Hounsfield values of various substances. (Hounsfield, 1980)

## 1. Introduction

In crime scenes and accidents, the standard operating protocols for personal identification is not difficult when the entire body is found. As a result, the investigators can directly collect the sample of the decrease such as facial photograph, DNA, fingerprint and dental record in order to compare to possible relatives or with ante-mortem profile (De Valck, 2006). However, the investigators are not always lucky. In severe accidents such aircraft crashes, only little information of the decrease is available, the skin and soft tissue may be completely burnt out and the skeleton can be broken into small pieces due to the impact. The skeleton examination in historical sites by archaeologists presents even more complication. The archaeologists need not only to identify general aspects of the skeleton, for instant age, sex, cause of death, stature and race, but also to estimate the period of death and the possibility to discover the particular person that might be significant in the history.

Several techniques have been applied to assist the identification of the decrease ranging from the simplest technique which may acquire the evidence from the personal belonging until using the advance scientific techniques. These techniques can be generally categorized into two methods, invasive and non-invasive. The invasive method includes biochemical analysis, microscopy, accelerator mass spectrometry radiocarbon dating (with standard C-14), ancient DNA analysis, histology and endoscope whereas the non-invasive technique involved the aid of engineering technologies such as radiographic analysis and computed tomography (CT) examination.

From 1975 – 2005, the archaeological researches had been increasingly conducted by means of non-invasive techniques which 112 of 245 researches have applied the non-invasive technique and the trend of investigation gradually moved from invasive to non-invasive examinations (Zweifel, et al., 2009). The first non-invasive technique has been presented to the public in 1896 which the radiographic analysis was used to examine the ibis mummy in Belgium (Van Tiggelen, 2004). Soon after that, archaeologist realized the importance of radiological technique and applied broadly to examine great numbers of mummy (Dedouit, et al., 2010; Friedrich, et al., 2010; Recheis, et al., 1999; Zweifel, et al., 2009). One main advantage of radiography includes the ability to access general aspects of mummy without releasing the bandages which may be destroyed important features or contaminated. In the early 1900s, another non-invasive medical examination device, computed tomography scanner, has been invented by Alessandro Vallebona, but the technology has remained unpopular until the 1970s which modern era of computed tomography scanner began (Hill, 2009). Not too long, computed tomography scanner became an effective tool in examination the autopsy. The computed tomography generally relies on medical imaging processing combined with reverse engineering principles which the object is captured the profile and presented the virtual three-dimensional models in computer. With these advanced features, the perspective of archaeology and forensic medicine has changed into three-dimensional aspect. Consequently, The two-dimensional radiographic image occlusion and the problem such uncertainty from bias of investigator in direct measurements are eliminated.

Apart from the advantages of computed tomography in forensic medicine, it also becomes an effective clinical diagnosis device in many hospitals. The use of three-dimensional model allows the surgeon to examine the abnormality of organs in any configurations which the two-dimensional technique may be inaccessible. Moreover, the three-dimensional models can be used to simulate the surgical operation prior surgery (Fürnstahl, et al., 2010), subsequently reduce operating time and increase safety of patients. Alternative uses of computed tomography include morphometric study (Chantarapanich, et al., 2008; Mahaisavariya, et al., 2002) and the evaluation the risk of implant usage (Mahaisavariya, et al., 2004; Sitthiseripratip, et al., 2003)

The purpose of this chapter is to present and discuss the medical imaging and reverse engineering techniques by means of demonstrating the application in craniometric study. Obviously, recent craniometric studies have been employed by two-dimensional techniques or direct measurement (Steyn & Işcan, 1997; Deshmukh & Devershi, 2006; Dayal, et al, 2008; Sangvichien, et al., 2008; Matamala, et al, 2009) such as the use of spreading caliper, sliding vernier calliper, mandibulometer and standard flexible steel tape. The diverse mentioned measurement techniques reflect the lack of engineering aids which the current trend in forensic medicine need the advanced technologies to provide the accurate measurements. Therefore, the scope of demonstration includes the brief detail of reverse engineering as to provide for who may not familiar with, data acquisition technique using computed tomography scanner, measurement of skull anatomical parameters and sex determination method based on logistic function. By this way of demonstration, the overview of forensic medicine by aid of advance medical imaging and reverse engineering is obtained.

## 2. Reverse engineering

Reverse engineering has been widely applied several years in clinical fields and forensic medicine (Aamodt, et al., 1999; Aghayev, et al., 2008; Fürnstahl, et al., 2010). Initially, reverse engineering was first used in free-form product designs which the conventional “Forward Engineering” has limited drawing functions and time consumption. Product design based on “Forward Engineering”, the process involves turning the conceptual product design to physical product whereas reverse engineering is inversed (Zhou & Xi, 2002).

