Finding Optimal Non-Overlapping Subset of Extracted Image Objects

We present a solution to the following discrete optimization problem. Given a set of independent, possibly overlapping image regions and a non-negative likeliness of the individual regions, we select a nonoverlapping subset that is optimal with respect to the following requirements: First, every region is either part of the solution or has an overlap with it. Second, the degree of overlap of the solution with the rest of the regions is maximized together with the likeliness of the solution. Third, the likeliness of the individual regions influences the overall solution proportionally to the degree of overlap with neighboring regions. We represent the problem as a graph and solve the task by reduction to a constrained binary integer programming problem. The problem involves minimizing a linear objective function subject to linear inequality constraints. Both the objective function and the constraints exploit the structure of the graph. We illustrate the validity and the relevance of the proposed formulation by applying the method to the problem of facade window extraction. We generalize our formulation to the case where a set of hypotheses is given together with a binary similarity relation and similarity measure. Our formulation then exploits combination of degree and structure of hypothesis similarity and likeliness of individual hypotheses. In this case, we present a solution with non-similar hypotheses which can be viewed as a non-redundant representation.