edges and contours– chapter 7. visual perception we don’t need to see all the color detail to...
TRANSCRIPT
Edges and Contours– Chapter 7
Visual perception
• We don’t need to see all the color detail to recognize the scene content of an image
• That is, some data provides critical information for recognition, other data provides information that just makes things look “good”
Visual perception
• Sometimes we see things that are not really there!!!
Kanizsa Triangle (and variants)
Edges
• Edges (single points) and contours (chains of edges) play a dominant role in (various) biological vision systems– Edges are spatial positions in the image where the
intensity changes along some orientation (direction)
– The larger the change in intensity, the stronger the edge
– Basis of edge detection is the first derivative of the image intensity “function”
First derivative – continuous f(x)• Slope of the line at a point tangent to
the function
)()(' xdx
dfxf
First derivative – discrete f(u)• Slope of the line joining two adjacent (to the selected
point) point
2
)1()1()('
ufufuf
u-1 u+1u
Discrete edge detection• Formulated as two partial derivatives
– Horizontal gradients yield vertical edges
– Vertical gradients yield horizontal edges
– Upon detection we can learn the magnitude (strength) and orientation of the edge
• More in a minute…
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I
),( vuv
I
NOTE
• In the following images, only the positive magnitude edges are shown
• This is an artifact of ImageJ
Process->Filters->Convolve… command
• Implemented as an edge operator, the code would have to compensate for this
Detecting edges – sharp image
Image VerticalEdges
5.00.05.0
HorizontalEdges
5.0
0.0
5.0
Detecting edges – blurry image
Image VerticalEdges
5.00.05.0
HorizontalEdges
5.0
0.0
5.0
The problem…• Localized (small neighborhood)
detectors are susceptible to noise
The solution
• Extend the neighborhood covered by the filter– Make the filter 2 dimensional
• Perform a smoothing step prior to the derivative– Since the operators are linear filters, we
can combine the smoothing and derivative operations into a single convolution
Edge operator
• The following edge operators produce two results– A “magnitude” edge map (image)
– An “orientation” edge map (image)
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),(),( tan
1
vu
vuvu
DD
x
y
Prewitt operator
• 3x3 neighborhood
• Equivalent to averaging followed by derivative– Note that these are convolutions, not matrix multiplications
101
101
101
HP
x
111
000
111
HP
y
101
1
1
1
H
P
y
1
0
1
111HP
y
Prewitt – sharp image
Prewitt – blurry image
Prewitt – noisy image
• Clearly this is not a good solution…what went wrong?– The smoothing just smeared out the noise
• How could you fix it?– Perform non-linear noise removal first
Prewitt magnitude and direction
Prewitt magnitude and direction
Sobel operator
• 3x3 neighborhood
• Equivalent to averaging followed by derivative– Note that these are convolutions, not matrix multiplications
– Same as Prewitt but the center row/column is weighted heavier
101
202
101
HP
x
121
000
121
HP
y
101
1
2
1
H
P
y
1
0
1
121HP
y
Sobel – sharp image
Sobel – blurry image
Sobel – noisy image
• Clearly this is not a good solution…what went wrong?– The smoothing just smeared out the noise
• How could you fix it?– Perform non-linear noise removal first
Sobel magnitude and direction
Sobel magnitude and direction
Sobel magnitude and direction
• Still not good…how could we fix this now? • Using the information of the direction (lots of randomly oriented,
non-homogeneous directions) can help to eliminate edged due to noise
– This is a “higher level” (intelligent) function
Roberts operator
• Looks for diagonal gradients rather than horizontal/vertical
• Everything else is similar to Prewitt and Sobel operators
01
101HR
10
012HR
Roberts magnitude and direction
Roberts magnitude and direction
Roberts magnitude and direction
Compass operators
• An alternative to computing edge orientation as an estimate derived from two oriented filters (horizontal and vertical)
• Compass operators employ multiple oriented filters
• To most famous are– Kirsch – Nevatia-Babu
Kirsch Filter
• Eight 3x3 kernel– Theoretically must perform eight convolutions– Realistically, only compute four convolutions, the other four
are merely sign changes
• The kernel that produces the maximum response is deemed the winner– Choose its magnitude– Choose its direction
Kirsch filter kernels
101
202
101
101
202
101
Vertical edges
210
101
012
210
101
012
L-R diagonal edges
012
101
210
012
101
210
R-L diagonal edges
121
000
121
121
000
121
Horizontal edges
Kirsch filter
Nevatia-Babu Filter
• Twelve 5x5 kernel– Theoretically must perform twelve convolutions– Increments of approximately 30°– Realistically, only compute six convolutions, the
other six are merely sign changes
• The kernel that produces the maximum response is deemed the winner– Choose its magnitude– Choose its direction
Nevatia-Babu filter