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A study of the facial aging - a multidisciplinary approach

Abstract

This paper describes a mathematical and graphical model for face aging. It considers the possibility of predicting the aging process by offering an initial quantification of this process as it applies to the face. It is concerned with physical measurements and a general law of time dependence. After measuring and normalizing a photograph of a person, one could predict, with a known amount of error, the appearance of that person at a different age. The technique described has served its purpose successfully, with a representative amount of patient data behaving sufficiently near the general aging curve of each parameter. That model uses a warping technique to emulate the aging changes on the face of women. Frequently the warping methods are based on the interpolation between images or general mathematical functions to calculate the pixel attributes. The implemented process considers the age features of selected parts of a face such as the face outline and the shape of the lips. These age features were obtained by measuring the facial regions of women that have been photographed throughout their lives. The present work is first concerned with discussing a methodology to define the aging parameters that can be measured, and second with representing the age effects graphically.


A Study of the Facial Aging – A Multidisciplinary Approach

Fabiana R. Leta

Mechanical Engineering Department. Universidade Federal Fluminense. R Passo da Pátria, 15 Centro. 24210-240 Niterói. RJ. Brazil

fabiana@ic.uff.br

Djenane Pamplona

Civil Engineering Department. Pontifícia Universidade Católica. R Marquês de São Vicente, 225 Gávea. 22453-900 Rio de Janeiro. RJ. Brazil

Hans I. Weber

Mechanical Engineering Department. Pontifícia Universidade Católica. R Marquês de São Vicente, 225 Gávea. 22453-900 Rio de Janeiro. RJ. Brazil

Aura Conci

Computer Sciences Department, Universidade Federal Fluminense. R Passo da Pátria,156. Centro. 24210-240. Niterói. RJ. Brazil

Ivo Pitanguy

Plastic Surgery Department, Pontifícia Universidade Católica. R Marquês de São Vicente, 225 Gávea. 22453-900 Rio de Janeiro. RJ. Brazil

This paper describes a mathematical and graphical model for face aging. It considers the possibility of predicting the aging process by offering an initial quantification of this process as it applies to the face. It is concerned with physical measurements and a general law of time dependence. After measuring and normalizing a photograph of a person, one could predict, with a known amount of error, the appearance of that person at a different age. The technique described has served its purpose successfully, with a representative amount of patient data behaving sufficiently near the general aging curve of each parameter. That model uses a warping technique to emulate the aging changes on the face of women. Frequently the warping methods are based on the interpolation between images or general mathematical functions to calculate the pixel attributes. The implemented process considers the age features of selected parts of a face such as the face outline and the shape of the lips. These age features were obtained by measuring the facial regions of women that have been photographed throughout their lives. The present work is first concerned with discussing a methodology to define the aging parameters that can be measured, and second with representing the age effects graphically.

Introduction

The bioengineering area has a broad application field and it has raised a great amount of interest in its multi-disciplinary aspect. In this field, one can highlight the interactive modeling of medical data, as a way to improve the data assessment and the necessary care to be given to patients. The scientific visualization in the medical area searches for the imaging representation of human beings and their biological mechanism. This representation utilizes, besides the biomedical data, due to its physical and mechanical concepts, Computer Graphics and Imaging Processing techniques in such a way that it can help physicians to study cases that were traditionally involved only with surgical praxis or photographs and papers. Several projects have proven to be useful in this task, exploiting the most recent computation methods and techniques.

The questions involving aging and the human longevity have been motivating the interest of several specialists who search for a better life quality to people. The idea of creating a model which pictures the quantitative face aging process, has motivated the research developed by the present research group [(Leta, 1998) (Pitanguy et al., 1998)]. Several papers describe the genetical and environmental aspects of qualitative face aging. The objective of this work is to contribute in this area of expertise through the graphical modeling and emulation of the human aging process. By knowing how the aging process occurs, new procedures to slow down or even diminishing such impacts, created in an empirical way, may be proposed. This technique is also useful to help in the recovery of a missing person, disappeared for a long time, provided that some adult phase photographs are available.

