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Expert systems for the dental aesthetic.


The phi relationship, 1.618:1, known as the Golden Proportion or Divine Proportion, has long been used by artists, architects, designers, engineers, musicians, photographers, sculptors, surgeons and stock analysts alike to achieve excellence in their results. The Golden Proportion results from the division of a straight line in such a way that the shorter part is to the longer part as the longer part is to the whole. This theory states that for any two objects to be in esthetical harmony, they should exist in the ratio of 0.618 to 1.0 (Ricketts, 1982 a, b).

An arrangement of teeth in Golden Proportion would yield relative widths of 1.618 : 1.0 : 0.618 for the central incisor, lateral incisor, and canine respectively.

We have applied this relationship in aesthetic dentistry. The proposed application is a graphic analyses and design tool that allow to see and apply golden proportion to any digital image.

Additionally the before and after patient's dental status could be easily compared. At the actual stage the software is used within the dental aesthetics area aiming to explore new ways for achieving a better cosmetic of dental crowns.

The goal of this software is to integrate simplicity and time efficient methods into the esthetical techniques of the clinicians and the technical expert daily routine.


The study was performed on 280 patients aged between 18 and 25 years. Part of the measurements were performed on natural teeth, on patients carefully selected to fulfil certain criteria (no prior orthodontic treatments, gaps), in order to determine statistically the accordance with the golden proportion. Other measurements were made on patients that had suffered aesthetic restoration treatments using comparative images prior and after the treatment for measuring the M-D dimensions of teeth.

A standardized frontal image of each subject's teeth was taken using a common digital camera (i.e. Canon Power Shot A 550; 7.1 Mp).

The images were downloaded on to a personal computer. To improve upon image accuracy, a zoom function of the program was used to allow more precise measurement The application was developed using Microsoft Visual C++ 2005, by a software developer.

The basis of the program is girding virtually over the existing pixels and recognizing them, after which the user will point out the points (pixels) and name them using A,B,C...

The next step is to determine which segments would be calculated and comparing the outcome (ratio) to the golden cut. Simple and easy to use this software will aid us later on in the completion of a study which will test the aesthetic awareness, the demand for it and last but not least the efficiency of the GOLDEN CUT software.


The main functions of the application are selected from the buttons presented and explained in the fig.1


The application allows the upload and display of the teeth in three different views (frontal and lateral), and permit the storage of a big number of photos. The measurements are done automatically based on the chosen points by clicking on the selected photo. (Fig. 2-3)




It is important to determine a mathematical or geometrical relationship between teeth in order to achieve an aesthetic restorative result. These findings are also supported by other investigations (Mahshid M, et al., 2004 & Gillen RJ, et al., 1994).

In our study based on experimental results the golden proportion (1.618 : 1.0) was found as report of the widths between the central right incisor and the lateral incisor in 37.5% of women and 25.7% of men.

Among them 14.6% of male subjects and 18.9% of female subjects have the width between their right lateral incisor in golden proportion with the width between their right canine. Within other studies (Preston JD, 1993) the data show that 46.2% of the male subjects and 49.5% of the female subjects have the width between their right central incisor in golden proportion with the width of the right lateral incisor, while 24.7% of males and 35.2% of females have the width between the right lateral incisor in golden proportion with the widths between their right canine. The difference of results might be explained by several specific factors such as the differences of the research methodology used as well as the differences of the ethnicity of the selected subjects.


The measurements have been done both on natural teeth and natural teeth compared with direct or indirect restorations. It has been carried out restorations with composite materials and porcelain veneer, together with acrylic prosthesis. In order to obtain suitable results (the golden proportion) the better way is to use iterative alternation of measurement and adjustment procedures (fig. 4, 5). Dentists need to exercise extreme caution when considering restorative treatment alone to correct anterior width proportion deficiencies.





The initial results made clear that the natural development of the aesthetic frontal group is more close to 0 Phi (golden proportion of 1 to 1.6), than any other medical intervention made by doctors and technicians alike.

This software is still at the beginning of its journey in application, but from primary results, it might have an impact on the way we understand, use and deliver aesthetics to our patients.

The area of application is also much larger than frontal teeth aesthetics, it could be used in different fields of expertise such as plastic surgery and many other fields the require an extra Eye for aesthetics.


Ricketts, R.E. (1982 a): The biological significance of the divine proportion. American Journal of orthodontic 81: 351-70.

Ricketts, R.E. (1982 b) : The divine proportion in facial esthetical. Clinical & Plastic Surgery. 9 : 401-22.

Mahshid M, et al., (2004). Evaluation of "golden proportion" in individuals with esthetical smile. J Esthet Restor Dent; 16: 185-192.

Gillen RJ, et al., (1994) Schwartz RS, Hilton TJ, Evans DB. An analysis of selected normative tooth proportions, Int J Prosthodont; 7: 410--417.

Preston, JD (1993). The golden proportion Revisited. J Esthet Dent; 5: 247-251
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Author:Biclesanu, Cornelia; Cherlea, Ioan Valeriu; Yassin, Adrian
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Date:Jan 1, 2008
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