Color Dipole Moments for Edge Detection

Dipole and higher moments are physical quantities used to describe a charge distribution. In analogy with electromagnetism, it is possible to define the dipole moments for a gray-scale image, according to the single aspect of a gray-tone map. In this paper we define the color dipole moments for color images. For color maps in fact, we have three aspects, the three primary colors, to consider. Associating three color charges to each pixel, color dipole moments can be easily defined and used for edge detection.

Digital Restoration of Ancient Papyri

Image processing can be used for digital restoration of ancient papyri, that is, for a restoration performed on their digital images. The digital manipulation allows reducing the background signals and enhancing the readability of texts. In the case of very old and damaged documents, this is fundamental for identification of the patterns of letters. Some examples of restoration, obtained with an image processing which uses edges detection and Fourier filtering, are shown. One of them concerns 7Q5 fragment of the Dead Sea Scrolls.

The Digital Restoration of Da Vinci's Sketches

A sketch, found in one of Leonardo da Vinci's notebooks and covered by the written notes of this genius, has been recently restored. The restoration reveals a possible self-portrait of the artist, drawn when he was young. Here, we discuss the discovery of this self-portrait and the procedure used for restoration. Actually, this is a restoration performed on the digital image of the sketch, a procedure that can easily extended and applied to ancient documents for studies of art and palaeography.

Dipole Vectors in Images Processing

Instead of evaluating the gradient field of the brightness map of an image, we propose the use of dipole vectors. This approach is obtained by adapting to the image gray-tone distribution the definition of the dipole moment of charge distributions. We will show how to evaluate the dipoles and obtain a vector field, which can be a good alternative to the gradient field in pattern recognition.

Dipole and Quadrupole Moments in Image Processing

This paper proposes an algorithm for image processing, obtained by adapting to image maps the definitions of two well-known physical quantities. These quantities are the dipole and quadrupole moments of a charge distribution. We will see how it is possible to define dipole and quadrupole moments for the gray-tone maps and apply them in the development of algorithms for edge detection.