Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
• Matching:
• Match the input hist to a specified hist.
•Given, random variables R and Z with p.d.f.’s fR and fZ .
•Problem – Transform Z:
=
( )~ , or find Ge(.)?
•Since we have already seen
mapped back U to
:
= ( )~
and
•If we go from RUZ
• =
=
= ( ), ~
( )=
( ( )) = Ge(r)
© 1992–2008 R. C. Gonzalez & R. E. Woods
and
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
• Express z in terms of u and u in terms of r.
• Why Matching –
Restore a degraded image using the characteristics of original
image.
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
Images from a stereo pair of inexpensive web cams.
Such cameras have different color characteristics of-the-shelf.
Can be corrected to match the other using histogram matching
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
• Global histogram – so far we covered global transformation.
• Local histogram – operating on a neighborhood.
– Define a neighborhood and compute histogram
– Perform equalization or matching transformation.
– Repeat for other points.
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
• High contrast image has wider range of pixel intensity value
than low contrast image?
• Output of a histogram equalization is given back as an input.
Will they be same?
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
• The kernel w in the equation is a square/rectangular
matrix.
• The convolution operates by moving this kernel.
• In the output image, a pixel at a given location, is the
weighted sum of pixels from the original image in the
neighborhood of location with the weights governed by
kernel.
• Kernel matrix is first rotated and then multiplied by
the neighborhood of center of the kernel
( , )∗ ( , )=
© 1992–2008 R. C. Gonzalez & R. E. Woods
( , ) ( − , − )
Digital Image Processing, 3rd ed.
Gonzalez & Woods
www.ImageProcessingPlace.com
Chapter 3
Intensity Transformations & Spatial Filtering
(1,1)
(1,0)
(−1,1)
(0,1)
(0,0)
(0, −1)
(−1,1)
(−1,0)
(−1, −1)
© 1992–2008 R. C. Gonzalez & R. E. Woods
( − 1, − )
( − 1, )
( − 1, + )
( , − )
( , )
( , + )
( + 1, − 1)
( + 1, )
( + 1, + )