Segmentation

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Segmentation

• Kyongil Yoon

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Segmentation

• Obtain a compact representation of what is
  helpful (in the image)
• No comprehensive theory of segmentation
• Human vision Grouping and Gestalt
• Proximity, similarity, common fate, common
  region, parallelism, closure, symmetry,
  continuity, familiar configuration

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Segmentation by clustering

• Partitioning vs. grouping
• Applications
• Background subtraction
• Shot boundary detection
• Image segmentation by clustering pixels
• Using simple clustering
• Agglomerative clustering (clustering by merging)
• Divisive clustering (clustering by splitting)
• K-means
• Using graph-theoretic clustering
• Affinity measure
• Normalized cut
• cut(A,B)/assoc(A,V) cut(A,B)/assoc(B,V)

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K-Means

• Choose k data points to act as cluster centers
• Until the cluster centers are unchanged
• Allocate each data point to cluster whose center
  is nearest
• Now ensure that every cluster has at least one
  data point possible techniques for doing this
  include supplying empty clusters with a point
  chosen at random from points far from their
  cluster center.
• Replace the cluster centers with the mean of the
  elements in their clusters.
• end

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Graph Eigenvectors

• Construct an affinity matrix
• Compute the eigenvalues and eigenvectors of the
  affinity matrix
• Until there are sufficient clusters
• Take the eigenvector corresponding to the largest
  unprocessed eigenvalue zero all components
  corresponding to elements that have already been
  clustered, and threshold the remaining components
  to determine which element belongs to this
  cluster, choosing a threshold by clustering the
  components, or using a threshold fixed in
  advance.
• If all elements have been accounted for, there
  are sufficient clusters
• end

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Segmentation by fitting a model

• To assert that pixels belong together to conform
  to some model
• Large scale explicit model
• Hough transform
• Three problems
• What is the line?
• Which points belong to which line?
• How many lines?
• Point space lt-gt line space
• xcos(t) ysin(t) r 0, (t, r) line space
• Half-infinite cylinder
• Quantization errors, difficulties with noise
• Fitting lines, fitting curves
• Least square
• Total least square

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Segmentation by fitting a model(2)

• Two big problems
• Robustness what if one data point is FAR, and
  all others fill well?
• Missing data which point is noise and which
  point is not?
• Robustness
• Outliers Improve the model either by giving the
  noise heavier tails or allowing an explicit
  outlier model
• M-estimators
• Assuming that somewhere in the collection of
  process close to our model is the real process,
  and it just happens to be the one that makes the
  estimator produce the worst possible estimates

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Segmentation by fitting a model(3)

• RANSAC (RAMdom SAmple Consensus)
• Searching for a random sample that leads to a fit
  on which many of the data points agree
• Determine n the smallest of points
  required k the of iterations required t
  the threshold used to identify a point that fits
  well d the of nearby points requiredUntil
  k iterations have occurred Pick n sample
  points Fit to that set of n points For each
  data point outside the sample Test distance
  if the distance lt t, it is close If there are d
  or more points close, this is a good fit.
  Refit the line using all these pointsEnd
• Use the best fit from this collection, using the
  fitting error as a criterion
• Need to choose 3 parameters
• of samples required (n)
• Telling whether a point is close (t)
• of points that must agree (d)

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Segmentation

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