Derivative-based optimization in colour image filtering an application for derivative learning

• Autores: A. Sapena, S. Morillas, José Camacho
• Localización: Modelling in Science Education and Learning, ISSN-e 1988-3145, Nº. 2, 2009, págs. 45-55
• Idioma: inglés
• DOI: 10.4995/msel.2009.3117
• Enlaces
  • Texto completo
• Resumen
  • español

    La noción de derivada de una función y su aplicación a la optimización de funciones es un problema interesante e ilustrativo para los estudiantes de ingeniería. En este trabajo, desarrollamos un aplicación del concepto de derivada para la optimización del filtrado de imágenes en color. Ello implica ajustar el parámetro del filtro para obtener un rendimiento óptimo de filtrado. Proponemos maximizar la calidad de la imagen filtrada representada por la relación señal-ruido (Peak Signal-to-Noise Ratio, PSNR), que es una función del parámetro del filtro. El valor óptimo del parámetro se obtiene mediante un algoritmo basado en la aproximación de la derivada de la función del PSNR de manera que se obtenga la imagen filtrada óptima.

  • English

    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.

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