DIFFERENTIATION-BASED EDGE-DETECTION USING THE LOGARITHMIC IMAGE-PROCESSING MODEL

The logarithmic image processing (LIP) model is a mathematical framewo rk which provides a specific set of algebraic and functional operation s for the processing and analysis of intensity images valued in a boun ded range. The LIP model has been proved to be physically justified by that it is consistent with the multiplicative transmittance and refle ctance image formation models, and with some important laws and charac teristics of human brightness perception. This article addresses the e dge detection problem using the LIP-model based differentiation. First , the LIP model is introduced, in particular, for the gray tones and g ray tone functions, which represent intensity values and intensity ima ges, respectively. Then, an extension of these LIP model notions, resp ectively called gray tone vectors and gray tone vector functions, is s tudied. Third, the LIP-model based differential operators are presente d,focusing on their distinctive properties for image processing. Empha sis is also placed on highlighting the main characteristics of the LIP -model based differentiation. Next, the LIP-Sobel based edge detection technique is studied and applied to edge detection, showing its robus tness in locally small changes in scene illumination conditions and it s performance in the presence of noise. Its theoretical and practical advantages over several well-known edge detection techniques, such as the techniques of Sobel, Canny, Johnson and Wallis, are shown through a general discussion and illustrated by simulation results on differen t real images. Finally, a discussion on the role of the LIP-model base d differentiation in the current context of edge detection is presente d.