Announcements

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Announcements

• Quiz solutions on the web page.
• Problem Set 5 on the web page. Due Thursday,
  April 1.
• Results from Problem Set 4

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Perceptual Grouping

• Extra Reading
• Laws of Organization in Perceptual Forms, Max
  Wertheimer (1923).
• http//psy.edu/classics/Wertheimer/Forms/forms.ht
  m

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Perceptual Grouping

• Perceptual grouping is about putting parts
  together into a whole
• Finding regions with a uniform property
• Linking edges into object boundaries
• Surfaces and objects are critical.
• Also, simpler objects such as lines

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Human perceptual grouping

• This has been significant inspiration to computer
  vision.
• Why?
• Perceptual grouping seems to rely partly on the
  nature of objects in the world.
• This is hard to quantify, we hypothesize that
  human vision encodes the necessary knowledge.

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Gestalt Principles of Grouping some history

• Behaviorists were dominant psychological
  theorists in early 20th century.
• To make psych scientific, wanted to view it as
  rules describing relation between stimulus and
  response, described as atomic elements.
• No role for mind.
• This meant no role for internal
  processing/inference/algorithms.
• Influential early behaviorist was Pavlov

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• Gestalt movement claimed atomic stimulus and
  response dont exist.
• The mind perceives world as objects, as wholes,
  not as atomic primitives.
• Cant understand psych without understanding how
  we perceive the world.

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I stand at the window and see a house, trees,
sky. Theoretically I might say there were 327
brightnesses and nuances of colour. Do I have
"327"? No. I have sky, house, and trees. It is
impossible to achieve "327 " as such. And yet
even though such droll calculation were possible
and implied, say, for the house 120, the trees
90, the sky 117 -- I should at least have this
arrangement and division of the total, and not,
say, 127 and 100 and 100 or 150 and 177. Max
Wertheimer, 1923
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I. A row of dots is presented upon a homogeneous
ground. The alternate intervals are 3 mm. and 12
mm.                                            
                                                  
                                                  
            Normally this row will be seen as
ab/cd, not as a/bc/de. As a matter of fact it is
for most people impossible to see the whole
series simultaneously in the latter grouping.
Max Wertheimer
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Gestalt Movement

• Perceptual organization was a big issue.
• How we perceive the world in terms of
  things/objects, not pixels.
• This was part of broader attack on behaviorism.
• Gestalt viewed mind as constructing
  representations of the world, no
  learning/behavior could be understood without
  understanding this.
• These representations were constructing by
  inferences of the mind.

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Issues in Perceptual Organization

• What is the role of an edge in an image? To what
  object (if any) does it belong?

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If you know what is in the next image, silently
raise your hand. Dont call out.
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(Bregman)
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Issues in Perceptual Organization

• What factors determine which parts of an image
  are combined in the same object?

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Proximity
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Good Continuation
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Good Continuation
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Common Form (includes color and texture)
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Connectivity
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Symmetry
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Symmetry
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Convexity (stronger than symmetry?)
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Good continuation also stronger than symmetry?
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Closure
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Closure
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Higher Level Knowledge
Sometimes, it doesnt play seem to play such a
big role.
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Higher level Knowledge
and sometimes it does. If you know what is in
the next image, silently raise your hand. Dont
call out.
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Other Factors

• Common fate (ie., common motion).
• Good continuation in time.
• Parallelism
• Collinearity

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Take Home Message

• We perceive the world in terms of objects, not
  pixels.
• What forms an object is determined by
  regularities and non-trivial inference.
• Gestalt Psychologists showed the importance of
  representation and inference.

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Computer Vision Again

• Divide P.O. approaches into two groups.
• Parametric We have a description of what we
  want, with parameters
• Examples lines, circles, constant intensity,
  constant intensity Gaussian noise.
• Non-parametric We have constraints the group
  should satisfy, or optimality criteria.
• Example SNAKES. Find the closed curve that is
  smoothest and that also best follows strong image
  gradients.

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The Meta-Algorithm

• Define what it means for a group to be good.
• Usually this involves simplifications
• Search for the best group.
• Usually this is intractable, so short-cuts are
  needed.

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Parametric Grouping Grouping Points into Lines

• Basic Facts about Lines

(a,b)

• (x,y) is on line if (x,y).(a,b) c
• ax by c
• Distance from (x,y) to line is
• (a,b).(x,y) ax by provided aa bb
  1

c
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Line Grouping Problem
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This is difficult because of

• Extraneous data Clutter
• Missing data
• Noise

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Precise Definition?

• Find a line that is close to as many points as
  possible.
• Close could mean with e pixels.
• Find k lines so that every point is close to one
  of them.
• Close could mean with e pixels.
• Or, could mimimize sum of squares distance from
  each point to nearest line.

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Brute Force Approach

• Try every possibility
• Every line (infinite)
• Fit a line to every subset of points
  (exponential).
• Discrete sampling
• Could sample slope and offset uniformly.
• Sample random lines
• Random lines likely to be good.

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RANSAC Random Sample Consensus

• Generate Lines using Pairs of Points
• How many samples?
• Suppose p is fraction of points from line.
• n points needed to define hypothesis (2 for
  lines)
• k samples chosen.
• Probability one sample correct is

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RANSAC for Lines Continued

• Decide how good a line is
• Count number of points within e of line.
• Parameter e measures the amount of noise
  expected.
• Other possibilities. For example, for these
  points, also look at how far they are.
• Pick the best line.

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(Forsyth Ponce)
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The Hough Transform for Lines

• A line is the set of points (x, y) such that
• y mx b
• For any (x, y) there is a line in (m,b) space
  describing the lines through this point. Just
  let (x,y) be constants and m, b be unknowns.
• Each point gets to vote for each line in the
  family if there is a line that has lots of
  votes, that should be the line passing through
  the points

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Mechanics of the Hough transform

• Construct an array representing m, b
• For each point, render the line ymxb into this
  array, adding one at each cell
• Questions
• how big should the cells be? (too big, and we
  cannot distinguish between quite different lines
  too small, and noise causes lines to be missed)

• How many lines?
• count the peaks in the Hough array
• Who belongs to which line?
• tag the votes
• Can modify voting, peak finding to reflect noise.
• Big problem if noise in Hough space different
  from noise in image space.

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Some pros and cons

• Run-time
• Complexity of RANSAC nnn
• Complexity of Hough nd

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Error behavior

• Hough handles error with buckets. This gives a
  larger set of lines consistent with point, but
  ad-hoc.
• Ransac handles error with threshold.
  Well-motivated for error in other points, but not
  for error in first 2 points.
• But works if we find some 2 points w/ low error.
• Error handling sloppy -gt clutter bigger problem.
• Many variations to handle these issues.

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Clustering Color/Intensity
Group together pixels of similar color/intensity.
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Parametric Clustering

• Each cluster has a mean color/intensity, and a
  radius of possible colors.
• For intensity, this is just dividing histogram
  into regions.
• For color, like grouping 3D points into spheres.

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K-means clustering

• Brute force difficult because many spheres, many
  pixels.
• Assume all spheres same radius just need sphere
  centers.
• Iterative method.
• If we knew centers, it would be easy to assign
  pixels to clusters.
• If we knew which pixels in each cluster, it would
  be easy to find centers.
• So guess centers, assign pixels to clusters, pick
  centers for clusters, assign pixels to clusters,
  .