The process of reverse engineering involves turning the physical product back to the virtual models (normally three-dimension) (Li, et al., 2002; Várady, et al., 1997). From the three-dimensional virtual models, the conceptual design can be obtained. Reverse engineering can be described as two phases which are digitization and reconstruction phase, as summarized in Fig. 1. The digitization phase involves the data acquisition of the physical model using various types of scanner. The initial geometry from the scanner is then obtained in three forms, point clouds, polygon model and series of image depending on the acquisition technique of each scanner. In the reconstruction phase, the obtained data is processed in order to reconstruct the three-dimensional model. with “At this step, the elimination of noise data and filtering of unnecessary data may also be performed. For the production phases, it may be added as a final step in reverse engineering. This phase employs various manufacturing processes to fabricate the three-dimensional virtual model. However, this phase may not be mandatory, because sometime the geometry is only stored in database without any further processing.

The digitization methods can be categorized into two approaches which are tactile approach (contact method) and non-contact approach (Li, et al., 2002; Várady, et al., 1997). For tactile approach, the device contacts to the physical object directly whereas the non-contact approach uses the medium in digitization instead without contact of device.

The characteristic of tactile approach is relatively simple. Touch probe is used in conjunction with robotic mechanism such as coordinate measurement machine (CMM), articulated arm or computer numerical control (CNC) devices to determine the position of the object (Cartesian coordinate). The accuracy is considered to be a main advantage of tactile approach, nevertheless the digitization process is quite slow and difficult to digitize complex geometry. A wide range of object can be applied with this approach regardless of color, shininess and transparency, this approach is not appropriate for deformable materials.

In non-contact approach, the medium is used to measure the physical object using the principle of reflection or penetration. Laser beam and white light are medium sources commonly found in many three-dimensional scanners and they rely on the principle of reflection. The medium travels from the generator to the object before reflects and transmits to the receiver unit. The determination of geometry can be processed using at least one two-

dimensional images combined with some optical parameters such as reflection angle, distance and time of flight. The initial geometry is presented in form of cloud point or of polygon model. Use of laser beam and white light has advantage in fast digitization and continuous data, but too shiny and transparent object present complication.

Even the laser beam and white light systems are applied in many forensic studies (Park, et al., 2006; Thali, et al., 2003; Vanezis, et al., 2000), but probably, the most efficient system for forensic studies is the use of non-contact device based on principle of penetration. This system uses the medium that can go though the object to capture both internal and external geometries. The most popular device is computed tomography scanner which involves the use of X-ray.

The digitization process initializes the transmission of the X-ray through the object. A set of data acquisitions is performed with the constant interval throughout entire object which subsequently give a series of slice image (Hounsfield, 1980). Each slice contains the information of object’s position and the value of Hounsfield unit (HU). The density of object is proportional to the Hounsfield value. The higher Hounsfield value indicates high-density object such as enameled and cortical bone whereas the lower Hounsfield value indicates low-density object such as cancellous bone, fat and soft tissue. Various Hounsfield values of various substances are given in Table 1. In order to reconstruct the three-dimensional model, the optimal Hounsfield values must be selected (threshold). After that the threshold regions of each slice are combined to construct the volumetric model.

For the computed tomography device, the speed of digitization and ability to examine the internal topology are considered to be superior, but the artifact (noise data) caused by metallic structure is drawback.

Substances | Hounsfield values |

Air | -1000 |

Fat | -70 to -90 |

Water | 0 |

Tissue | +20 to +35 |

Blood Volume | Approx. +40 |

Bone | +900 |

## 3. Data acquisition of skull

Specimen of 104 dry cadaveric skulls donated by the Department of Anatomy, Faculty of Medicine, Khon Kaen University, Thailand is used to demonstrate the application of advanced medical imaging and reverse engineering technologies in craniometric study. The cadaver includes 63 males with average age of 55.16 years (standard deviation 18.38 years) and 41 females with average age of 49.00 years (standard deviation 17.94 years). The age rages from 17–81 years at the time of death. The skulls are placed in acrylic box with a set of four. The reverse engineering technique by means of spiral computed tomography scanner (Siemens AG, Germany) is used to capture the profile of each skull as shown in Fig. 3. The data acquisition protocol is axial scan with tube voltage of 120 kV and tube current of 100 mA. The digitization is performed with 1.5-mm slice thickness and the reconstruction is done at 1-mm thickness. Each slice contains the volumetric data that represent the density and position (contour) of the skull. The computed tomography images are then processed with medical image processing software (Mimics, Materialise NV, Belgium). To begin the reconstruction of three-dimensional model, a proper Hounsfield value (normally +900 for bone structure) is selected. After that, the threshold regions are used to calculate the complete topology of three-dimensional skull. The reconstruction process of skull model is illustrated in Fig. 4.

