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Math Help - Neoclassical Canon formula for the face?

  1. #1
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    Neoclassical Canon formula for the face?

    I posted an earlier thread about golden ratios being used for face attractivness. My wife and I are trying to calculate our score based on a scale from 1 - 10 (10 being perfect)

    Based on the work of Kendra Schmid and her use of Neoclassical cannons to help determine attractiveness we are struggling with our results and how to convert them to something more meaningful ( score from 1 - 10 )

    Here is a quote from Dr Schmids research:

    "Neoclassical Canons view the face in proportions and have been proposed by artists dating back to the renaissance period as guides to drawing beautiful faces (Farkas et al.10 1985). The basic premise is that portions of an attractive face should follow certain defined ratios. Farkas et al. (1985) summarizes these principles in nine Neoclassical Canons and their variations. Four of the canons deal with vertical measurements, four with horizontal measurements, and one with angles of inclination. Only six of these can be tested from the frontal views of the images. Therefore, only those six canons (listed in Table 3) are used to investigate their relationship with attractiveness of a face.

    Formula No. Description

    2 Forehead height = Nose length = Lower face height
    5 Interocular distance = Nose width
    6 Interocular distance = Right or left eye fissure width
    7 Mouth width = 1.5 Nose width
    8 Face width = 4 Nose width

    Table 3: Description of Neoclassical Canons (Formula number given by Farkas (1985))
    As shown in Table 3, some canons use two measurements (e.g. Formula 5 and 8) while others use three (e.g. Formula 2). To consistently measure compliance with the canons (i.e. equality to proposed ratios) with different numbers of features, we use the coefficient of variation. The coefficient of variation is defined as the ratio of the standard deviation of the distances to the mean of the distances. For a canon with three distances, using a ratio would require pair-wise comparisons of these distances, but using the coefficient of variation allows us to incorporate all three distances into one value while adjusting for the size of the face (dividing by the mean). A value of zero for the coefficient of variation says there is no variation in the distances (they are equal). For non-zero values, the larger the value, the more the face differs from the canon. Using this approach, we compute the degree of match with each canon (i.e. coefficient of variation) for all the faces and store it in a database."

    Below are one set of measurements we've taken:

    Formula No. Description
    Forehead height = 52
    Nose length = 49
    Lower face height 57
    Interocular distance = 29
    Nose width =31
    Interocular distance = 29
    Right or left eye fissure width = 28
    Mouth width = 45
    Face width = 113

    What would the formula look like to calculate our score from 1 - 10?

    Thanks for all the help
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  2. #2
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    Anyone have insight or something for us to get started with? I'm assuming we take the ratio of the measurement (e.g. interocular disatnce / nose width) but we're just not sure how that figures maps to a scale of 1 to 10.

    Thanks
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  3. #3
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    OK, after doing some more research we're now able to calculate the coefficient of variation for our measurements. For example we calculated the CV for formula #2 to be: 0.4489 so I'm assuming when we map this to a scale of 1-10 (10 having a CV value of 0 we again need to assign an "ugly" value to our CV result correct?

    Thanks
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    MHF Contributor Bruno J.'s Avatar
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    Are you a troll? Do you realise this is a mathematics forum?
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    Quote Originally Posted by Bruno J. View Post
    Are you a troll? Do you realise this is a mathematics forum?
    that was helpful...I'm trying to figure out what linear equation to use in order to map the results of my coefficient of variation into so my results map from a scale of 1 to 10.
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    MHF Contributor Bruno J.'s Avatar
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    The point is, this has nothing to do with analysis, topology or differential geometry. It barely has anything to do with high school math!

    Sorry for being rude. You'll probably have better luck elsewhere though!
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  7. #7
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    Quote Originally Posted by Bruno J. View Post


    The point is, this has nothing to do with analysis, topology or differential geometry. It barely has anything to do with high school math!

    Sorry for being rude. You'll probably have better luck elsewhere though!
    No worries, is there a more appropriate forum or section I should post too? It does seem like a relatively basic question but I can't seem to find an answer.

    Thanks
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