Digital Object Identifier (DOI) 10.1007/s10032-003-0105-0 IJDAR (2003) 6: 115–125 Matching of graphical symbols in line-drawing images using angular signature information S. Tabbone, L. Wendling, K. Tombre LORIA, B.P. 239, 54506 Vandœuvre-l` es-Nancy Cedex, France Received: 7 October 2002 / Accepted: 1 December 2002 Published online: 4 July 2003 – c  Springer-Verlag 2003 Abstract. In this paper, a method for matching com- plex objects in line-drawings is presented. Our approach is based on the notion of F -signatures, which are a special kind of histogram of forces [17,19,28]. Such histograms have low time complexity and describe signatures that are invariant to fundamental geometrical transformations such as scaling, translation, symmetry, and rotation. This article presents a new application of this notion in the field of symbol identification and recognition. To improve the efficiency of matching, we propose using an approx- imation of the F -signature from Fourier series and the associated matching. Key words: F -signatures – Fourier series – Symbol recog- nition – Graphics recognition 1 Introduction In this paper, which is a thorough extension of work pre- sented in [25], we propose a method for the recognition of complex symbols in technical drawings based on the notion of F -signatures, which is a particular histogram of forces [17,19,28]. The aim is to define a signature for each object found in a line-drawing. A preliminary step consists in defining a set of sam- ples that will be used as models for the symbols to be found. The signatures used allow us to represent the at- traction forces that are exerted between the parts of an object following a set of directions and are discriminant features for achieving an accurate classification. Further- more, such a signature has low time complexity and al- lows us to recover fundamental geometric tranformations like rotation, translation, scale factor (considering only the shape of the F -signature), and symmetry. A brief overview of pattern recognition approaches in the field of symbol recognition is given in Sect. 2. Then the notion of histogram of forces and its properties are Correspondence to : S. Tabbone (e-mail: tabbone@loria.fr) recalled in Sect. 3. An approximation of such signatures is performed to achieve efficient matching by taking di- rectly into account the rotation factor (Sect. 4). Exper- imental studies and a discussion about the advantages and limitations of our approach are given in Sect. 5. 2 Related work Despite the large quantity of technical documentation floating around, there have been relatively few studies on how to integrate graphics-rich information into an in- dexing process. For instance, in this case, it is crucial to be able to index not only on textual labels but also on symbols or even larger graphical components. This in turn requires efficient ways of recognizing symbols [5] or at least identifying symbol signatures. The relatively low volume of work in this area is probably due to the huge variety of symbols encountered, depending on the type of documentation to be processed. Also, the large vari- ability of the symbols encountered in technical drawings requires the use of invariant descriptors for identification and recognition and hence the development of efficient and useful invariants [29]. Simple geometrical characteristics have been used to classify the shape of objects: the degree of compactness and the degree of ellipticity (the axes being given by the moments of order 0 to 2 [26]). Nevertheless, these fea- tures and their combination often yield inconsistent re- sults. The perimeter has a strong effect on the computa- tion of compactness, and when the drawing is not sharp, the use of such a feature may yield a bad classification. Furthermore, approaches based on feature descriptors [3, 10,14] are sensitive to noise and are not robust to occlu- sion. A polygonal approximation of the objects could be a solution to this problem. However, it induces loss of infor- mation, which may result in lower recognition rates. The degree of ellipticity is also not suited to the classification of this type of object. Maes [16], for example, has pre- sented a string-matching technique to the problem of rec- ognizing and classifying polygons; but the strengh of this