Class 07: Drawings as Values

Held: Tuesday, 8 September 2009

Summary: We consider another way to think about image. In particular, we consider what we call the drawings as values model, in which we describe images by transforming and composing simple pictures.

Related Pages:

• EBoard.
• Lab: Drawings as Values.
• Reading: Drawings as Values.
• Due: Lab Writeup 1: Scripting the GIMP Tools.

Notes:

• EC/Academic: This week is the kickoff of the Department's Thursday Extras series. Jerod Weinman will be discussing Efficient machine learning for computer vision-based depth perception.
• EC/Support: Women's Soccer, Wednesday at 5:30.
• CS Table this Friday (noon, JRC224A): Technology and Disability. We will be reading A blind person's interactions with technology. No EC for attending, but you might find the discussion interesting. I'll have copies of the paper available
• Are there questions on Assignment 2?
• Two readings for tomorrow: Writing Your Own Procedures and How Scheme Evaluates Expressions (version 2).

Overview:

• Representing images.
• Thinking about drawings through composition/decomposition.
• Pure approaches vs impure approaches.

Representing Images

• As you may recall, one of the initial themes of this course is that there is more than one way to represent an image.
• Early on, we considered multiple ways to draw smiley faces.
• In this course, we will also consider multiple computational ways to think about images.
  • You've seen one: We can describe images by the GIMP commands necessary to create them.
  • More precisely, we can describe images computationally by a series of calls to the MediaScript GIMP Tools procedures.
  • We're about to explore another.

Drawings

• The drawing representation takes a very different perspective.
• We start with a few basic values (the unit square and the unit circle).
• We add a few operations
  • Scaling
  • Shifting
  • Recoloring
  • Grouping
• We see what benefits (and obstacles) this new approach gives us.
• Once we've described a drawing, we can create an image from it using drawing->image.
• This model of images models one of the ways we sometimes think about images: Every image can be thought of as a composition of simpler components.
  • We just take that idea to the extreme.

Purity

• Note that the definition of drawings uses induction, in much the same way that the definition of whole numbers uses induction.
• For whole numbers:
  • 0 is a whole number
  • If w is a whole number, 1+w is a whole number
• For drawings
  • The unit circle is a drawing.
  • The unit square is a drawing.
  • If d is a drawing, then a shifted version of d is a drawing.
  • If d is a drawing, then a scaled version of d is a drawing.
  • If d1 and d2 are drawings, the grouping of d1 and d2 is a drawing.
• When we build a new whole number from a previous whole number (by adding 1), we don't affect the previous whole number.
• Similarly, when we build a new drawing from a previous drawing, we don't affect the previous drawing.
• Contrast this with the GIMP tools, in which each command changes (sometimes irrevocably) the underlying image.
• When operations do not affect the underlying data structure, we call them pure operations.

Representing Drawings

• There is an underlying representation.
• You shouldn't need to know it.
• But it can be helpful to look.