## 4. Three-dimensional computerized craniometric study

The anatomical landmarks in craniometric study are categorized in to median and bilateral landmarks (Rooppakhun, et al., 2010). The median landmarks are approximately located on sagittal plane. Each of them has only one location. There are 13 median landmarks which the specific definitions can be described as follows:

*Glabella (GL)*- the most anterior point of frontal bone between supraorbital in the sagittal plane.*Bregma (BR)*- the crossing of the coronal and sagittal sutures on the top of the skull.*Opisthocranium (OPC)*- the most posterior point in midline of inion bone which length of the skull is maximum when measure from Galbella point.*Nasion (NA) -*the intersection point of the internasal and frontonasal sutures in the sagittal plane.*Opistion (OPS)*- the most posterior midsagittal point on the posterior margin of the foramen magnum.*Basion (BA)*- the most anterior point of the great foramen magnum in the sagittal plane.*Orale (OR)*- the midpoint on the intersection of posterior alveolar sockets rim of the cavities of two upper central incisors.*Prosthion (PR)*- the lowest, most anterior point on the alveolar portion of the premaxilla, in the median plane, between the upper central incisors.*Staphylion (STA)*- point in the medial line (interpalatal suture) of the posterior part of the hard palate where it is crossed by a line drawn tangent to the curves of the posterior margins of the palate.*Nasospinale (NAS)*- the lowest point of lower anterior nasal aperture in mid-sagittal plane.*Gnathion (GN)*- The midpoint on the lower border of the mandible in the sagittal plane.*Pogonion (PG)*- The most projecting point of the chin in the standard sagittal plane.*Infradentale (ID)*- The anterior superior point on the mandible at its labial contact between mandibular central incisors.

For the bilateral landmarks, each of them is located on both sides of skull. There are 17 bilateral landmarks which the specific definitions can be described as follows:

*Euryon (EU)*- the lateral point on either side of the greatest transverse diameter of the skull.*Staphanion (ST)*- the intersection of the superior temporal line and the coronal suture.*Frontotemporale (FT)*- the most anterior point on either side of temporal crest of the minimum transverse breadth of frontal bone.*Bolton (BO)*- The superior point of the curvature between occipital condyle and posterior margin of foramen magnum.*Orbitale (ORB)*- the most inferior point of each infraorbital rim.*Ectoconchion (EC)*- the most lateral point on each orbital's margin where a line running parallel to upper orbital border cut the lateral orbital margin.*Maxillo-frontale (MF)*- the intersection point on anterior lacrimal crest and fronto-maxillary sutures.*Supraorbitale (SOR)*- the most superior point of each superior orbital rim.*Zygonion (ZG)*- The most lateral point on the outline of each zygomatic arch.*Zygomaxillare (ZM)*- The most interior point on each zygomatico-maxillary sutures.*Nasal (NS)*- The most lateral point on each nasal's margin where maximum nasal breadth.*Endomolare (ENM)*- the most medial point of internal curvature surface of alveolar ridge corresponding to second molar tooth.*Coronion (CO)*- The most superior point on each coroniod process.*Condylion superior (CS)*- the most superior point on each mandibular condyle.*Conlylion laterale (CDL)*- the most lateral point on each mandibular condyle.*Gonion (GO)*- the point at each mandibular angle that is defined by dropping a perpendicular from the intersection point of the tangent lines to the posterior margin of the mandibular vertical ramus and inferior margin of the mandibular body or horizontal ramus.*Laterla infradentale (LID)*- the midpoint of a line tangent to the outer margins of the cavities of the lateral incisor of each lower canine teeth.

In order to better understand the previous described definitions, every landmark is also illustrated in Fig. 5.

Each of the three-dimensional models of skull is used to determine the anatomical landmark according to previous description. Only one investigator locate the entire landmarks in every skull to avoid uncertainty of intra-observer. The anatomical landmarks are then used to obtain 40 craniometric parameters as shown in Table 2. The measurements are interpreted using statistical analysis and reported in form of average values and standard deviation regarding to gender. In order to distinguish craniometric parameters of each gender, an unpaired t-test is utilized for analysis. A p-value < 0.05 is a significant level that used to determine the difference. In addition, the linear regression and the correlation coefficient are also used for the pair-wise tests.

