Algorithms for Openings of Binary and Label Images with Rectangular Structuring Elements

Two new families of algorithms for computing openings of binary and label images are presented in this paper. The first family of algorithms is based on an horizontal scan, and a vertical scan that takes the result of the horizontal scan as input. With the results of these two scans it is possible to compute an opening with respect to a rectangle of any size. The second family of algorithms is based on the construction of an exhaustive list of rectangles included in an object. Rectangles of this list all have a maximal extension, i.e. no larger rectangle included in a region contains them. The opening then results from filling the output image with rectangles larger than the structuring element. After a description of the algorithms we provide a comparison of several algorithms in terms of computation time efficiency. The comparison shows that some of the new algorithms advantageously compete with existing algorithms.