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This paper introduces a supervised discriminant Hausdorff distance that fits into the framework for automatic face analysis and recognition proposed in [A. Pujol et al.,2002]. Our proposal relies solely on face shape variation contrarily to most of the successful model-based approaches, and results show comparable performance to them. The whole framework is based in a new set of Hausdorff measures and defines face-shape based similarity measures and supervised criteria to add discriminant capabilities to the Hausdorff distance. The paper presents experimental results supporting the proposed methodologies.