As also shown in Table 2, the craniometric parameters of male are larger than female. Thirty-one of forty parameters show the statistical significant differences among both genders, especially, Maximum cranial breadth, Facial length, Orbital height-left, Orbital height-right, Palatal breadth, Bicoronion breadth, Bizygometic breadth, Maxillary breadth, Upper facial height, Orbital breadth-left, Orbital breadth-Right, Nasal height, Bicondylar breath, Bi-gonion breadth, Coronion height-left, Coronion height-right, Mandibular body length-left, Mandibular body length-right, Maximum mandibular length-left and Maximum mandibular length-right which present the p-value << 0.001. For Maximum cranial breadth, Facial length, Orbital height-left, Orbital height-right, Palatal breadth, Bicoronion breadth are considered to be relatively different as the p-value < 0.01. The parameters such Ramus height-left, Ramus height-right, Symphysic height shows some degrees of significance. In addition, nine parameters do not present the statistical differences which are Maximum frontal breadth, Anterior inter-orbital breadth, Nasal breadth, Palatal length, Mandibular angle-left, Mandibular angle-right, Notch length-left, Notch length-right, and Symphysic breadth.

From the pair-wise tests, the correlations of craniometric parameters are different among male and female population. Table 3 and Table 4 show the sample of correlations of craniometric parameters which correlation coefficient (r) are above 0.500. In both populations, the bilateral anatomy presents some degrees of correlation which can be signified the facial symmetry. The linear regression equations are considered to be useful to predict the craniometric parameters in forensic medicine. For example, the defected skull usually miss some landmarks, the use of known craniometric parameters can be used to determine the missing parameters. However, it should be noticed that the obtained missing parameters may not be always precise. The possibility of being can only be determined, but the accuracy strongly depends on the correlation coefficient. The regression scatters plot and 95% interval bands of some pair-wise tests are plotted in Fig. 6 and Fig. 7.

Craniometric Parameter | Landmark | Average (S.D.) | p-value | |

Male | Female | |||

Maximum cranial length | GL-OPC | 173.6 (5.2) | 165.4 (6.4) | << 0.001 |

Maximum cranial breadth | EU L -EU R | 144.9 (5.6) | 141.2 (5.5) | 0.001361 |

Maximum frontal breadth | ST L -ST R | 115.8 (6.7) | 113.3 (6.7) | 0.070663 |

Minimum frontal breadth | FT L -FT R | 94.9 (5.1) | 91.4 (4.9) | 0.000584 |

Basion-brema height | BA-BR | 138.6 (4.8) | 132.4 (5.2) | << 0.001 |

Nasion-basion length | NA-BA | 101.8 (4.0) | 96.0 (3.4) | << 0.001 |

Foramen magnum length | BA-OPC | 36.7 (2.1) | 34.5 (2.4) | 0.000006 |

Foramen magnum breadth | BO L -BO R | 30.5 (2.1) | 28.9 (1.8) | 0.000051 |

Nasion-bregma length | NA-BR | 112.9 (4.2) | 107.3 (6.0) | 0.000002 |

Facial length | BA-PR | 96.1 (5.4) | 92.9 (5.5) | 0.004704 |

Bi-orbital breadth | EC L -EC R | 97.4 (3.8) | 94.0 (3.8) | 0.000024 |

Bi-zygometic breadth | ZG L -ZG R | 133.7 (5.1) | 127.7 (5.2) | << 0.001 |

Maxillary breadth | ZM L –ZM R | 104.5 (5.3) | 99.1 (4.9) | 0.000001 |

Upper facial height | NA-PR | 70.3 (4.2) | 66.2 (4.6) | 0.000019 |

Orbital breadth-left | EC L -MF L | 41.2 (2.2) | 39.6 (2.4) | 0.000743 |

Orbital breadth-right | EC R -MF R | 41.5 (2.0) | 39.8 (2.0) | 0.000044 |

Orbital height-left | ORB L -SOR L | 36.2 (2.3) | 34.7 (2.5) | 0.002714 |

Orbital height-right | ORB R -SOR R | 36.3 (2.5) | 34.9 (2.1) | 0.004341 |

Anterior inter-orbital breadth | MF L -MF R | 21.0 (2.2) | 20.7 (2.4) | 0.497642 |

