Designing a Fast Convolution Under the LIP Paradigm Applied to Edge Detection

The Logarithmic Image Processing model (LIP) is a robust mathematical framework for the processing of transmitted and reflected images. It follows many visual, physical and psychophysical laws. This works presents a new formulation of a 2D–convolution of separable kernels using the LIP paradigm. A previously stated LIP–Sobel edge detector is redefined with the new proposed formulation, and the performance of the edge detectors programmed following the two formulations (the previous one and the new one proposed) is compared. Another operator, Laplacian of Gaussian, is also stated under the LIP paradigm. The experiments show that both methods obtain same results although our proposed method is much faster than the previous one.