Luigi P. Cordella

A (sub)graph isomorphism algorithm for matching large graphs

We present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs. A first version of the algorithm has been presented in a previous paper, where we examined its performance for the isomorphism of small and medium size graphs. The algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs; its features are analyzed in detail with special reference to time and memory requirements. The results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented, confirming the effectiveness of the approach, especially when working with large graphs.

Performance evaluation of the VF graph matching algorithm

The paper discusses the performance of a graph matching algorithm tailored for dealing with large graphs in computer vision without using information about the topology of the graphs to be matched. The algorithm, presented in more detail in other papers (and publicly available on the WWW as VF), is now discussed with reference to its computational complexity and memory requirements. The performance analysis is carried out by theoretically characterizing the matching time and the required memory in the best and worst cases. The theoretical analysis is completed by tests on a database of graphs randomly generated. The algorithm is compared with the one proposed by Ullmann (1976): experimental results confirmed the theoretical expectations, highlighting the overall efficiency of the algorithm. Some results obtained by researchers who recently used the algorithm in application domains requiring a massive use of graph matching techniques are finally reported.

From Local Maxima to Connected Skeletons

In picture processing it is often convenient to deal with a stick-like version (skeleton) of binary digital images. Although skeleton connectedness is not necessary for storage and retrieval purposes, this property is desirable when a structural description of images is of interest. In this paper a parallel procedure is described which, applied to a connected image, originates a connected skeleton made by the union of simple digital arcs. The procedure involves a step by step propagation of the background over the image. At every step, contour elements either belonging to the significant convex regions of the current image or being local maxima of the original image are selected as skeleton elements. Since the final set so obtained is not ensured to be connected, the configurations in correspondence of which disconnections appear are investigated and the procedures to avoid this shortcoming are given. The presence of the whole set of local maxima among the skeleton elements ensures the possibility of recovering the original image by means of a reverse distance transform. The details of the program implementing the proposed algorithm on a parallel processor are finally included.

Reliability Parameters to Improve Combination Strategies in Multi-Expert Systems

Abstract: Recognition systems based on a combination of different experts have been widely investigated in the recent past. General criteria for improving the performance of such systems are based on estimating the reliability associated with the decision of each expert, so as to suitably weight its response in the combination phase. According to the methods proposed to-date, when the expert assigns a sample to a class, the reliability of such a decision is estimated on the basis of the recognition rate obtained by the expert on the chosen class during the training phase. As a consequence, the same reliability value is associated with every decision attributing a sample to a same class, even though it seems reasonable to take into account its dependence on the quality of the specific sample. We propose a method for estimating the reliability of each single recognition act of an expert on the basis of information directly derived from its output. In this way, the reliability value of a decision is more properly estimated, thus allowing a more precise weighting during the combination phase. The definition of the reliability parameters for widely used classification paradigms is discussed, together with the combining rules employing them for weighting the expert opinions. The results obtained by combining four experts in order to recognise handwritten numerals from a standard character database are presented. Comparison with classical combining rules is also reported, and the advantages of the proposed approach outlined.

Symbol recognition in documents: a collection of techniques?

Abstract. Various techniques have been used or simply proposed, during the last 10 years, for recognizing symbols in documents. Differences depend on both application field and researchers cultural background. We bring the methods most commonly used in the representation, description, and classification phases to the attention of the reader, and we discuss the main recognition strategies. We briefly review a number of papers, that are representative of the various approaches.

Recovering dynamic information from static handwriting

It is generally agreed that the advantage of on-line character recognition methods with respect to off-line ones mostly relies on the availability of dynamic information. This mainly concerns the order in which the strokes forming characters have been drawn. In this paper we present and discuss a method which attempts, in the off-line case, to recover part of the lost script dynamics. The method makes it possible to reconstruct one of the most likely trajectories followed by the writer while drawing characters. It is based on a suitable implementation of good continuity criteria which take into account direction, length and width of the strokes making up characters. The algorithm either subdivides or unfolds the digital ribbon forming isolated characters as well as groups of connected characters, by solving the ambiguities which arise at every joint. Experimental results are reported and discussed.

Visual Form 2001

This short paper surveys methods for planar shape recognition and shape smoothing and processing invariant under viewing distortions and possibly partial occlusions. It is argued that all the results available on these problems implicitly follow from considering two basic topics: invariant location of points with respect to a given shape (i.e. a given collection of points) and invariant displacement of points with regard to the given shape.

A method for improving classification reliability of multilayer perceptrons

Criteria for evaluating the classification reliability of a neural classifier and for accordingly making a reject option are proposed. Such an option, implemented by means of two rules which can be applied independently of topology, size, and training algorithms of the neural classifier, allows one to improve the classification reliability. It is assumed that a performance function P is defined which, taking into account the requirements of the particular application, evaluates the quality of the classification in terms of recognition, misclassification, and reject rates. Under this assumption the optimal reject threshold value, determining the best trade-off between reject rate and misclassification rate, is the one for which the function P reaches its absolute maximum. No constraints are imposed on the form of P, but the ones necessary in order that P actually measures the quality of the classification process. The reject threshold is evaluated on the basis of some statistical distributions characterizing the behavior of the classifier when operating without reject option; these distributions are computed once the training phase of the net has been completed. The method has been tested with a neural classifier devised for handprinted and multifont printed characters, by using a database of about 300000 samples. Experimental results are discussed.

Graph matching: a fast algorithm and its evaluation

A graph matching algorithm is illustrated and its performance compared with that of a well known algorithm performing the same task. According to the proposed algorithm the matching process is carried out by using a state space representation: a state represents a partial solution of the matching between two graphs, and a transition between states corresponds to the addition of a new pair of matched nodes. A set of feasibility rules is introduced for pruning states corresponding to partial matching solutions not satisfying the required graph morphism. Results outlining the computational cost reduction achieved by the method are given with reference to a set of randomly generated graphs.

An efficient algorithm for the inexact matching of ARG graphs using a contextual transformational model

The paper illustrates an algorithm for the inexact matching of attributed relational graphs. A sample graph is considered matchable with one of the prototypes if, by using a defined set of syntactic and semantic transformations, it can be made isomorphic to the graph of the prototype. The applicability of a transformation is contextually defined, i.e. each transformation can be defined with reference to a prototype, and can be applied only when the sample graph is being matched with that prototype. The reduction of the computational complexity with respect to a brute-force approach is given with reference to an OCR application.