EDGE DETECTION Stages of the Canny Algorithm * Large

1
Edge Detection
2
Edge Detection

• Edges characterize boundaries of objects in image
• A fundamental problem in image processing
• Edges are areas with strong intensity contrasts
• A jump in intensity from one pixel to the next
• Edge detected image
• Reduces significantly the amount of data,
• Filters out useless information,
• Preserves the important structural properties

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• Our goal is to extract a line drawing
  representation from an image
• Useful for recognition edges contain shape
  information
• invariance

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Need of Edge Detection

• Digital artists use it to create image outlines.
• The output of an edge detector can be added back
  to an original image to enhance the edges
• Edge detection is often the first step in image
  segmentation
• Edge detection is also used in image registration
  by alignment of two images that may have been
  acquired at separate times or from different
  sensors

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Ideal and Ramp Edges
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Thick Edge

• The slope of the ramp is inversely proportional
  to the degree of blurring in the edge.
• We no longer have a thin (one pixel thick) path.
• Instead, an edge point now is any point contained
  in the ramp, and an edge would then be a set of
  such points that are connected.
• The thickness of an edge is determined by the
  length of the ramp.
• The length is determined by the slope, which is
  in turn determined by the degree of blurring.
• Blurred edges tend to be thick and sharp edges
  tend to be thin

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First and Second Derivatives
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Second Derivatives

• Produces 2 values for every edge in an image (an
  undesirable feature)
• An imaginary straight line joining the extreme
  positive and negative values of the second
  derivative would cross zero near the midpoint of
  the edge. (zero-crossing property)
• Quite useful for locating the centers of thick
  edges

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Noise Images

• First column images and gray-level profiles of a
  ramp edge corrupted by random Gaussian noise of
  mean 0 and ? 0.0, 0.1, 1.0 and 10.0,
  respectively.
• Second column first-derivative images and
  gray-level profiles.
• Third column second-derivative images and
  gray-level profiles.

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Observation

• Fairly little noise can have such a significant
  impact on the two key derivatives used for edge
  detection in images
• Image smoothing should be serious consideration
  prior to the use of derivatives in applications
  where noise is likely to be present.

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Edge Point

• To determine a point as an edge point
• Determine the transition in grey level associated
  with the point which is significantly stronger
  than the background at that point.
• Use threshold to determine whether a value is
  significant or not.
• Note that the points two-dimensional first-order
  derivative must be greater than the specified
  threshold

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Gradient Operator

• first derivatives are implemented using the
  magnitude of the gradient.

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Gradient Direction

• Let ? (x,y) represent the direction angle of the
  vector ?f at (x,y)
• ? (x,y) tan-1(Gy/Gx)

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Gradient Masks
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Diagonal edges with Prewitt and Sobel Masks
Sobel masks have slightly superior
noise-suppression characteristics which is an
important issue when dealing with derivatives.
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Example

• Original Image
• Gx, component of the gradient in the
  x-direction
• Gy, component of the gradient in the
  y-direction
• Gradient image,
• Gx Gy

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Example
Same sequence as previous figure, but with
original image smoothed with a 5 x 5 averaging
filter
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Example

• Diagonal edge detection
• Result of using the Prewitt masks
• Result of using the Sobel masks

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Laplacian
Laplacian masks
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Laplacian of Gaussian (LOG)

• Laplacian combined with smoothing as a precursor
  to find edges via zero-crossing.

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Mexican Hat
positive central term surrounded by an adjacent
negative region (a function of distance) zero
outer region

• Laplacian of a Gaussian
• 3-D plot
• Image (black is negative, gray is the zero plane,
  and white is positive)
• Cross-section showing zero-crossings
• 5x5 mask approximation to (a)

the coefficient must be sum to zero
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Linear Operation

• Second derivation is a linear operation
• Thus, ?2f is the same as convolving the image
  with Gaussian smoothing function first and then
  computing the Laplacian of the result

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Example

• Original image
• Sobel Gradient
• Spatial Gaussian smoothing function
• Laplacian mask
• LoG
• Threshold LoG
• Zero crossings

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Zero Crossing LoG

• Approximate the zero crossing from LoG image
• Threshold the LoG image by setting all its
  positive values to white and all negative values
  to black.
• Zero crossings occur between positive and
  negative values of the thresholded LoG.

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Zero Crossing vs. Gradient

• Attractive
• Zero crossing produces thinner edges
• Noise reduction
• Drawbacks
• sophisticated computation.
• Gradient is more frequently used.

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Edge Linking and Boundary Detection

• Edge detection algorithm are followed by linking
  procedures to assemble edge pixels into
  meaningful edges.
• Basic approaches
• Local Processing
• Global Processing via the Hough Transform
• Global Processing via Graph-Theoretic Techniques

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Problems with Edge Detection Methods

• Most of these partial derivative operators are
  sensitive to noise,
• Use of these masks produces thick edges or
  boundaries,
• Gives spurious edge pixels due to noise.

To overcome the effect of noise, smoothing
operation is performed before edge detection
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Smoothing based Edge Detection

• Two operators which use smoothing
• Marr-Hildreth operator
• Laplacian of Gaussian function (LOG)
• Follows 2-Operations
• Smoothing
• Applying Laplacian operator
• Or generate the combined mask of LOG
• Canny Edge Detector

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Canny Edge Detection

• Normally, edge operators use one threshold for
  whole image

Sobel output
Sobel output
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Canny Edge Detector (J. Canny 1986)

• An "optimal" edge detector means
• Good detection - the algorithm should mark as
  many real edges in the image as possible.
• Good localization - edges marked should be as
  close as possible to the edge in the real image.
• Canny edge detector uses two threshold values to
  detect weak and strong edges

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Canny Edge Detector

• Stages of the Canny Algorithm
• Noise reduction
• Finding the intensity gradient of the image
• Non-maximum suppression
• Tracing edges through the image and hysteresis
  thresholding

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Stages of the Canny algorithm

• Noise reduction raw image is convolved with a
  Gaussian filter
• Finding the intensity gradient of the image
• Intensity gradient is estimated from the smoothed
  image using simple horizontal and vertical
  difference operators
• Gradient direction together with the gradient
  magnitude then gives an estimated intensity
  gradient at each point in the image
• Canny algorithm uses both gradient magnitude and
  direction in the edge detection

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Stages of the Canny algorithm

• Non-maximum suppression
• A search is carried out to determine if the
  gradient magnitude assumes a local maximum in the
  gradient direction
• From this stage, referred to as non-maximum
  suppression, a set of edge points in the form of
  a binary image are obtained
• Output of this stage is sometimes referred to as
  "thin edges"

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Stages of the Canny Algorithm

• Large threshold gives true edges
• Small threshold gives false edges
• Canny algorithm does not use same threshold for
  whole image
• It does thresholding with hysteresis
• Thresholding with hysteresis requires
• two thresholds high and low
• Therefore we begin by applying a high threshold

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Stages of the Canny Algorithm

• This marks out the edges we can be fairly sure
  are genuine.
• Starting from these, using the directional
  information derived earlier, edges can be traced
  through the image.
• While tracing an edge, we apply the lower
  threshold, allowing us to trace faint sections of
  edges as long as we find a starting point.

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Stages of the Canny algorithm
.contd
Original image
Smoothing by Gaussian convolution
Differential operators along x and y axis
Non-maximum suppression finds peaks in the image
gradient
Hysteresis thresholding locates edge strings
Edge map
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Sobel
Canny
LOG
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Sobel
Canny
LOG
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Sobel
Canny
LOG