Tomography and Applications Preface: How to rebuild a binary image from its multi-level description based on generalized salient pixels

In DiscreteTomography,several classes of binary images presenting different kind of convexity have been considered for their reconstruction from projections. In Digital Image Analysis convexity estimators are among the most important shape descriptors. Shape feature extraction and representation plays an important role in many categories of applications like for example shape retrieval, shape recognition and classification, shape approximation and simplification, and so on. In this talk, we present a multi-level description of a binary image based on a special kind of convexity. In particular, the so called generalized salient pixels provides a decomposition of the image into Q-convex hulls at different levels and they are stored in a matrix called, GS-matrix (where GS stands for GeneralizedSalient). Therefore, there is a one to-one correspondence between the binary image and its GS-matrix. We show how to build the GS-matrix from the binary image and viceversa how to rebuild the binary image from its GS-matrix. Then, we play with GS-matrices to see how changes can modify the rebuild images. In Mathematical Morphology, a wide range of operators permits to process images for edge detection, noise removal, image enhancement and image segmentation, to mention some common usage. Among them, the two most basic operations are erosion and dilation. Virtually all other mathematical morphology operators can be defined in terms of combinations of erosion and dilation along with set operators such as intersection and union. We start by defining a new “erosion”operation based on the interaction of GS-matrix binary image and we investigate some consequences.