EE663 Image Processing Edge Detection 2

1
EE663Image ProcessingEdge Detection 2

• Dr. Samir H. Abdul-Jauwad
• Electrical Engineering Department
• King Fahd University of Petroleum Minerals

2
Image Features

• Image features may appear in two contexts

• Global properties of the image (average gray
  level, etc) global features
• Parts of the image with special properties (line,
  circle, textured region) local features

• Here, assume second context for image features

• Local, meaningful, detectable parts of the image

• Detection of image features
• Detection algorithms produce feature
  descriptors
• Example line segment descriptor coordinates of
  mid-point, length, orientation

3
Edge Detection

• Definition of edges

• Edges are significant local changes of intensity
  in an image.
• Edges typically occur on the boundary between two
  different regions in an image.

4
Edge Detection

• Examples

5
Edge Detection

• Goal of edge detection

• Produce a line drawing of a scene from an image
  of that scene.
• Important features can be extracted from the
  edges of an image (e.g., corners, lines, curves).
• These features are used by higher-level computer
  vision algorithms (e.g., segmentation,
  recognition).

6
Edge Detection

• Not that easy

7
Edge Detection

• What causes intensity changes?

• Geometric events
• object boundary (discontinuity in depth and/or
  surface color and texture)
• surface boundary (discontinuity in surface
  orientation and/or surface color and texture)
• Non-geometric events
• specularity
• shadows (from other objects or from the same
  object)
• inter-reflections

8
Edge Detection

• Edge descriptors

• Edge normal unit vector in the direction of
  maximum intensity change.
• Edge direction unit vector to perpendicular to
  the edge normal.
• Edge position or center the image position at
  which the edge is located.
• Edge strength related to the local image
  contrast along the normal.

9
Modeling Intensity Changes

• Edges can be modeled according to their intensity
  profiles

• Step edge
• the image intensity abruptly changes from one
  value to one side of the discontinuity to a
  different value on the opposite side.

• Ramp edge
• a step edge where the intensity change is not
  instantaneous but occurs over a finite distance.

10
Modeling Intensity Changes

• Ridge edge
• the image intensity abruptly changes value but
  then returns to the starting value within some
  short distance
• generated usually by lines

11
Modeling Intensity Changes

• Roof edge
• a ridge edge where the intensity change is not
  instantaneous but occurs over a finite distance
• generated usually by the intersection of surfaces

12
Edge Detection

• The four steps of edge detection

• Smoothing suppress as much noise as possible,
  without destroying the true edges.
• Enhancement apply a filter that responds to
  edges in the image
• Detection determine which edge pixels should be
  discarded as noise and which should be retained
  (usually, thresholding provides the criterion
  used for detection).
• Localization determine the exact location of an
  edge (sub-pixel resolution might be required for
  some applications, that is, estimate the location
  of an edge to better than the spacing between
  pixels). Edge thinning and linking are usually
  required in this step.

13
Edge Detection

• Edge detection using derivatives

• Calculus describes changes of continuous
  functions using derivatives.
• An image is a 2D function, so operators
  describing edges are expressed using partial
  derivatives.
• Points which lie on an edge can be detected by
  either

• detecting local maxima or minima of the first
  derivative
• detecting the zero-crossing of the second
  derivative

14
Edge Detection

• Edge detection using derivatives cont.

15
Edge Detection

• Differencing 1D signals

• To compute the derivative of a signal, we
  approximate the derivative by finite differences
• Computing the 1st derivative

16
Edge Detection

• Computing the 1st derivative cont.

Backward difference
Forward difference
Central difference
17
Edge Detection

• Computing the 1st derivative cont.

• Examples using the edge models and the mask -1
  0 1 (centered about x)

18
Edge Detection

• Computing the 2nd derivative

• This approximation is centered about x 1
• By replacing x 1 by x we obtain

19
Edge Detection

• Computing the 2nd derivative cont.

20
Edge Detection

• Computing the 2nd derivative cont.

• Examples using the edge models

21
Edge Detection

• Image derivatives

Image I
22
Edge Detection

• Image derivatives

Image I
23
Derivatives and Noise

• Derivatives are strongly affected by noise
• obvious reason image noise results in pixels
  that look very different from their neighbors
• The larger the noise - the stronger the response

• What is to be done?
• Neighboring pixels look alike
• Pixel along an edge look alike
• Image smoothing should help
• Force pixels different to their neighbors
  (possibly noise) to look like neighbors

24
Derivatives and Noise
Increasing noise

• Need to perform image smoothing as a preliminary
  step
• Generally use Gaussian smoothing

25
Edge Detection

• Possible detectors

• Gradient operators
• Roberts
• Prewitt
• Sobel
• Gradient of Gaussian (Canny)
• Laplacian of Gaussian (Marr-Hildreth)
• Facet Model Based Edge Detector (Haralick)

26
Edge Detection Using the Gradient

• Definition of the gradient

• To save computations, the magnitude of gradient
  is usually approximated by

27
Edge Detection Using the Gradient

• Properties of the gradient

• The magnitude of gradient provides information
  about the strength of the edge
• The direction of gradient is always perpendicular
  to the direction of the edge

• Main idea

• Compute derivatives in x and y directions
• Find gradient magnitude
• Threshold gradient magnitude