The paper presents a combinatorial algorithm to find the straight skeleton of the inner isothetic cover of a digital object imposed on a uniform background grid. The isothetic polygon (orthogonal polygon) tightly inscribes the given digital object. The algorithm stated here finds the straight skeleton of any isothetic polygon (simple or non-simple) in \(\varvec{O(\frac{n}{g} \log \frac{n}{g}})\) time in a single traversal by applying combinatorial rules, where n is the number of pixels on the boundary of the digital object and \(\varvec{g}\) is the grid size on which the digital object is imposed. To find the straight skeleton of non-simple orthogonal polygon, the polygon is divided into sub-parts which are a set of simple orthogonal polygons. The straight skeleton is generated for each of the sub-parts and the corresponding results are merged. The orthogonal polygon containing holes is cut at each holes and the polygon becomes hole-free. The algorithm to obtain the straight skeleton is applied on it. The disconnected hole parts are rejoined and the result is merged. The straight skeleton is useful shape descriptor of digital object. This algorithm stated here has applications in shape analysis.