A methodology to model the aging of human face allows us to recover the face aging process. This methodology consists of: defining the variations of certain face regions, where the aging process is perceptible; measuring the variations of those regions for a period of time in a group of people and finally making up a model through the measurements based on personal features. That could be used as a standard to a whole group in order to design aging curves to the facial regions defined. Having those characteristic data and plots, graphical computation/imaging processing techniques are to be used, designing a graphical emulation of face aging.

Mathematical Modeling of Face Aging

Human society values beauty and youth. It is well known that the aging process is influenced by several parameters such: feeding, weight, stress level, race, religious factors, genetics, etc. Finding a standard set of characteristics that could possibly emulate and represent the aging process is a difficult proposition.

This standard set was obtained through a mathematical analysis of some face measurements in a specific group of people, whose photographs in different ages were available. To each person in the group, there were, at least, four digitized photographs. The oldest of them was taken as a standard to the most recent one. Hence, some face alterations were attained through the passing of time for the same person. The diversity of the generated data has led to the designing of a mathematical model, which enabled the acquiring of a behavior pattern to all persons of the same group.

The first step consisted in the selection of the group to be studied. Proposing the assessment of the face aging characteristics it will be necessary to have a photographic follow-up along time for a group of people, in which their face alterations were measurable. The database used in this work consisted of files of patients who were submitted to plastic surgery at Ivo Pitanguy’s Clinic or Santa Casa de Misericórdia Hospital.

After analyzing 342 white Caucasian female patients, between 18 and 70 years of age who had been submitted to a plastic surgery in the ear, and 420 who have had a nose surgery, 40 cases were selected for the assessing of aging curves. The available photographs were digitized in a 600 dpi scanning resolution.

The aging parameters were acquired through the measuring of specific coordinates over the face. The selection of these points was based on the anthropometry of the face (Horswell et al., 1988) (Psillakis et al., 1987). Other facial measurements can be seen in (DeCarlo et al., 1998). In our research the measurements were performed in frontal and profile photographs for each selected patient in at least two different ages. Considering that the intra-pupilar distance is, to begin with, the only feature that does not change over time, this parameter was taken to normalize the dimensions obtained from the different persons’ ages. This is due to the fact that, in general, the usual measurements try to compare the diverse individuals and not an evaluation of the same person over time, i.e., the reference of aging to be used is to be found in each individual.

Through the digitized photographs of the study group, the coordinates of the important points of Figure 1 and 2 were measured (Pitanguy et al., 1996). In the frontal photographs there were taken 26 measurements and in the profile ones, at least 17 measurements. To each studied case, there were a total of four photographs: two frontal ones and two profile ones in different ages.



Starting with the coordinate readings: the following measurements were calculated in the frontal views:

- interpupilar distance;

- height of the front (left and right laterals);

- height of the eyebrow (in three positions to each eyebrow);

- height of the palpebral (eyelid) hollow (left and right);

- height of the mandible (in seven different positions);

- height of nose;

- height of the superior lip;

- thickness of the lip;

– size and angle of the nasolabial wrinkle (left and right).

The distance between the pupils divided linear measurements of each patient frontal photographs. The factor used to normalize the profile images was the distance between the level of the pupils and the lowest point of the mental region. The distance must be the same of its similar in the frontal image.

For measurement of the parameters, the coordinates of the points (Figure 2) were obtained according to the following procedure:

(1st) A line passing through points (b) and (o) was drawn.

(2nd)The line bo was rotated together with the entire image, until bo became a vertical line.

(3rd) From the pupil (c) a horizontal line perpendicular to bo was drawn.

(4th) Definition of points a (forehead), g (nasion), h and i (nose), j (subnasion), m and n (mouth), k and j (nasolabial fold), p and q (mandible) and d, e and f (ear).

