  In this paper we will consider an unknown binary image, of which the length
of the boundary and the area of the image are given. These two values together
contain some information about the general shape of the image. We will study
two properties of the shape in particular. Firstly, we will prove sharp lower
bounds for the size of the largest connected component. Secondly, we will
derive some results about the size of the largest ball containing only ones,
both in the case that the connected components are all simply connected and in
the general case.
