Recognition of shapes by morphological attributed relational graphs

Skeletons represent a powerful tool for qualitative shape matching because they resume, synthesize and help the understanding both of the object shape and of its topology. The aim of this work is mainly on using the potential strength of skeleton of discrete objects in computer vision and pattern recognition where features of objects are needed for classification. In this paper we propose a method to improve the topological skeleton representation of a binary shape. This allows to find a graph model characterized by efficient and effective attributes, leading to a more correct discrimination between shapes by an attributed graph matching algorithm. Introduction A classical technique in pattern recognition is to work on a contour representation of the object to extract the features to classify it. An alternative approach consists in representing the object by a pattern obtained by thinning it as much as possible. The result of this process is a set of idealised lines which is called the skeleton or medial axis of the input pattern and it is the thinnest representation of the original pattern that preserves the topology, aiding synthesis and understanding. The methods to accomplish this are called thinning or skeletonisation. The detection of end points, junction points and curve points of medial axis is important for a structural description that captures the topological information embedded in the skeleton. The skeleton can be converted into a graph associating the end points and the junctions with the vertices and the curve points with the edges. The graph can then be used as an input to graph matching algorithms. In this paper we introduce a method to approximate the skeleton representation of an object, starting from its characteristic points (end points, junction points and curve points). From the approximated skeleton we build an attributed relational graph to organize in a structured way information about object shape and topology embedded in its medial axis. This structural representation allows the comparison of different objects by graph matching algorithms. [5, 6, 10, 11, 16]. 1 From objects to morphological skeletons Digital skeletons can be used to represent objects in a binary digital image for shape analysis and classification [9, 12]. Most of the existing algorithms to generate digital skeletons produce a non-connected skeleton, which is useless for shape description applications since homotopy is not preserved and characteristic points such as junction points or endpoints in the continuous case are lost. On the contrary, a thinning process guarantees the condition for obtaining one-pixel thick and connected skeletons [13]. A digital set can be skeletonised by using morphological operators so as to preserve these important properties by thinning the set with structuring elements (SE) preserving homotopy, i.e. homotopic SEs. The skeleton can be obtained by thinning the input image with a series of homotopic SEs and their rotations until stability is reached [15] and the object is reduced to a set of one-pixel width connected lines. If the skeleton is considered as a connected graph each vertex can be labelled as an end point or a junction point, while an edge is just made of curve points. In [3] two different new methods to identify end points and to detect junctions using mathematical morphology have been proposed. We recall here the definitions of end points, junctions points and curve points. Definition 1. A point of a one-pixel width digital curve is an end point if it has a single pixel among its neighbourhood. Definition 2. A point of a one-pixel width digital curve is defined as a junction point if it has more than two curve pixels among its neighbourhood. Definition 3. A point of a one-pixel width digital curve is defined as a curve point if it has two curve pixels among its neighbourhood. In this way a skeleton of an object can be considered as the union of the end points, the junctions and the curve points of , i.e. "! #$ % & ' ( ) +*,! -/.102 ' ( 3 54 As a consequence, a skeleton can be partitioned into 6 branches 7185 , 9: <;2=24 4 42=26 , i.e.