Nasal breadth | NS L -NS R | 27.0 (2.2) | 26.8 (2.2) | 0.632101 |

Nasal height | NA-NAS | 52.7 (3.0) | 49.6 (3.1) | 0.000003 |

Palatal length | OR-STA | 42.6 (4.2) | 42.6 (4.4) | 0.952028 |

Palatal breadth | ENM L -ENM R | 39.1 (3.1) | 37.6 (2.4) | 0.006430 |

Bi-coronion breadth | CO L -CO R | 98.6 (5.2) | 94.3 (5.8) | 0.002652 |

Bi-condylar breadth | CDL L -CDL R | 123.1 (5.2) | 118.7 (5.1) | 0.000870 |

Bi-gonion breadth | GO L -GO R | 99.1 (6.3) | 92.8 (6.2) | 0.000113 |

Coronion height-left | CO L -GO L | 62.3 (4.9) | 57.2 (4.8) | 0.000065 |

Coronion height-right | CO R -GO R | 62.83 (5.2) | 57.5 (4.8) | 0.000043 |

Mandibular angle-left* | CS L -GO L -GN | 112.4 (5.1) | 113.9 (6.4) | 0.298443 |

Mandibular angle-right* | CS R -GO R -GN | 112.4 (5.5) | 112.8 (5.6) | 0.759332 |

Mandibular body length-left | GO L -PG | 92.0 (4.8) | 87.0 (4.9) | 0.000083 |

Mandibular body length-right | GO R -PG | 92.5 (4.9) | 87.6 (5.0) | 0.000128 |

Maximum mandibular length-left | CS L -PG | 119.8 (6.1) | 114.6 (5.1) | 0.000383 |

Maximum mandibular length-right | CS R -PG | 120.6 (6.1) | 115.0 (5.0) | 0.000079 |

Notch length-left | CO L -CS L | 35.3 (2.7) | 34.1 (4.2) | 0.202213 |

Notch length-right | CO R -CS R | 35.1 (2.7) | 33.7 (4.0) | 0.105663 |

Ramus height-left | CS L -GO L | 58.2 (5.0) | 55.2 (4.5) | 0.010815 |

Ramus height-right | CS R -GO R | 58.3 (4.6) | 55.3 (4.7) | 0.010342 |

Symphysic breadth | LID L -LID R | 23.1 (6.0) | 23.7 (6.0) | 0.689146 |

Symphysic height | GN-ID | 31.6 (3.5) | 26.5 (3.1) | 0.011128 |

Craniometric Parameter (x vs. y) | Regression (Correlation, r) | |

Maximum mandibular length-left vs. -right | y = 0.916x + 10.470 | (0.920) |

Mandibular angle-left vs. -right | y = 0.976x + 2.630 | (0.904) |

Mandibular body length-left vs. -right | y = 0.883x + 11.227 | (0.860) |

Coronion height-left vs. -right | y = 0.908x + 6.233 | (0.858) |

Orbital height-left vs. -right | y = 0.875x + 4.561 | (0.835) |

Orbital breadth-left vs. -right | y = 0.741x + 10.969 | (0.835) |

Ramus height-left vs. -right | y = 0.724x + 16.146 | (0.835) |

Notch length-left vs. -right | y = 0.761x + 8.239 | (0.770) |

Bi-orbital breadth vs. Orbital breadth-left | y = 0.400x + 2.283 | (0.685) |

Bi-zygometic breadth vs. Bi-orbital breadth | y = 0.473x + 34.210 | (0.643) |

Upper facial height vs. Symphysic height | y = 0.485x – 2.733 | (0.636) |

Maximun cranial breadth vs. Bi-zygometic breadth | y = 0.109x + 17.063 | (0.626) |

Basion-brema heigth vs. Nasion-bregma length | y = 0.516x + 41.339 | (0.594) |

Nasal height vs. Upper facial height | y = 0.840x + 25.980 | (0.592) |

Palatal length vs. Facial length | y = 0.734x + 64.806 | (0.570) |

Nasion-basion length vs. Bi-coronion breadth | y = 0.730x + 24.429 | (0.533) |

Bi-condylar breadth vs. Bi-zygometic breadth | y = 0.528x + 67.980 | (0.570) |

Craniometric Parameter (x vs. y) | Regression (Correlation, r) | |

Mandibular body length-left vs. -right | y = 0.930x + 6.626 | (0.922) |

Maximun mandibular length-left vs. -right | y = 0.883x + 13.821 | (0.904) |

Coronion height-left vs. -right | y = 0.889x + 6.599 | (0.895) |

Notch length-left vs. -right | y = 0.831x + 5.335 | (0.880) |

Ramus height-left vs. -right | y = 0.912x + 4.958 | (0.871) |

Orbital breadth-left vs. -right | y = 0.693x + 12.370 | (0.849) |

Orbital height-left vs. -right | y = 0.728x + 9.680 | (0.839) |

Mandibular angle-left vs. -right | y = 0.737x + 28.837 | (0.832) |

Upper facial height vs. Nasal height | y = 0.522x + 15.065 | (0.765) |

Bi-orbital breadth vs. Orbital breadth-left | y = 0.478x - 5.357 | (0.759) |

Minimun frontal breadth vs. Maximum frontal breadth | y = 0.997x + 22.127 | (0.723) |

