"SIGBOVIK 2024 is the eighteenth edition of this esteemed conference series, which was formed in 2007 to celebrate the inestimable and variegated work of Harry Quale Bovik. We especially welcome the three neglected quadrants of research: joke realizations of joke ideas, joke realizations of serious ideas, and serious realizations of joke ideas."

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Idea seriousness →

Last year's SIGBOVIK paper

Bean There, Done That

A mathematical model of bean sculptures

Bean construction Millennium Park opens
Parliament Cloud Gate
Annual visitors 3 million 5 million
Construction cost (Restoration alone) $4.5 billion $23 million

\(\frac{5,000,000}{3,000,000}\) > 1

\(\frac{\$23,000,000}{\$4,500,000,000}\) < 1

Bean sculptures

  • Singlehandedly put Chicago on the map
  • Naturally, every city wants one
  • NYC got one
  • Ottawa had one since the 60s

Research questions

  1. How do we mathematically describe the space of bean sculptures?
  2. How do we help every city find their own unique bean?

Method

Bean Components

  • A quadratic Bézier curve
  • Each has three control points
  • The middle one is constrained for maximum beaniness

Bean Components

  • This is enough for our bean examples:

However...

Turning other landmarks into beans

Novel beans

  • We can combine multiple segments to make composite beans
  • But how do we make sure the result is still smooth?
  • We'll use signed distance functions

Signed Distance Functions

  • A function \(f: \mathbb{R}^n \mapsto \mathbb{R} \)
  • A function that describes, for any point in space, the distance to the surface of a shape
  • Positive means it's outside the shape, negative means it's inside

Signed Distance Functions

  • A circle: for \(f(X) = \vert X \vert - r \)

Signed Distance Functions

  • Combining two SDFs with a union \(\min(d_1, d_2)\)

Signed Distance Functions

  • Combining two SDFs with a smooth union \(d_1 + kg(d_2 - d_1)/k\)

Combining Curves

  • Combining two curves instead of circles:

In 3D

Automatically replacing landmarks

Markov-Chain Monte Carlo (MCMC) Optimization

  1. Pick random starting parameters
  2. Mutate the reference to create a proposal
    • If the proposal is better than the reference, make it the new reference
    • If it's worse, randomly still make it the proposal, where this is less likely to happen the farther from the target it is
  3. Go back to step 2 (until you run out of patience)
  4. Use the best option you've encountered

What does "better" mean?

  • Compare the opaque pixels between a bean and a landmark
  • Maximize intersection: as many black pixels as possible
  • Minimize union: as few red + cyan pixels as possible

In action

Results

Thank you