The Geometry in Face Recognition

Back in my teens when I was doing a cartooning course, I was amazed to learn about the geometry involved in human anatomy
Adulthood is when growth stops: this is the tallest one gets in one’s life. At that point, Height= 7.5/8 heads

Leonardo da Vinci's drawing, Vitruvian Man, is based on the correlations of ideal human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise De architectura. Vitruvius described the human figure as being the principal source of proportion among the classical orders of architecture. Vitruvius determined that the ideal body should be eight heads high. 

  • the length of the outspread arms is equal to the height of a man
  • the maximum width of the shoulders is a quarter of the height of a man.
  • the distance from the elbow to the tip of the hand is a quarter of the height of a man.
  • the distance from the elbow to the armpit is one-eighth of the height of a man.
  • the foot is one-seventh of the height of a man.
  • the distances from below the chin to the nose and the eyebrows and the hairline are equal to the ears and to one-third of the face.

It was a revelation that caricaturing was about mocking that wonderful geometry & proportions and exaggerating the distinct features of  a face to create a comic effect.
While trying out the Microsoft Cognitive Services Face API code samples, I found it awesome that facial geometry can now be abstracted to a set of numbers conveyed through JSON. So just as infrastructure can now be represented as code (to make its deployment easy and automated), the human face & body can be represented by a JSON file!

Face "landmarks" or specific points that exist on every face — the top of the chin, the outside edge of each eye, the inner edge of each eyebrow, etc. can help mainly with emotion analysis, pose estimation. Geometrical features alone may not carry enough information for face recognition though.

There are lots of ways to do face landmark estimation. Some machine learning algorithms analyze using 68 specific points

The Microsoft Cognitive Services Face API can analyze a face in an image & return 27 predefined landmark points. The points returned are in units of pixels, just like the face rectangular frame.
In addition to marking face features in an image, face landmarks can also be used to accurately calculate the direction of the face.
Attributes give extra information regarding selected faces. Head pose is one of the attributes that represents face orientation in 3D space according to roll, pitch and yaw angles

Amazon Rekognition APIs can analyze faces & return 25 facial landmarks & 9 facial attributes

Facebook’s algorithms are able to recognize your friends’ faces after they have been tagged only a few times. Facebook can recognize faces with 98% accuracy which is pretty much as good as humans can do!

 Beauty is the combination of golden ratio proportions in many facial markers, the most important of which are the positions, shapes and proportions of all aspects of the eyes, nose, mouth, chin and eyebrows.

Related scientific disciplines:
Anthropometry is the scientific study of the measurements and proportions of the human body.
Cephalometry – Study and measurement of the head
Craniometry – Measurement of the human cranium
Kinanthropometry – Study of human growth and performance
Morphometrics – Quantitative study of size and shape
Phrenology – Pseudoscientific study of human characteristics according to shape of the skull
Physiognomy – Pseudoscientific assessment of a person's character or personality from their outer appearance

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