Maximun cranial breadth vs. Bi-zygometic breadth | y = 0.624x + 39.615 | (0.662) |

Symphysic height vs. Upper facial height | y = 0.784x + 42.987 | (0.641) |

Facial length vs. Palatal length | y = 0.507x - 4.481 | (0.637) |

Maxillary breadth vs. Bi-orbital breadth | y = 0.474x + 46.949 | (0.609) |

Anterior interorbital breadth vs. Bi-coronion breadth | y = 1.638x + 60.166 | (0.590) |

Maximum cranial length vs. Nasion-basion length | y = 0.314x + 43.994 | (0.584) |

## 5. Sex determination using logistic regression analysis

The determination of sex from skeleton is one of the critical components in forensic medicine as well as archaeology. The determination can be interpreted based on the average data from craniometric parameters of certain population. The accuracy of sex determination depends on several factors which one of them is osteological elements. Various osteological elements have been used to predict sex of skeleton which includes femur (Yaşar Işcan & Shihai, 1995), tibia (Steyn & Işcan, 1997), pelvis (Durić, et al., 2005), skull (King, et al., 1998), humerus (Işcan, et al., 1998; Robinson & Bidmos, 2009), hyoid (Mukhopadhyay, 2010), talus (Murphy, 2002a) and calcaneus (Murphy, 2002b). However, among aforementioned elements, the best for prediction is pelvis, follow by skull and long bone (Durić, et al., 2005, Işcan, 2005). Rather than osteological element, population variation and method of data processing (data acquisition and statistical analysis) are also among important factors.

Logistic regression analysis is a method to analysis multi-variate analysis which aims to predict the probability of occurrence of an event under consideration by fitting the raw data using to a logit function logistic curve. The advantage of logistic regression is less of parameter restrictions than discriminant analysis and regression analysis. The output from the logistic regression analysis can only be “Yes” or “No” which normally designated as “0” and “1”, respectively.

Basically, logistic regression function (Z) is written in form of

where β_{0} is called intercept and β_{1}, β_{2}, β_{3},β_{4}, …,β_{n} and β_{n+1} are regression coefficients of x_{1}, x_{2}, x_{3}, x_{4}, …,x_{n} and x_{n+1} variable, respectively. From the following logistic model of Z, the probability of event (P.E.) under consideration can be calculate through

In equation (2) e is a natural logarithm, its value is approximately 2.71828.

The probability of event varies from “0” to “1”. The near “1” value means the independent variables influences the probability of event whereas the value close to “0” means the independent variables have little effect to probability of event.

In this study, a binary logistic regression using forward stepwise is applied to determine sex based on average data of craniometric parameters in previous section. The fitting process excludes the measurement with high co-linearity. The probability from logistic regression function, “0” indicates male whereas “1” indicates female, respectively. All statistical analysis is preformed using statistic commercial software (SPSS, SPSSTM Inc, United States of America).

There are three logistic regression models used in sex prediction. *Model A* uses only cranial parameters whereas *Model B* uses only mandibular parameters. *Model C* uses combination of cranial and mandibular parameters. From the analysis, the coefficient (β), standard error of means and significant value are reported as shown in Table 5 to Table 7.

For *Model A*, there are four significant predictors (p < 0.05) in mandible parameters which are Nasion-basion length, Palatal length, Upper facial height and Maxillary breadth. The function is as follows:

Craniometric Parameter | Coefficient (β) | Standard error of mean (S.E.) | Significant level |

Intercept | 76.340 | 15.9577 | 0.00000 |

Nasion-basion length | -0.387 | 0.0984 | 0.00008 |

Palatal length | 0.362 | 0.1238 | 0.00349 |

Upper facial height | -0.497 | 0.1608 | 0.00199 |

Maxillary breadth | -0.197 | 0.0708 | 0.00530 |

Craniometric Parameter | Coefficient (β) | Standard error of mean (S.E.) | Significant level |

