Image processing

1
Image processing

• Enhancement and restoration

2
Image Histogram

• is a chart that shows the distribution of
  intensities in an indexed or intensity image.
• The image histogram function imhist creates this
  plot by making n equally spaced bins, each
  representing a range of data values. It then
  calculates the number of pixels within each range.

3
Histogram of stars and Pout

• I imread('ngc4024l.tif')
• figure, imhist(I,255)

• I imread(pout.tif')
• figure, imhist(I,255)

4
Histogram equalization

• Let H(p) be the input histogram and that
  the input gray-scale is po, pk

• The intention is to find a monotonic pixel
  brightness qT(p) such that the output
  histogram G(q) is uniform over the whole output
  brightness scale qo, qk

• The histogram is a discrete probability density
  function.
• The monotonic property of the transform T implies

5
Histogram equalization

• The aim is to produce an image with equally
  distributed brightness levels over the whole
  brightness scale.

6
Histogram equalization

• Assume image of MxN pixels
• The equalized histogram corresponding to the
  uniform probability density function f whose
  function value is a constant
• The equalized histogram can be obtained precisely
  only for the idealized'' continuous probability
  density, in which case the sum equation becomes

7
Histogram equalization

• The desired pixel brightness transformation T can
  then be derived as
• The integral in the above equation is called the
  cumulative histogram, which is approximated by a
  sum for digital images.

8
Histogram equalization

• So the resulting histogram is not equalized
  ideally.
• The discrete approximation of the continuous
  pixel brightness transformation form the above
  equation is

9
Histogram equalization

• I imread('pout.tif')
• J histeq(I)
• imshow(I)
• figure, imshow(J)

10
filter2 and imfilter for image filtering.

• filter2(h,A) filters the data in A with the
  two-dimensional filter in the matrix h.
• A filter is to be specified by matrix h with
  fspecial.
• h fspecial(type)
• h fspecial(type,parameters)
• Imfilter is for multidimensional image filtering
• B imfilter(A,H)
• B imfilter(A,H,option1,option2,...)
• Filter Options
• 'corr imfilter performs multidimensional
  filtering using correlation, which is the same
  way that filter2 performs filtering. When no
  correlation or convolution option is specified,
  imfilter uses correlation.
• 'conv imfilter performs multidimensional
  filtering using convolution.

11
fspecial

• h fspecial(type)
• h fspecial(type,parameters)
• h fspecial(type) creates a two-dimensional
  filter, h, of the specified type.
• fspecial returns h as a correlation kernel, which
  is the appropriate form to use with imfilter.
  type is a string having one of these values
• 'gaussian' for a Gaussian lowpass filter
• 'sobel' for a Sobel horizontal edge-emphasizing
  filter
• 'prewitt' for a Prewitt horizontal
  edge-emphasizing filter
• 'laplacian' for a filter approximating the
  two-dimensional Laplacian operator
• 'log' for a Laplacian of Gaussian filter
• 'average' for an averaging filter
• 'unsharp' for an unsharp contrast enhancement
  filter

12
Average and Median filter

• For example, for averaging filter for the window
  of size of 3x3, the filtered image K is obtained
  as
• K filter2(fspecial('average',3),I)/255
• Median filter
• L medfilt2(I,3 3)

13
Noise removal

• IMNOISE function add a noise to image.
• J IMNOISE(I,TYPE,...) Add noise of a given TYPE
  to the intensity image I. TYPE is a string that
  can have one of these values
• 'gaussian' Gaussian white noise with
  constant mean and variance
• 'localvar' Zero-mean Gaussian white noise
  with an intensity-dependent variance
• 'poisson' Poisson noise
• 'salt pepper' "On and Off" pixels
• 'speckle' Multiplicative noise

14
Add noise

• I imread(pout.tif')
• J imnoise(I,'gaussian')
• figure, imshow(J)

15
Filtering a Region

• specify a region using roipoly function. If you
  call roipoly with no input arguments, the cursor
  changes to a cross hair when it is over the image
  displayed in the current axes. You can then
  specify the vertices of the polygon by clicking
  on points in the image with the mouse.
  Doubleclick to finish.
• I imread('pout.tif')
• imshow(I)
• BW roipoly
• imshow(BW)

16
roifilt2

• use the roifilt2 function to process a region of
  interest.
• When you call roifilt2, you specify an intensity
  image, a binary mask, and a filter.
• roifilt2 filters the input image and returns an
  image that consists of filtered values for pixels
  where the binary mask contains 1's, and
  unfiltered values for pixels where the binary
  mask contains 0's.
• This type of operation is called masked
  filtering.

17
Region of interest filtering

• h fspecial('unsharp')
• I2 roifilt2(h,I,BW)
• figure, imshow(I2)