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In this paper we will consider an unknown binary image, of which the lengthof the boundary and the area of the image are given. These two values togethercontain some information about the general shape of the image. We will studytwo properties of the shape in particular. Firstly, we will prove sharp lowerbounds for the size of the largest connected component. Secondly, we willderive 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 inthe general case.

Boundary and shape of binary images