THEORETICAL ADVANCES B. Raducanu Æ M. Gran˜a Æ F. X. Albizuri Æ A. d’Anjou A probabilistic hit-and-miss transform for face localization Received: 14 July 2003 / Accepted: 10 February 2004 / Published online: 18 May 2004 Ó Springer-Verlag London Limited 2004 Abstract Face localization is needed for any face pro- cessing procedure whose applications range from bio- metric identification to content-based image retrieval. It consists in giving the image coordinates of the face. In this paper we propose a probabilistic pattern matching procedure for face localization in greyscale images sim- ilar to the morphological hit-and-miss-transform (HMT), which we call probabilistic HMT (PHMT). This procedure is defined on the morphological multiscale fingerprints (MMF), which are image features extracted from the morphological erosion/dilation scale spaces. The face location is estimated as the maximum likeli- hood image window matching both erosive and dilative MMF models of the object. The MMF models are computed at a discrete set of scales. The MMF models may be built up from a small set of training face images and do not involve numerically sophisticated training algorithms. Training does not use non-face sample images. Therefore resampling is not needed for the construction of the MMF models. The experimental results on the NIST Mugshot Identification Database endorse our claims about the accuracy and robustness of the proposed procedure. Keywords Computer vision Æ Face localization Æ Hit-and-miss transform Æ Mathematical morphology Æ Morphological scale spaces Introduction Object detection can be defined as deciding whether some visual pattern corresponding to the object occurs in the image (pattern detection). Object (pattern) local- ization consists in giving the image coordinates of its location. Pattern detection is an unavoidable step for pattern localization and pattern recognition. Whatever the procedure employed, pattern detection is a two-class classification problem [1, 2], in which one of the classes corresponds to the universal set minus the patterns to be detected. Two basic approaches of giving answers to the detection problem exist. The first is the optimal Bayesian decision approach which tries either to model the a posteriori distributions of both classes so that the detection decision is given by the maximum a posteriori class probability, or to construct some equivalent deci- sion function (such as it is the case with artificial neural networks or ANN). The second kind of approach at- tempts to model only the positive class. The detection decision then becomes a hypothesis testing upon the pattern class conditional probability. It becomes a maximum likelihood (ML) approach when the locus of the global maximum of the conditional probability over the image gives the location of the detected object. The advantage of hypothesis testing is the simplicity of the model parameter estimation procedures. Its disadvan- tages are a greater ratio of false alarms and a lack of robustness. In this paper, we propose a procedure based on combining hypothesis testing with probabilistic models constructed from dual image features. The idea of combining dual features follows an analogy with the morphological HMT and it is intended to improve the robustness of hypothesis testing detection approaches. Here the basic test is performed on the similitude of the MMF spatial distributions in the test image relative to the model constructed from a set of training images. A recent review of face detection and localization is given in [3]. The classical representatives of the ap- proaches modelling both face and non-face classes are the ones based on artificial neural networks (ANN) [4, 5, 6, 7, 8, 9], either multilayer perceptron or self-organizing maps. The ANN is used to build up a non-parametric model that realizes the decision surface between the positive and negative classes. More recently, Liu [10] uses the concept of support non-faces, which are non- face images that lie within the face image region, to train B. Raducanu Æ M. Gran˜a (&) Æ F. X. Albizuri Æ A. d’Anjou Department of CCIA, Universidad del Pais Vasco, Spain E-mail: ccpgrrom@si.ehu.es Pattern Anal Applic (2004) 7: 117–127 DOI 10.1007/s10044-004-0207-4