A new method for edge detection from N-dimensional digital image
Meng Qingzhang
Electronic Engineering Dept.
Tsinghua University
Shi Jiuhao
Research Institute of Petroleum
Exploration and Development
China
Abstract
A n-dimensional digital image can be represented by a fitted hypersurface. Some significant in-formation of the image can be then obtained through studying the characteristics of the hyper the greytone value the 2nd -class Legendre polynomial is selected as the orthogonal basis function. And the coefficients are derived by minimizing the total squared estimation error. Theoretically, a conclusion is that all of the operators for edge detection cab be generalized from these coefficients. The obviousness of an edge is tested by the F-distribution variables for the hypersurface gradients and Laplacians, and the direction at an edge point is coded in [ O, 2p] in a defined sampling interval. For calculating the coefficients a recursive model is designed. The experimental results are obtained from processing a 3-bands airborne image.
Introduction
There have been a lot of edge detection theories and algorithms in digital image processing books and papers. Most of them are based on the principle of Zero-crossing points from D. Marr's theory about human visual mechanism for extracting the edge information from images. Practically, the methods can be divided into two classes. One is based on the picture greytone features and another is based on the spatial gradient and Laplacian features of the picture. For the first, the thresholding techniques are usually used directly, and for the second, the operator techniques are used. They are usually successful for 2-dimensional edge and line extraction.
In multiband and multitime images such as those acquired by Landsat and SPOT, however, different objects respond in different bands. It is hence advantageous to use the information from all of the bands and times of the same scene in edge and lineament detection. In 1981, Morgenthaler and Rosenfeld generalized the Prewitt operators to n-dimensions by fitting a hyoperquadric surface. However, the noise is not introduced into the formulation. In 1982, Chittineni developed the multidimensional edge and line detection theory by fitting a hyper surface to noisy picture function in the neighborhood of an image point using basis functions. Also in Chittineni's paper, the statistical tests are devised for the detection of significant edges and lines and the properties of the operators are studied for rotational invariance. It is the purpose of this paper to generalize the Sobel operators to n-dimensionals by fitting an adjusted hyperquadric surface. The noise is introduced into the formulation here. And also, the directions of the edges which are detected by the hypersurface fitting are quantified in a defined intervals from zero to 2. It is very useful for lineament detection in applications such as geological exploration. Furthermore, experimental results are presented.
