This activity aims to be able to be familiar with different noise models by applying them on an image and then restore the degraded image by implementing various spatial filters.
Noise are random variables that are characterized by a probability density function or PDF. In this activity, different noise models were applied on an ungraded image.
First is the Gaussian noise which is also known as normal noise model. The PDF of a Gaussian random variable, z, is given by
where z represents gray level, myu is the average value of z and sigma is its standard deviation.
Next is the Erlang or Gamma noise which is given by
The mean and variance of this density are given by
, respectively.
The Exponential noise has the PDF given by
and has the mean and variance given by
Then we have the Uniform noise with PDF given by
and has mean and variance given by
The Impulse or Salt-and-Pepper noise has PDF given by
Finally, we have the Rayleigh noise which has the PDF given by
The mean and variance of the Rayleigh noise is given by
These noises were created using the built-in function grand in Scilab and then applied on an ungraded image.
The corrupted images were then restored using different filters. First is the Arithmetic mean filter. represent the set of coordinates in a rectangular subimage window of size m x n, which has center at point (x,y). The arithmetic mean filtering process computes the average value of the corrupted image g(x,y) in the are defined by S sub xy. The value of the restored image f at point (x,y) is simply the mean computed using the pixels int he region defined by S sub xy.
The Geometric mean filter will restore an image with the use of the equation below.
The Harmonic mean filtering operations is given by the expression
This filter works better for salt noise than the pepper noise.
The Contraharmonic mean filtering operations yields a restored image based on the expression
where Q is the order of the filter. This filter is suited in treating salt-and-pepper noise. Positive values of Q will eliminate pepper noise while negative values omits salt noise. Thus, it cannot remove both noise simultaneously.
I was able to finish this activity and obtained MANY images. All files were deleted after the CSRC reset our computers. Unfortunately, I didn't have backup of my files. I guess, 5/10 is enough for me since I don't have pictures to show that I have finished this activity. :-(
Anyway, I want to thank Gilbert for guiding me in this activity.
Noise are random variables that are characterized by a probability density function or PDF. In this activity, different noise models were applied on an ungraded image.
First is the Gaussian noise which is also known as normal noise model. The PDF of a Gaussian random variable, z, is given by
where z represents gray level, myu is the average value of z and sigma is its standard deviation.Next is the Erlang or Gamma noise which is given by
The mean and variance of this density are given by
, respectively.The Exponential noise has the PDF given by
and has the mean and variance given by
Then we have the Uniform noise with PDF given by
and has mean and variance given by
The Impulse or Salt-and-Pepper noise has PDF given by
Finally, we have the Rayleigh noise which has the PDF given by
The mean and variance of the Rayleigh noise is given by
These noises were created using the built-in function grand in Scilab and then applied on an ungraded image.The corrupted images were then restored using different filters. First is the Arithmetic mean filter. represent the set of coordinates in a rectangular subimage window of size m x n, which has center at point (x,y). The arithmetic mean filtering process computes the average value of the corrupted image g(x,y) in the are defined by S sub xy. The value of the restored image f at point (x,y) is simply the mean computed using the pixels int he region defined by S sub xy.
The Geometric mean filter will restore an image with the use of the equation below.
The Harmonic mean filtering operations is given by the expression
This filter works better for salt noise than the pepper noise.The Contraharmonic mean filtering operations yields a restored image based on the expression
where Q is the order of the filter. This filter is suited in treating salt-and-pepper noise. Positive values of Q will eliminate pepper noise while negative values omits salt noise. Thus, it cannot remove both noise simultaneously.I was able to finish this activity and obtained MANY images. All files were deleted after the CSRC reset our computers. Unfortunately, I didn't have backup of my files. I guess, 5/10 is enough for me since I don't have pictures to show that I have finished this activity. :-(
Anyway, I want to thank Gilbert for guiding me in this activity.
Great stuff! Thanks!!
ReplyDeleteRegards,
photo restoration