Ordinarily, filters are derived from the optimization of certain expressions with respect to the mean squared metric. We construct a family of linear and nonlinear processors (filters) for image recognition that is lp-norm optimum in terms of tolerance to input noise and discrimination capabilities. The lp norm is the generalization of the usual mean squared (l2) norm, which we obtain by replacing the exponent 2 with any positive constant p (usually p≥1). These processors are developed by minimizing the lp norm of the filter output that is due to the input scene and the output that is due to input noise. We use the lp norm to measure the size of the filter output that is due to noise so that we can obtain greater freedom in adjusting the noise robustness and discrimination capabilities. We give a unified theoretical basis for developing these filters. This family of filters includes some of the existing linear and nonlinear filters, giving us a subfamilies of processors, which we denote by Hqσ and Hq. The values of q control the discrimination capabilities and the robustness of the processors. The parameter σ is the standard deviation of the noise process.
© 1999 Optical Society of AmericaPDF Article