A new algorithm to extract the lines and edges through orthogonal projections

The present paper provides a generalization to the approach proposed by Frei and Chen to masks of any even dimension for line and edge detection in digital images. In the work presented in ICCS2004 we proposed the generalization to masks of odd dimension. We are completed with masks of even dimension and therefore the decomposition of Euclidean space in direct sum of the three subspaces: edge, line and uniform. We propose in this paper, first, a new algorithm based on the use of the norm projection vector as the best guarantee against the angle of projection since its use is independent of the chosen convolution masks. This will reduce the computational time of operations. Second, we designed the multiplicative factor of the standard deviation, f, allows us to modify the threshold value to decide which candidate pixel is an edge or line. Because the calculation of the average of all standard deviations implies a high computational time, we propose a new logarithmic model that acts automatically depending only on the size of the image and the size of the mask used. It is completed with the application of the designed algorithm to the synthetic and real image.