Enumeration of Shortest Isothetic Paths Inside a Digital Object

The computation of a shortest isothetic path (SIP) between two points in an object is important in various applications such as robot navigation and VLSI design. However, a SIP between two grid points in a digital object laid on a uniform 2D isothetic square lattice may not be unique. We assume that each discrete path consists of a sequence of consecutive grid edges that starts from the source point and ends at the sink point. In this paper, we present a novel algorithm to calculate the number of such distinct shortest isothetic paths between two given grid points inside a digital object, with time complexity \(O(S/g^2)\), where S is the total number of pixels in the digital object, and g is the grid size. The number of available SIPs also serves as a metric for shape registration.

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