For the profile photographs we can highlight the following Cartesian linear measurements Yi which were obtained for each person (i), at ages t1 and t2 in each scanned photograph:

- length of the forehead (ac)y;

- size of ear;

- size of the ear lobes;

- size of the nasolabial wrinkle;

- height of superior lip;

- thickness of lip;

- angle of the neck with the horizontal;

- angle of the superior lip with vertical;

- nose angles;

- angle of the nasolabial wrinkle with vertical;

- ear inclination;

- tragus angle to the pupil with the vertical line;

where ()y are the vertical components of the measurements.

The measurements taken over the images represent the face parameter, which is assessed according to aging. Disposing the measurements of the face parameters has become necessary in order to create a model that allows the representation of the face aging.

To characterize the aging, some functions were analyzed, among them the growing function. In this work it was selected the p function to represent the generic curve defined by a combination of second order polynomials, which represents the behavior of each face parameter over time, i.e., with aging. The choice of these functions is due to its simplicity and to the obtained good fitting results.

In (Pitanguy et al., 1996) one may find details of the used methodology to obtain the curves of aging of the face parameters. In figures 3, 4 and 5 the aging curves of the frontal and profile parameters are presented (Pitanguy et al., 1998) (Leta et al., 1999).




The results of some frontal and profile curves u(t) can be used to predict the magnitude of a face parameter Yi (t2) when Yi (t1) is known, where t1 and t2 are two different ages.

Assessing the results presented in Figures 3, 4 and 5, one may perceive the following characteristics due to aging: growing of the mentonean region and front, reduction of the lip thickness with enhancing of the superior lip, growing of the nose length, among other aspects.

Graphical Representation of Aging

Facial Aging Warping

The Computer Graphic techniques applied to promote a metamorphosis process over images and objects are classified as Morphing and Warping. These techniques have been applied in different areas, like in the generation of special effects in the entertainment industry and other artistic areas. Image processing applications of warping are increasingly important. These applications include corrections in satellite imaging distortions or ultrasonic medical imaging. Other class of applications is facial animation. They include videophones, automated face recognition or psychological studies.

Digital image warping has received a lot of interest in recent years. A number of algorithms to implement this technique is subject of recent. The frequently used warping algorithms transform an image based upon contour interpolation. Working with two different images, a contour selection process is applied to each image. This process defines the image area where the graphical transformations will be set on. The in-between images are generated by a color pixel variation plus a bi-dimensional mapping applied over the two previous images. The color of each pixel in two different images is combined.

The distortion method can be sub-divided in front and reverse mapping. Using front mapping, each pixel of the source image is copied to its final position in the target image. In the reverse mapping each pixel of the target image is equalized to the correspondent pixels in the source image. In both techniques the issue is to define how pixels in the source image will be linked to the pixels in the known or unknown final image.

This paper focuses on a new range of facial animation application: the facial age characterization. To graphically represent the proposed model of face aging, the warping method was used. This method involves the deformation of an image starting with control segments that define the edges of the images. Those segments are defined in the original image and their positions are changed to a target image. From those new positions the new color (gray level) of each pixel in the image is determined.

The definition of edges in the face is a fundamental step, since in that phase the applied aging curves are selected. Hence, the face is divided in influencing regions according to their principal edges and characteristics.

Considering the face morphology (Pitanguy et al., 1977) and the modeling of the face aging developed, the face was divided in five basic regions (Figure 6):


(A) frontal – limited by the line of the hair base in the front and eyebrows,

(B) orbitary – defined by eyebrow and eyelid hallow;

(C) nasal – involving nose region;

(D) orolabial – defined by the mouth and nasolabial wrinkle;

(E) mentonean – corresponding to the inferior part of the face, including mandible and lateral hollow.

Control segments that define the principal face edges characterize those regions. Those control segments define the mapping process among pixels of the source image and the target image. The target image is obtained from the inverse mapping of the source image, i.e., with the new control segment positions, each pixel of the new image has its color (grayscale) defined by the corresponding pixel in the target image. This image corresponds to the face in the new age, which was obtained through the application of the numerical modeling of the frontal face aging.

