellipse Fitting Using Orthogonal Hyperbolae and Stirling's Oval , 1998, Graph. Model. Image Process..

[12]  Paul L. Rosin A survey and comparison of traditional piecewise circular approximations to the ellipse , 1999, Comput. Aided Geom. Des..

[13]  Stan Z. Li Toward global solution to MAP image restoration and segmentation: using common structure of local minima , 2000, Pattern Recognit..

[14]  Paul L. Rosin On serlio’s constructions of ovals , 2001 .

[15]  José Martínez-Aroza,et al.  A measure of quality for evaluating methods of segmentation and edge detection , 2001, Pattern Recognit..

[16]  Michael Werman,et al.  A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Hans-Jürgen Warnecke,et al.  Orthogonal Distance Fitting of Implicit Curves and Surfaces , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Muhammad Sarfraz Fitting curve to planar digital data , 2002, Proceedings Sixth International Conference on Information Visualisation.

[19]  Kuntal Sengupta,et al.  A Curve Fitting Problem and Its Application in Modeling Objects in Monocular Image Sequences , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  William H. Press,et al.  Numerical recipes in C , 2002 .

[21]  G. A. Watson,et al.  A class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances , 2003 .

[22]  N. Chernov,et al.  Statistical efficiency and complexity of curve fitting algorithms , 2003 .

[23]  Nikolai I. Chernov,et al.  Statistical efficiency of curve fitting algorithms , 2003, Comput. Stat. Data Anal..

[24]  Mihalis Exarhos,et al.  Identification of geometrical shapes in paintings and its application to demonstrate the foundations of geometry in 1650 B.C , 2005, IEEE Transactions on Image Processing.

[25]  Mihalis Exarhos,et al.  Determination of the method of construction of 1650 B.C. wall paintings , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.