Abstract: In order to reconstruct an angiographic arborescence, two images are acquired according to orientations substantially perpendicular to each other of an arborescence (IVA,CX) to be reconstructed. By a follow-up operation of the segments, the coordinates of the arborescence segments are reconstructed. Indeterminations resulting from the too small number of acquisitions effected are removed by emitting hypotheses (AV, IV) on forms deductible from the recorded acquisitions and by verifying those hypotheses with respect to a model. The model has the particularity of being structural, that is to say substantially descriptive. In this structural model, each arborescence segment is characterized by a number, by a direction (49-54), and by the numbers, direction and number of segments preceding or following it. By operating in this way, it has been proved that angiographic images may be reconstituted in a more rapid and simple way.