The definition of the straight-line segment will control the warping process, leading to a series of tests until the visual result was adequate to the results obtained from the aging curves. The extremes of the segments are interpolated according to the previously defined curves.

Horizontal and vertical orienting auxiliaries lines were defined to characterize the extreme points of the control segments (Figure 7-a). Some points, that delimit the control segments, are marked from the intersection of the auxiliary lines with the contour of the face, eyebrow, superior part of the head and the eyes. Others are directly defined without the use of auxiliary lines, such as: eyelid hollow, eyebrow edges, subnasion, mouth, nasolabial wrinkle and nose sides. On the whole, 50 points are marked on the face (Figure 7-b).


The auxiliary lines are not defined taking in account the symmetry of the face. The distance between the pupils will define them and specific control points define the remaining auxiliary lines. Since the most important asymmetry that is perceptible is in the nose, we decided not to use the mean point between the pupils to define the control points of the nose.

Interpolation and Mapping

Once the control segments characterize the target image, the following step of the warping process can be undertaken, corresponding to the transformations of the original points to the new positions in the target image. The transformations applied to the segments are given by the aging curves presented in item 2. Traditionally those techniques of warping use linear interpolations. In the present work, however, the target segments are calculated by polynomial interpolations, based on aging curves.

The segments interpolation to the new positions in the target image is defined by the curves presented in the last item. So the extremes of each segment obey specific rules determined by the curves themselves. In Figure 8, one can observe an example of control segment interpolation. The transformations F and G of segment 4s (source image) in segment 4t (target image). The transformation F (4,0) is applied to the initial coordinates of the segment G(4,1) to the final coordinates (4,1). The F function represents the height variation of the front – central direction and G side direction.


In general, for each segment, there is an associated transformation, whose behavior can be observed by the curves presented in Figure 3, 4 and 5. The only segments that do not suffer any transformation are the contour of the eyes and the superior side of the head.

Imaging Post-processing

The warping technique is a geometrical transformation of digital image. Thus it susceptible to aliasing (Wolberg, 1990). Since the images are processed in the discrete dominion. Considering an image as a rectangle of points and knowing that the mapping of warping takes points from the origin image to arbitrary points in the target image, thus two effects can occur while processing a warping filter in this image: (1) points in the target image do not receive any information of the origin image; (2) more than one point in the target image can receive the same information from the origin image (several pixels can be mapped to the same pixel).

To minimize the aliasing effect, special filters can be applied over the image. Applying a filter to an image means to operate over each pixel: the gray level of each pixel is replaced by the average value of the gray levels of the neighborhood of the pixel. The usage of these filters softens the aliasing and noise effect, but the image loses the definition of certain contours (Gonzalez et al., 1993).

Another important aspect of image enhancing and aging realism refers to the color alterations and texture of the face (Burt et al., 1995). It is well known that with aging the skin tends to be stained and the eyes and hair tend to become lighter. Besides the differences in the color of the skin, in aging people, the wrinkles get deeper, what in an image is perceived by the variation of the gray level.

The developed program also performs shape transformations according to the created aging curves, not including any quantification over the alterations made in texture and skin and hair color. Thus, to partially emulate this effect, the program allows the insertion of small stains in the face and also performs a subtle lightening of the darker hues in the image, which are located in the hair, eyebrows and iris. After the application of these effects, an anti-aliasing filter can be applied to smooth the "stains" caused in the image and the effects due to warping.

Results

The presented results in the following figures refer to the emulations made on the frontal photographs, principal focus of this paper, with the objective to apply the developed program to other persons outside the analyzed group. The comparisons with other photographs of the tested persons depend on their quality and on the position in which they were taken.

