A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
Shapes Recognition Using the Straight Line Hough Transform: Theory and Generalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Experimental Comparison of Range Image Segmentation Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ellipse fitting using orthogonal hyperbolae and Stirling's oval
Graphical Models and Image Processing
A survey and comparison of traditional piecewise circular approximations to the ellipse
Computer Aided Geometric Design
A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Orthogonal Distance Fitting of Implicit Curves and Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Curve Fitting Problem and Its Application in Modeling Objects in Monocular Image Sequences
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Invariant Fitting of Planar Objects by Primitives
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Computational and Applied Mathematics
Statistical efficiency and complexity of curve fitting algorithms
Statistical efficiency and complexity of curve fitting algorithms
Determination of the Method of Construction of 1650 B.C. Wall Paintings
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Journal on Computing and Cultural Heritage (JOCCH)
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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.