The problem of placing a number of specific shapes in order to minimise material waste is commonly encountered in the sheet metal, clothing and shoe-making industries. It is driven by the demand to find a layout of non-overlapping parts in a set area in order to maximise material utilisation. A corresponding problem is one of compaction, which is to minimise the area that a set number of shapes can be placed without overlapping. This paper presents a novel connectivity based approach to leather part compaction using the no-fit polygon (NFP). The NFP is computed using an image processing method as the boundary of the Minkowski sum, which is the convolution between two shapes at given orientations. These orientations along with shape order and placement selection constitute the chromosome structure.