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It may thus be helpful to introduce on the field of study a metric which is not the natural Euclidian one. In this paper, we are especially concerned with a particular metric : the géodésie distance function. Expérience has shown that this metric is well suited to deal with connectivity problems, and provides rigorous définitions of topological transformations performed by auto- matic image analysers capable of manipulating itérative algorithms (e.g., reconstruction of particles from masks, etc.). It should be noted that in a field of study with its géodésie metric, a simply connected particle behaves as if it were convex. This fact is very helpful in extending to particles of any shape the transformations and measurements which are usually defined only for convex particles (e.g. length of a particle, etc.). In this paper, we have tried to présent ail these différent con¬ sidérations in an intuitive way. Some of them raise several mathematical difficulties which are either not presented here, or avoided by the simple assumption that ail of the objects under study contain their own boundary. For more information, see (1). 2 - HOW LONG IS A FIBRE ? In image analysis, many specimens contain long narrow particles (e.g. glass or asbestos fibres, eutectic alloy lamellae, neuron arms, etc.). Workers concerned with such specimens usually want to know the distribution function of the length of these particles. But what is the length of a particle ? Let us consider such a particle. In order to compute its length, we can measure the distance between its two ends (see figure 1-1). This method unfortunately does not work for round or twisted fibres (see fig. 1-2). Figure 1 ; The définition of the length of a particle as the length of the segment of line between its two ends is not always effective.