Intercept | 70.589 | 18.7774 | 0.00017 |

Bi-gonion breadth | -0.184 | 0.0631 | 0.00347 |

Coronion height-left | -0.310 | 0.1042 | 0.00289 |

Mandibular angle-right | -0.208 | 0.0812 | 0.01033 |

Mandibular body length-right | -0.125 | 0.0888 | 0.15810 |

Craniometric Parameter | Coefficient (β) | Standard error of mean (S.E.) | Significant level |

Intercept | 88.202 | 24.4335 | 0.00031 |

Coronion height-left | -0.276 | 0.1242 | 0.02614 |

Nasion-basion length | -0.596 | 0.1741 | 0.00062 |

Palatal length | 0.581 | 0.2032 | 0.00422 |

Upper facial height | -0.567 | 0.2186 | 0.00956 |

where

NA-BA = Nasion-basion length (unit: millimeter)

OR-STA = Palatal length (unit: millimeter)

NA-PR = Upper facial height (unit: millimeter)

ZM_{ L }–ZM_{ R }= Maxillary breadth (unit: millimeter)

For *Model B*, there are four significant predictors (p < 0.05) in mandibular parameters which are Bigonion breadth, Coronion height-left, Mandibular angle-right and Mandibular body length-right. The function is as follows:

where

GO_{ L }-GO_{ R }= Bi-gonion breadth (unit: millimeter)

CO_{ L }-GO_{ L }= Coronion height-left (unit: millimeter)

CS_{ R }-GO_{ R }-GN = Mandibular angle-right (unit: degree)

GO_{ R }-PG = Mandibular body length-right (unit: millimeter)

For *Model C*, there are four significant predictors in cranial and mandibular parameters (p < 0.05) which are Coronion height-left, Nasion-basion length, Palatal length, and Upper facial height. The function is as follows:

where

CO_{ L }-GO_{ L }= Coronion height-left (unit: millimeter)

NA-BA = Nasion-basion length (unit: millimeter)

OR-STA = Palatal length (unit: millimeter)

NA-PR = Upper facial height (unit: millimeter)

The set of skulls are tested according to logistic regression models (*Model A, Model B and Model C*) to evaluate the accuracy as reported in Table 8.

Model | Male | Female | Overall |

Model A | 92.1 | 90.2 | 91.3 |

Model B | 85.0 | 86.2 | 85.5 |

Model C | 95.0 | 93.1 | 94.2 |

The logistic regression analysis revealed that 4 of 21 cranial parameters and 4 of 11 mandibular parameters are significant predictors (p < 0.05). The Basion-nasion length and Bigonion breadth are the most dimorphic of the cranial and mandibular measurement, respectively. For the best prediction model, *Model C* which includes both cranial and mandibular parameters is recommended.

In order to predict the gender by the parameters in *Model C*, the probability of being female can be calculated using equation (2) whereas the probability of being male is then inversed (1-P).

The accuracies from *Model C* of the present study are compared to previous studies on sexual dimorphism using the skull of some previous studies based on South African white, South African black, Indian and Thai population. Table 9 shows a comparison of measurement techniques and average accuracies obtained from the present study and previous studies which derived from many populations.

To the best of author’s knowledge, there is only one study (Sangvichien, et al., 2007) that determine the sex of skull based on logistic function using on four parameters which as Nasion-basion length, Maximum breadth of the cranium, Facial height, and Bi-zygometic breadth. This presented the accuracy 88.8% for overall sex classification and 82.9% and 92.1% among females and males, respectively.

From the table, it reveals that the present study yields higher accuracies than the many previous studies. Therefore, the *Model C* presents in this study can be used to determine the gender of skeleton for intact skull in forensics and archaeology. However, in order to ensure the effectiveness of logistic regression, three skulls with known gender from Thammasat University Hospital, Thammasat University, Thailand are used to test the concept. The skull No.1 and skull No. 3 are adult males whereas the skull No. 2 is adult female.

Based on logistic regression Model C which is consider to be the best model for sex prediction in Thais’ skull, Coronion height-left, nasion-basion length, palatal length, upper facial height are measured and predicted the gender. As shown in Table 10, all cases are predicted the gender correctly (3/3). Hence, the determination of sex based on the Model C of logistic regression is considered to be accurate.

