A new nonlinear operator for multiresolution signal and image analysis

In the present paper, we introduce a new nonlinear operator well adapted to various processing and analysis on any nonuniformly sampled signals. This operator is based on the Hausdorff metric, which is very convenient for point sets comparison. We expose the properties of this nonlinear operator, especially for various transformations of the signal, like translation and scaling. We give some examples of applications using this operator and discuss their similarity with correlation and wavelet transforms. Then we extend the description of its behavior to affine transforms, with an application to shape matching and object recognition.