An application-case for derivative learning: Optimization in colour image filtering

Related to the notion of derivative of a function, its application to function optimization is an interesting and illustrative problem for Engineering students. In the present work, we develop an application of the derivative concept to optimize the filtering of a colour image. This implies to optimize the value of the filter parameter to maximize performance. We propose to maximize the quality of the filtered image represented by the Peak Signal to Noise Ratio (PSNR), which is a function of the filter parameter. The optimal value for the parameter is obtained by means of an algorithm based on the approximation of the derivative of the PSNR function so that finally the optimum filtered image is obtained.