A new algorithm for number of holes attribute filtering of grey-level images

In this paper we present a new algorithm for filtering a grey-level image using as attribute the number of holes of its connected components. Our approach is based on the max-tree data structure, that makes it possible to implement an attribute filtering of the image with linear computational cost. To determine the number of holes, we present a set of diverse pixel patterns. These patterns are designed in a way that the number of holes can be computed recursively, this means that the calculations done for the components of the image can be inherited by their parent nodes of the max-tree. Since we do not need to re-calculate the attribute data for all connected components of the image, the computation time devoted to the attribute computation remains linear.