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- Our goal is to extract
a “line drawing” representation from an image
- Useful for recognition:
Edge Detection Ref: Forsyth+Ponce Ch. 7,8 Trucco+Verri Ch. 4 Our - - PowerPoint PPT Presentation
Edge Detection Ref: Forsyth+Ponce Ch. 7,8 Trucco+Verri Ch. 4 Our - - PowerPoint PPT Presentation
Edge Detection Ref: Forsyth+Ponce Ch. 7,8 Trucco+Verri Ch. 4 Our goal is to extract a line drawing representation from an image Useful for recognition: edges contain shape information invariance Edge detection Derivatives
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Edge detection
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Derivatives
- Edges are locations with high image
gradient or derivative*
- Estimate derivative using finite
difference
- Problem?
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Smoothing
- Reduce image noise by smoothing with
a Gaussian
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Convolution is Associative
- We compute derivative of smoothed
image:
- Since convolution is associative:
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Separable Convolution
- Note that G can be factored as
and computed as two 1-D convolutions
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Edge orientation
- Would like gradients in all directions
- Approximate:
– Compute smoothed derivatives in x,y directions – Edge strength – Edge normal
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Canny Edge Detection
- Compute edge strength and orientation
at all pixels
- “Non-max suppression”
– Reduce thick edge strength responses around true edges
- Link and threshold using “hysteresis”
– Simple method of “contour completion”
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Non-maximum suppression: Select the single maximum point across the width
- f an edge.
Slides by D. Lowe
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Non-maximum suppression At q, the value must be larger than values interpolated at p or r.
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Examples: Non-Maximum Suppression
courtesy of G. Loy
Original image Gradient magnitude Non-maxima suppressed
Slide credit: Christopher Rasmussen
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fine scale high threshold
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coarse scale, high threshold
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coarse scale low threshold
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Linking to the next edge point
Assume the marked point is an edge point. Take the normal to the gradient at that point and use this to predict continuation points (either r or s).
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Edge Hysteresis
- Hysteresis: A lag or momentum factor
- Idea: Maintain two thresholds khigh and klow
– Use khigh to find strong edges to start edge chain – Use klow to find weak edges which continue edge chain
- Typical ratio of thresholds is roughly
khigh / klow = 2
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Example: Canny Edge Detection
courtesy of G. Loy
gap is gone
Original image Strong edges
- nly
Strong + connected weak edges Weak edges
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Problem?
- Texture