A comparison between the first absolute central moment and the gradient of Gaussian when detecting edges in presence of Gaussian noise

The gray-level absolute central moment of the first order provides ridges at gray-level discontinuities as well as a conventional gradient of Gaussian (GoG). A mass center b of the gray-level variability can also be associated to the first absolute central moment. When given a starting point p, vector b indicates the path which joins p to the nearest gray-level discontinuity as well as the gradient of the GoG magnitude. However, when the right configuration of the operator is chosen, vector b indicates a point which is closer to the discontinuity than p, regardless of the distance between p and the discontinuity. Therefore, when using vector b, gray-level discontinuities can be located with an iterative approach. In this paper, the edge detection properties of the first absolute central moment are compared with those of the GoG. The text was submitted by the authors in English. Marcello Demi was born in Cecina, Italy, in 1956. He graduated in electronic engineering from the University of Florence, Italy, in 1985. He is currently head of the Computer Vision Group at the CNR Institute of Clinical Physiology in Pisa, senior scientist for ESAOTE Spa, and he teaches a course on medical image processing at the Faculty of Applied Physics, University of Pisa. His research interests are cardiovascular image processing systems, contour tracking of moving deformable objects, and filtering schemes inspired by the early stages of biological vision systems. He has 80 scientific publications and his objective is the development of common projects with people who work in the area of biological vision for the purpose of both understanding biological vision and developing image processing systems. Francesco Faita was born on June 28, 1973, in La Spezia (Italy). In 2001, he graduated from Universitá degli Studi di Pisa obtaining the degree of electronic engineer. Since 2001, he has been working as a research fellow at the Institute of Clinical Physiology of the Italian National Research Council. His main research interests lie in computer vision, in particular, in the field of ultrasound imaging. Elisabetta Bianchini was born in Lucca, Italy, in 1975. She received her degree in electronic engineering from the University of Pisa, Italy, in 2004. Since 2004, she has been a junior researcher at CNR, the Italian National Research Council, at the DSP lab in IFC (Institute of Clinical Physiology). Vincenzo Gemignani was born on October 10, 1969, in Viareggio (Italy). In 1995, he graduated from Universitá degli Studi di Pisa obtaining the degree of electronic engineer. Since 1996, he has been working as a research fellow at the Institute of Clinical Physiology of the Italian National Research Council. His main research interests lie in digital signal processing, in particular, in field real-time image analysis.