Targil 2 Image enhancement and edge detection.

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Targil 2 Image enhancement and edge detection.
For both we will use image derivatives.
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Image enhancement

• Histogram enhancement (histogram equalization)
• Reducing noise (smoothing, median)
• Sharpening

• Emphasize the details
• Make the edges stronger
• Problem we magnify the noise

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Sharpening Subtracting The Laplacian
F(x)
F(x)
F(x)
F(x)-F(x)
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Reminder Convolution
image
Kernel, Convolver
For example
means that
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Image derivatives
(Convolve with 1 -1)
(Convolve with 1 -1T)
A better kernel
(Convolve with ½1 0 -1)
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Image derivatives (cont)

• Problem the image is not continuous.
• A better approximation
• Locally approximate the image with a smooth
  surface.
• Compute the derivatives of this surface.

Popular kernels
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The second derivative
Check that
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The Laplacian
Equation
The matrix
Subtracting the Laplacian
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Sharpening Example
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Edge Detection
Why do we need it ?

• A compact representation of the image
• More robust to light changes.
• Easier to follow (tracking and computations of
  camera motion)
• Segmentation usually, edges are located at
  transitions between objects
• Used for texture analysis

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Edge Detection
Wide edge
Noise

• What are edges ?
• How to find the edges ?
• How to compute the exact location of an edge ?

Texture
T-junction
Transition between objects
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The gradient
The vector of derivatives
Edge Size
Edge Direction
Derivative in Direction ?
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The gradient
Original
Gradient
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Example Derivatives
Ix
-1 0 1


-1 0 1

Iy

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Gradient
Ix2 Iy2

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Edge Localization-Zero Crossing
Where exactly is the edge ?
f
Zero crossing of f
f
Problem f is very noisy Smooth first !
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A smoothing with a 2D Gaussian
1 1
(We usually use the binomial coefficients
instead.)
1 2 1
1 3 3 1
1 4 6 4 1
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Canny Edge Detection

• Computing the image derivatives Gx, Gy
• Smoothing with a Gaussian.
• Using simple derivative kernels.
• Compute the edge direction
• Take only the local maxima in that direction (to
  get an edge with width 1)
• Hysteresis Edge linking with two thresholds
• Q. What will be the width of the Gaussian?

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Example
Original
Canny