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A rectangle blanket is a set of non-overlapping axis-aligned rectangles, usedto approximately represent the two dimensional image of a shape approximately.The use of a rectangle blanket is a widely considered strategy for speeding-upthe computations in many computer vision applications. Since neither therectangles nor the image have to be fully covered by the other, the blanketbecomes more precise as the non-overlapping area of the image and the blanketdecreases. In this work, we focus on the rectangle blanket problem, whichinvolves the determination of an optimum blanket minimizing the non-overlappingarea with a given image subject to an upper bound on the total number ofrectangles the blanket can include. This problem has similarities withrectangle covering, rectangle partitioning and cutting / packing problems. Theimage replaces an irregular master object by an approximating set of smalleraxis-aligned rectangles. The union of these rectangles, namely, the rectangleblanket, is neither restricted to remain entirely within the master object, norrequired to cover the master object completely. We first develop a binaryinteger linear programming formulation of the problem. Then, we introduce fourmethods for its solution. The first one is a branch-and-price algorithm thatcomputes an exact optimal solution. The second one is a new constrainedsimulated annealing heuristic. The last two are heuristics adopting ideasavailable in the literature for other computer vision related problems.Finally, we realize extensive computational tests and report results on theperformances of these algorithms.

Rectangle Blanket Problem: Binary integer linear programming formulation and solution algorithms