Decomposition of partially occluded strings in the presence of errors

A partially occluded scene in an image consists of a number of objects that are partially obstructed by others. By validating a partially occluded image one aims to generate a sequence of concatenated and possibly overlapping objects that corresponds to the input image. This is a theoretical study of partially occluded strings (considered as one-dimensional images) allowing for the presence of errors in each occluded object appearing in the input. Using the unit cost edit distance as our measure of errors, for some small integer k ≥ 0, we present a sequential algorithm for validating a k-approximate one-dimensional image x of length n over a dictionary [Formula: see text] of m objects each having equal length τ in O(nd) time where d = mτ is the size of the dictionary. </jats:p