Inflating an Artists Sketch

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Inflating an Artists Sketch

• Chapter 2 Hoffman
• Nicole J., Victor W., and Nicole T.

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Visual Processing Faults

• How can the mind interpret objects incorrectly?

In this optic illusion line A appears to have
more length than line B.
In this illusion, two parallel lines appear
curved away from one another.
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Everything you perceive visually is actually a
construction of mental processes receiving
sensory input.

• Construction implies similar methods of visual
  interpretation rules
• Even these rules are fallible sometimes one rule
  overrides another, sometimes they compromise, and
  often they deal with probabilities
• The Fundamental Problem of Vision An image at
  the eye has countless possible interpretations

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The fundamental problem of seeing depth

• The image at the eye has two dimensions
  therefore it has countless interpretations in
  three dimensions
• There is a principled ambiguity each time you
  need to see depth because of the construction of
  your 3D interpretation from the 2D image
• However, individuals construct depth according to
  rules so the visual system is biased and will
  only construct worlds that conform to the visual
  rules

Why is it easier to shape a 3D image from the
Necker cube than either of the other cube
viewpoints?
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The fundamental role of visual rules

• You construct visual worlds from ambiguous images
  in conformance to visual rules
• These rules are implicit
• Rather than violate the rules we will construct
  impossible 3D interpretations

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Rule of generic views

• Construct only those worlds for which the image
  is a stable view (i.e. generic)
• Generic views vs. accidental views
• The probability of an accidental viewpoint is
  very low almost nothing

Why does the V vertex make more visual sense
than the chopsticks vertex on the right?
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Rule 1 (generic views)

• Always interpret a straight line in an image as a
  straight line in 3D
• We see this Kopfermann figure as having straight
  lines in 2D therefore as having straight lines in
  3D
• This figure violates Rule 1 for generic visual
  representations
• To see this figure as a cube we must rotate our
  view so that it is generic

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Rule 2 (generic views)

• If the tips of two lines coincide in an image,
  then always interpret them as coinciding in 3D
• Example If you alter the view slightly, a
  generic view is obtained and the cube is seen...

Rules 12 predict this generic viewpoint
and allow us to construct the cube.
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Rules 3 (generic views)

• Always interpret lines colinear in an image as
  colinear in 3D
• The attached boxes violate the rule of generic
  views but are predicted by rule 4, the rule of
  proximity

Even with our current restrictions by visual
rules, this simple drawing can be interpreted in
countless manners
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Rule 4 (rule of proximity)

• Interpret elements nearby in an image as nearby
  in 3D
• Figure The circles surrounding the Necker cube
  inherit their depth from the portion of the cube
  nearest to them

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The rule of projection

• Visual process by which three dimensions are
  smashed to two
• Lead to the discovery of linear and natural
  perspectives in art
• Supported by visual characteristics - sometimes
  vision can reveal depth where it is not present
• Example stereovision 3D world is revealed in
  this image by crossing your eyes...

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Rule 5 (projection)

• Always interpret a curve that is smooth in an
  image as smooth in 3D

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Surface Normals

• Lines which indicate the local orientation of the
  surface of a 3D object rendered in 2D
• Often used by geometers vision researchers
• foreshortening normals w/ smaller angles have
  shorter projected lengths, normal parallel to
  your vision appears as a dot
• Any line, including a normal line, has its
  longest projection when it is perpendicular to
  your line of sight
• Examples writing implement experiment

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Rules 6 7 (projection)

• Where possible, interpret a curve in an image as
  the rim of a surface in 3D
• Where possible, interpret a T-junction in an
  image as a point where the full rim conceals
  itself the cap conceals the stem

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Principle directions and curvatures

• Def. principle directions - Directions in which
  the surface curves most and least
• These are always perpendicular to each other at
  every smooth point on any surface
• Def. principle curvatures - Curvatures of the
  surface of an object corresponding to its
  principle directions
• Def. silhouette 3D image projected on 2D the
  outline of the image is known as its bound, and a
  silhouettes bound is projected by an objects
  rim

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Surfaces curve in three ways

• Convex, concave, and saddle
• Convex regions bound the material of objects
• Concave regions bound pockets of air
• Saddle regions provide a transition between
  convex and concave regions

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Rules 8 9 (projection)

• Interpret each convex point on a bound as a
  convex point on a rim
• Interpret each concave point on a bound as a
  saddle point on a rim

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Rule 10

• Construct surfaces in 3D that are as smooth as
  possible

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Compared with human visual creative abilities,
NASAs IMP is a 6 million bucket of bolts