In binary tomography, several algorithms are known for reconstructing binary images having some geometrical properties from their projections. In order to choose the appropriate reconstruction algorithm it is necessary to have a priori information of the image to be reconstructed. In this way we can improve the speed and reduce the ambiguity of the reconstruction. Our work is concerned with the problem of retrieving geometrical information from the projections themselves. We investigate whether it is possible to determine geometric features of binary images if only their projections are known. Most of the reconstruction algorithms based on geometrical information suppose $hv$-convexity or connectedness about the image to be reconstructed. We investigate those properties in detail, and also the task of separating 4- and 8-connected images. We suggest decision trees for the classification, and show some preliminary experimental results of applying them for the class of $hv$-convex and connected discrete sets. ` `