ARTi

Your face as a password

Chapter 1

Painting your face with invisible dots

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Answer

Chapter 2

Turning your nose into numbers

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Answer

Chapter 3

The neural network that learns you

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Answer

Chapter 4

Outsmarting the tricksters

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Answer

YOUR GOAL

Master of Your face as a password

Ch 2 · Turning your nose into numbers
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marcus The geometry of a smile

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marcus Condensing features into a vector

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marcus Mapping the face as a grid

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Turning your nose into numbers

marcus Map the curves of your nose to learn how Face ID turns features into numbers.

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marcus Measuring distance between two faces

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marcus Apple Face ID Mathematics

Invisible beams trace the shape of your face, Turning your smile into a secure digital space.

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The geometry of a smile

marcus Math helps the system recognize your face even when tilted or angled differently.

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Fun Fact

Facial geometry: Your face has about eighty landmarks, and the distance between your pupils remains mathematically constant throughout adulthood.

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Condensing features into a vector

marcus Complex facial features are compressed into a single string of numbers called a vector.

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Quiz

What is the compressed string of numbers that represents your facial features called?

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Gossip

Would you rather have a super-long password or biometric scans?

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Quiz

Which mathematical operation allows the system to recognize your face when you tilt your head?

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Quiz

Why does the system convert your 3D facial mesh into a vector embedding instead of keeping the raw 3D file?

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Quiz

How many numbers typically make up the vector embedding used in facial recognition systems?

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Quiz

What mathematical formula is used to measure the straight-line distance between two facial vectors?

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Quiz

What mathematical tool is used to represent the 3D coordinates of your facial features?

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Quiz

In linear algebra, what does transforming a 3D facial mesh allow the computer to do?

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Quiz

What must the calculated mathematical distance between your scan and the saved template be to unlock your phone?

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