For years, anthropologists and facial surgeons have tried to identify the most important features defining the cranial-facial geometry of humans (Farkas 1981). The problem is not simple, considering that a small part of a human face can express millions of different shapes (Altobelli 1994).

Facial surgeons use sets of landmarks (Figure 7.1) in the skull and the face to perform reconstructive or corrective surgery. Forensic artists use similar sets of landmarks when they sculpt facial clay models to identify the remains of individuals, or when they compose age-adjusted photographs of missing

Computer-Graphic Facial Reconstruction John G. Clement and Murray K. Marks, Editors

Copyright © 2005, Elsevier Ltd All rights reserved

Figure 7.1

Facial landmarks can be used to establish points of reference for digital analysis. Using these landmarks, specific regions in a sample's face could be located and matched against regions stored in databases. From Farkas (1981).

Computer-Graphic Facial Reconstruction John G. Clement and Murray K. Marks, Editors

Copyright © 2005, Elsevier Ltd All rights reserved children. Landmarks are anatomical locations in the skull or the face where identifiable concavities or convexities exist to accommodate facial features such as lips or eyes, or to provide supporting points for the insertion of muscular tissue into bony tissue. Research has been conducted to identify the location and shape of the most appropriate landmarks for forensic analysis and plastic surgery. Tables have been published describing distances and arcs between facial landmarks in the head, face, eye orbits, nose, mouth, and ears, which use sex and age as predicting variables (Farkas 1981). Tables of cranial landmarks that use sex and age as predicting variables are also available (Saksena 1987).

Forensic experts know that strong anatomical relationships exist between certain facial and cranial landmarks. For example, Farkas' facial glabella (g) corresponds to Iscan's bony glabella. Farkas' facial gonion (go) is identical to Iscan's bony gonion, while Farkas' facial endocanthion (en) corresponds to the bony landmark (mo) used in cephalometry (Farkas 1981, Iscan 1993). However, no statistical studies have been conducted to validate or characterize the relationships between facial and cranial landmarks. Likewise, a statistical correlation between the bony-tissue and soft-tissue landmarks around eye orbits, nose, mouth, ear, and head has yet to be made. Research into assessing the most probable landmark values and interlandmark proportions, given conditioning sets richer than those used by Farkas (sex and age), requires significant effort. Studies relating facial or cranial features given anthropo-metric information, such as ethnicity, race, height, or combinations of these gathered from parents, are also not available. The importance of these assessments is clear when considered within the context of current methods used for forensic reconstruction of faces from skulls, or for composition of age-adjusted photographs.

Forensic artists create facial models by superimposing clay at specific locations of the skull, aligned around cranial and facial landmarks. The amount and shape of clay is for the most part decided by the artists on the basis of experience and the available information about the victim, such as sex, race, ethnicity, estimated age, skeletal type, bone constitution, hair, etc. However it is well known that most of the information needed to recognize a face is captured in less than 10 per cent of the tissue, particularly around the eyes, nose, lips, and ears. Nonetheless, most forensic artists decide the amount of clay and facial traits at these regions on a subjective basis, using heuristic rules such as "Vietnamese are thinner than Caucasians", "blacks have wider noses than Caucasians", and so on. Since the number of facial traits is large, and the number of interlandmark proportions is even larger, it is not rare to find traces of "preferred" traits among the faces reconstructed by the same artist. Clearly, a method for selecting the most probable facial features, given anthro-pometric information, would be a tremendous asset.

Our research uses Bayesian networks to narrow down the set of most probable features given anthropometric information. The premise is that a set of Bayesian networks may assist humans to reconstruct faces from skulls or to compose age-adjusted photographs. Not having normative studies relating facial landmarks to other parameters, Bayesian networks can provide the basis for assessing the correspondences between facial landmarks to other parameters, including cranial landmarks, race, ethnicity, age, skeletal frame, etc.

For the estimation of the most probable face of a missing child, given early photographs, three-dimensional (3D) models can be created from photographs or from artist-composed sketches. Facial features can be extracted from these models and given to a morphing program, which could adjust the features against facial norms modeled by a Bayesian network matching the characteristics of the child. The Bayesian network could also estimate the most probable age-induced changes in the facial features of the child, given the known parameters. The estimated features could be given to the morphing program to adjust them in order to blend the estimated age-caused facial growth into the original face.

A Bayesian network is shown near the end of this chapter, in Figure 7.11. In this context a Bayesian network is a graph created from the anthropo-metric data and expert knowledge. The network can explain how a set of variables, in this case the most probable features of a person, can be obtained given known values of sex and age. In the network of Figure 7.11, each outer node represents a variable associated to a facial index and related to some specific landmarks.

Information about the shape of a skull can be obtained from a set of cranial images containing transversal slices. These images can be processed to extract the information of the cranial contours in order to build a 3D model. Once that model is created, a matching template process can locate discrete landmarks in the model. The skull model can be updated each time new evidences are fed to the Bayesian networks. Figure 7.2 shows the main stages of this process.

A related problem is the estimation of indices associated with the facial landmarks given the shape of the skull. A series of transversal cuts of a human skull can be processed in order to get a 3D model of the skull. The landmarks can be automatically located from the 3D model, and the thickness of the tissue and the relation between the landmarks can be displayed.

This chapter outlines a method to model a human skull (by building its graphic model) and a method to locate templates of facial regions (such as nasal fissures, ocular fissures, etc.). The chapter also discusses how a set of cranial landmarks' locations are deduced from the spatial position of the located templates. This method will permit automatic updates of the results given by a Bayesian network. Section 2 of this paper briefly describes the techniques

3D model with located landmarks

3D model with located landmarks

Figure 7.2 Main stages involved in obtaining a graphical model with the most probable features of a face.

used to process the initial images. Section 3 shows how a 3D model of the skull is built. Section 4 presents a technique to locate discrete landmarks on the model. Section 5 discusses a method used to estimate indices using a Bayesian network. Section 6 gives the conclusions derived from this work.

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