Population | Measurement Technique | Statistical Analysis Method | Average Accuracies |

South African White (Steyn & Işcan, 1997) 44 males 47 females | Direct measurement | Discriminant function | 80% - 86% |

South African black (Franklin, et al, 2005) 182 males 150 females | 3D tactile digitizer | Discriminant function | 75% - 80% |

Indian (Deshmukh & Devershi, 2006) 40 males 34 females | Direct measurement | Discriminant function | 85% - 90% |

Thai (Sangvichien, et al., 2007) 66 males 35 males | Direct measurement | Logistic function | 83% - 92% |

South African black (Dayal, et al, 2008) 60 males 60 males | Direct measurement | Discriminant function | 80% - 85% |

Combination (Matamala, et al, 2009) 149 males 77 males | Direct measurement | Discriminant function | 82% |

Thai (Present study) 63 males 41 males | Three-dimensional CAD Model | Logistic function | 93% - 95% |

Craniometric Parameter | Skull No.1 | Skull No.2 | Skull No.3 |

Intercept | 88.202 | 88.202 | 88.202 |

Coronion height-left | 69.63 | 53.12 | 72.09 |

Nasion-basion length | 105.07 | 95.24 | 101.06 |

Palatal length | 58.50 | 45.82 | 55.17 |

Upper facial height | 76.91 | 72.26 | 71.81 |

Regression Analysis (Z) | -3.26 | 2.43 | -0.59 |

Probability of event (P.E.) | 0.037 | 0.919 | 0.357 |

Prediction Gender | male | female | male |

Exact Gender | male | female | male |

Result | correct | correct | correct |

## 6. Outlook

Since there is possibility to find skull as fragment bone in forensics and archaeology, then the assessment of necessary craniometric parameters becomes complex. Although the missing craniometric parameters can be predicted using correlation as shown in Table 3 and Table 4, but some correlation coefficients among these craniometric parameters are mostly inferior. With low correlation coefficient, the equation may not be an appropriate solution to determine those missing craniometric parameters.

As a result, a purposed alternative is to reconstruct defected skull surface based on the mirror surface topology of normal side with aids of Computer Aided Design technique as shown in Fig. 8. In fact, this technique is a standard protocol for implant design in cranial reconstruction (Müller, et al., 2003). The purposed alternative relies on the discovery that the symmetric between left and right of bilateral craniometric parameters as presented in Table 2. However, this concept should be further investigated to ensure the usability.

## 7. Conclusion

This study presents advantages of using advance medical imaging and reverse engineering through computed tomography scanner to reconstruct the three-dimensional model of skulls. This is very useful to analyze and measure craniometric parameters based on virtual model. Generally, in forensic medicine and archaeological researches, the study relies on direct measurement and other two-dimensional techniques which may not be accurate. The measurement errors can be influenced by human error, instrumental error, image magnification and image occlusion. The advantage of three-dimensional computed tomography technique includes the analysis of specimen without destruction or damage of specimens as well as the ability to analyze the specimens in configuration which the conventional technique cannot provide. Comparing to the other reverse engineering technologies, computed tomography presents the superior ability in accessing the internal geometry which the other tools find the difficulty in data capturing.

In the craniometric analysis, the medians and bilateral landmarks are accessed. From the analysis, the result reveals that Thai male presents the craniometric parameters greater than Thai female, especially, Maximum cranial breadth, Facial length, Orbital height-left, Orbital height-right, Palatal breadth, Bicoronion breadth, Bizygometic breadth, Maxillary breadth, Upper facial height, Orbital breadth-left, Orbital breadth-Right, Nasal height, Bicondylar breath, Bi-gonion breadth, Coronion height-left, Coronion height-right, Mandibular body length-left, Mandibular body length-right, Maximum mandibular length-left and Maximum mandibular length-right. In both populations, the bilateral anatomy presents some degrees of correlation which may be concluded the facial symmetry.

Logistic regression is used to derive functions for sex determination based on average numerical values which obtained from craniometric parameters. Three models are purposed, *Model A* is based on cranial parameters, *Model B* is based on mandible parameters and *Model C* is based on both cranial and mandibular parameters. From the result, *Model C* provides the best accuracy among other models which is 94.2%. The prediction equation relies on four parameters which are Coronion height-left, Nasion-basion length, Palatal length, and Upper facial height which subsequently produce logistic regression as in equation (5).

As seen in Table 9, our study yields higher accuracies than other previous studies. This is due to two main factors, the accurate landmark identification by the three-dimensional technique and developing logistic regression function from difference sample.

In addition, the authors suggest that the techniques described in this chapter which includes data acquisition, three-dimensional computerized craniometric study and sex determination based on logistic regression function can effectively be applied to the other osteological elements in specific race.

## Acknowledgments

The research is supported the funding and facilities in part by the National Metal and Material Technology Center (MTEC), National Science and Technology Development Agency (NSTDA) of Thailand and Suranaree University of Technology, Thailand. In addition, the authors are grateful to Department of Anatomy, Faculty of Medicine, Khon Kaen University, Thailand for providing cadaveric skull specimens.