Beyond self-duality in morphological image analysis

Most morphological operators occur by pair of dual operators as highlighted by the erosion/dilation and opening/closing pairs. In practice, one decides to apply an operator or its dual depending on whether the targeted image structures are darker or brighter than their neighbourhood. Nevertheless, the same type of image structures may appear brighter than their neighbourhood in a region of the image definition domain but brighter in another. In this situation, self-dual rather than dual operators should be used. However, self-dual operators still assume that image structures roughly correspond to image extrema. Therefore, this model does not apply to complex images representing a partition of the space into image objects of arbitrary intensity values such as satellite images displaying landscapes with fields of various crop types. In this paper, we revisit the notion of self-duality, propose two new self-dual morphological filters, and show that it is possible to go beyond self-duality either by considering self-complementary operators or by substituting the image extrema paradigm with the more general concept of flat zones.