Morphological multiscale fingerprints from connected transformations

In this paper a multiscale study based on the use of morphological connected transformations is presented. In particular, the morphological opening and closing by reconstruction are used as connected transformations. These transformations have the characteristic of preserving contours without introducing new information, in addition to smoothing the processed image as the size of the structuring element increases. Due to this, both connected filters and the identity are used as primitives to introduce two operators that allow a multiscale treatment to the processed image in accordance with the scale parameter. The multiscale morphological operators are called opening–closing by reconstruction and closing–opening by reconstruction, respectively. In the case of the opening–closing by reconstruction transformation, the propagation of extrema when the structuring element enlarges has an interesting behavior. In addition, the fingerprints of the image given as a function of regional maxima, regional minima and scale parameter are defined. Finally, the proposals of this work are illustrated with some examples.