The application of the method showed the occurrence of small errors in the results. An assessment was made of the new positions, of the control segments. It consisted in: after aging an image, from the first age to the second one, through the use of polynomial interpolation of the control segments in the photographs (image) in the age i1, the new positions are then compared with the ones in the photograph of image i2. A very small error was observed , considering that some parameters were not applicable to the new images. The processed images were qualitatively compared with the person’s photograph at the same age (Leta, 1998). In the subsequent images, some of these results are shown.

In the following figures (9 , 10 and 11 ), an example of the aging is presented. To enhance the analysis a collage, between the real photograph and the processed aged image of the real photograph, was used. It consisted in the composition of two half faces, using the cutting line, i.e. the vertical auxiliary line that crosses through the center of the face (half the inter-pupil distance). Thus, it is possible to observe the differences of the face format that appears while aging and renewing. Some features must be pointed out such as: the enlarging of the length and width of the nose, enlarging of the whole mentonean region (not only the hollow region), also the eyelid hollow, very subtle falling of the eyebrow, thinning of the lips with the enlarging of the nasion and the superior part of the lip, enlarging of the front and changing in the nasolabial wrinkle.

Images in Figure 12 show: (a) and (b) original photographs; (c) the changes made with aging process; and (d) a collage between the middle of the manipulated image in the right side with 62 years old with the original photograph at the same age.


In the following figure, a result of the profile aging simulation is showed. Regions in such a way that the defined points (Figure 2) fit the new coordinates, based on the profile aging curves (Figure 5), manipulated the photograph of the patient at age 45.

Conclusions

Modeling biological phenomena is a great deal of work, especially when the biggest part of the information about the subject involves only qualitative data. Thus, the research developed in (Leta, 1998) had as a challenge in the designing of a model to represent the face aging from qualitative data.

Due to its multi-disciplinary character, the developed methodology to model and emulate the face aging, involved the study of several other related fields, such as medicine, engineering, computing, statistics and mathematics.

One of the most important aspects was to develop a model that could quantify the biomechanical process of face aging. Many pieces of information and data were the source to be processed in order to generate the aging curves. From those curves, it was developed a graphical emulation of the aging process, considering individual characteristics and the proposed face aging pattern.

The obtained results show that the modeling can be applied to the images and to the acquiring data and curve fitting and also generalized to people not belonging to the study group. The errors due to the process of modeling are considered negligible, as being related to biological data (Pitanguy et al., 1996) (Leta, 1998). The graphical results are qualitatively good, even considering the small errors summed up to those inherent to the warping process. Several factors have contributed to those errors, such as: part of the universe of the used data had made surgery, the photographs had variations in enlarging and illumination; people with hair over the front, smiling or inadequately positioned, among others. Among those errors, the most frequent ones are (1) the nasolabial wrinkle, due to a poor definition of its inferior limit; and (2) the lip thickness because the influence of make-up and face expression.

Extracting those pieces of information from the curve fitting demanded a very deep analysis that, for each and every case, reduced the number of points to be adjusted. If the available sampling has a photographic position and illumination control, it will be possible to acquire the aging curves with even smaller errors.

The possibilities opened by the presented method and some further research on this field can lead to new proposals of enhancing the current techniques of plastic face surgery. It is possible to suggest the ideal age to perform face lifting. Once the most affected aging regions are known and how this process occurs over time. Missing persons can be recognized based on old photographs using this technique.

For sure, more enhancing must be made, providing better answers and results. This article represents a pioneer research in the modeling of face aging and its graphical emulation, based on aging curves. More has to be researched and developed like: male face aging process, curve controlling instead of segment controlling, automatic pattern recognition of the face, extension to a tri-dimensional model, comparison of the polynomial fitting to other methods, evaluation through finite elements analysis of the effect of stress on the face, studying of the face variations for texture and color with age, among other suggestions.

Presented at DINAME 99 – 8th International Conference on Dynamics Problems in Mechanics, 4-8 January 1999, Rio de Janeiro. RJ. Brazil. Technical Editor: Hans Ingo Weber.

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  • Publication Dates

    • Publication in this collection
      13 Dec 2000
    • Date of issue
      2000
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