Contour Extraction

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Contour Extraction
Lecture 10
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Canny Edge Detection

• Steps
• Canny enhancer
  
• Image smoothing by Gaussian filter
• Computing the image gradient
• Non-maximum suppression
• Thin multi-pixel wide ridges down to single
  pixel width
• Linking and thresholding
• Low, high edge-strength thresholds
• Accept all edges over low threshold that are
  connected to edge over high threshold

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CANNY_ENHANCER

• The input is image I
  G is a zero mean Gaussian
  filter (std ?)
• J I G (smoothing)
• For each pixel (i,j) (edge enhancement)
• Compute the image gradient
• ?J(i,j) (Jx(i,j),Jy(i,j))
• Estimate edge strength
• Mag(i,j) (Jx2(i,j) Jy2(i,j))1/2
• Estimate edge orientation
• Dir(i,j) arctan(Jy(i,j)/Jx(i,j))
• The output are images Mag and Dir

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How do we detect edges?

• Mag has large values at edges
• Find local maxima

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• but it also may have wide ridges around the
  local maxima (large values around the edges)

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Graphical Interpretation
x
x
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Non-maximum suppression Select the single
maximum point across the width of an edge.
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NONMAX_SUPRESSION (Mag,Dir)

• Consider 4 directions Del (1,0),(1,1),(0,1),(
  -1,1)
• 
  Del- (-1,0),(-1,-1),(0,-1),(1,1)
• For each pixel (i,j) do
• Find the direction of gradient (normal to the
  edge) d
  (Dir(i,j)?/8) mod ?/4
• If Mag(i,j) is smaller than at least one of its
  neigh. along d then IN(i,j)0, otherwise,
  IN(i,j) Mag(i,j)
• If Mag(i,j)ltMag((i,j)Del(d)) then IN(i,j)0
• Else If Mag(i,j)ltMag((i,j)Del-(d)) then
  IN(i,j)0
• Else INMag(i,j)
• The output is the thinned edge image IN

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Thresholding

• Edges are found by thresholding the output of
  NONMAX_SUPRESSION
• If the threshold is too high
• Very few (none) edges
• High MISDETECTIONS, many gaps
• If the threshold is too low
• Too many (all pixels) edges
• High FALSE POSITIVES, many extra edges

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Edge Hysteresis (Lag)

• Idea Maintain two thresholds thigh and tlow
• Use thigh to find strong edges to start edge
  chain
• Use tlow to find weak edges which continue edge
  chain
• Typical ratio of thresholds is roughly
• thigh / tlow 2

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HYSTERESIS_THRESH(IN,Dir,Tlow,Thigh)Edge Linking

• For all pixels in IN scanning in a fixed order
• Locate the next unvisited pixel s.t.
  IN(i,j)gtThigh
• Starting from IN(i,j), follow the chains of
  connected local maxima, in both directions
  perpendicular to the edge normal, as long as
  INgtTlow.
• Mark all visited points, and save the location of
  the contour points.
• Output a set of lists describing the contours.

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Canny Edge Detection (Example)
Strong connected weak edges
Original image
Strong edges only
Weak edges
courtesy of G. Loy
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Effect of threshold
original

? 1
? 1
Thigh 255 Tlow 220
Thigh 255 Tlow 1
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Effect of threshold and of ? (Gaussian kernel
size)
original

? 1
? 2
Thigh 120 Tlow 1
Thigh 120 Tlow 1
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?? ????
? 0.002
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Salt Pepper noise
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Edge Linking

• The next step is to try to collect these pixels
  together into a set of edges lines, contours.
• The practical problem may be much more difficult
  than the idealized case
• Small pieces of edges may be missing
• Small edge segments may appear to be present due
  to noise where there is no real edge, etc.

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In general, edge linking methods can be
classified into two categories Local Edge
Linkers -- where edge points are grouped to form
edges by considering each point's
relationship to any neighbouring edge points.
Global Edge Linkers -- where all edge points
in the image plane are considered at the same
time and sets of edge points are sought according
to some similarity constraint, such as points
which share the same edge equation.
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• Local Edge Linking Methods
• Most edge detectors yield information about the
  magnitude of the gradient at an edge point and,
  more importantly, the direction of the edge in
  the locality of the point.
• This is obviously useful when deciding which edge
  points to link together since edge points in a
  neighbourhood which have similar gradients
  directions are likely to lie on the same edge.

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• Local edge linking methods usually start at some
  arbitrary edge point and consider points in a
  local neighbourhood for similarity of edge
  direction.
• If the points satisfy the similarity constraint
  then the points are added to the current edge
  set.
• If the points do not satisfy the constraint then
  we conclude we are at the end of the edge, and so
  the process stops.
• A new starting edge point is found which does not
  belong to any edge set found so far, and the
  process is repeated.
• An advantage of such methods is that they can
  readily be used to find arbitrary curves.

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• Other methods have posed the edge linking problem
  as
• A graph or tree search problem

Linkage rule
?Mag(pi) ? max
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• Other methods have posed the edge linking problem
  as
• A graph or tree search problem

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• Other methods have posed the edge linking problem
  as
• A graph or tree search problem
• Dynamic programming problem -- where functions
  measuring the error in the fitting of an edge to
  a set of points are minimized to find the best
  fitting edges in the image
• Many other edge linking techniques exist