From hyperconnections to hypercomponent tree: Application to document image binarization

In this paper, we propose an extension of the component tree based on at zones to hyperconnections (h-connections). The tree is dened by a special order on the h-connection and allows non at nodes. We apply this method to a particular fuzzy h-connection and we give an ecient algorithm to transform the component tree into the new fuzzy h-component tree. Finally, we propose a method to binarize document images based on the h-component tree and we evaluate it on the DIBCO 2009 benchmarking dataset: our novel method places rst or second according to the dierent evaluation measures. Hierarchical and tree based representations have become very topical in image processing. In particular, the component tree (or Max-Tree) has been the subject of many studies and practical works. Nevertheless, the component tree inherits the weaknesses of the at zone approach, namely its high sensitivity to noise, gradients and diculty to manage disconnected objects. Even if some solutions have been proposed to preserve the component tree [5, 4], it seems that a more general framework for grayscale component tree [1] based on non at zones becomes necessary. In this article, we propose a method to design grayscale component tree based on h-connections. The h-connection theory has been proposed in [7] and developed in [1, 3, 4, 8, 9]. It provides a general denition of the notion of connected component in arbitrary lattices. In Sec. 2, we present the h-connection theory and a method to generate a related hierarchical representation. This method is applied to a fuzzy h-connection in Sec. 3 where an algorithm is given to transform a Max-Tree into the new grayscale component tree. In Sec. 4, we illustrate the interest of this tree with an application on document image binarization. 2 H-component Tree This section presents the basis of the h-connection theory [7, 1] and gives a denition of the h-component tree. The construction of the tree is based on the z-zones [1] of the h-connection, together with a special partial ordering. Z-zones are particular regions where all points generate the same set of hyperconnected (h-connected) components and the entire image can be divided into such zones. Under a given condition, the Hasse diagram obtained in this way is acyclic and provides a tree representation. Let L be a complete lattice furnished with the partial ordering ≤, the inmum , the supremum. The least element of L is denoted by ⊥ = L. We assume the existence of a sup-generating