Digital Image ProcessingImage Restoration Noise models and additive noise removal 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 1 Image Restoration 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 2 Image Restoration What is noise (in the context of image processing) and how can it be modeled? What are the main types of noise that may affect an image? What are the possible solutions? Subjective Vs Objective (Enhancement Vs Restoration) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 3 Degradation Model for a Digital Image 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 4 Noise Models 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 5 Noise and Noise Models Gaussian (normal) Impulse (salt-and-pepper) Uniform Rayleigh Gamma (Erlang) Exponential 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 6 Effect of Noise on Images & Histograms Gaussian Exponential Impulse (salt-and-pepper) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 7 Effect of Noise on Images & Histograms Rayleigh Gamma (Erlang) Uniform 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 8 Noise Models: Gaussian Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 9 Noise Models: Rayleigh Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 10 Noise Models: Erlang (Gamma) Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 11 Noise Models: Exponential Noise Where 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 12 Noise Models: Uniform Noise 1 , if a z b p( z ) b a 0 otherwise The mean and variance are given by ab (b a ) 2 , 2 2 12 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 13 Noise Models: Impulse (Salt and Pepper) Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 14 Effect of Noise on Images & Histograms 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 15 Effect of Noise on Images & Histograms 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 16 Effect of Noise on Images & Histograms 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 17 Periodic Noise (Example) Spatially Dependent Case 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 18 Applicability of various noise models 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 19 Estimation of noise parameters 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 20 Estimation of noise parameters (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 21 Estimation of noise parameters (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 22 Estimation of noise parameters 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 23 Restoration of noise-only degradation Filters to be considered 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 24 Mean Filters: Arithmetic mean filter Causes a certain amount of blurring (proportional to the window size) to the image, thereby reducing the effects of noise. Can be used to reduce noise of different types, but works best for Gaussian, uniform, or Erlang noise. 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 25 Mean Filters: Geometric mean filter – A variation of the arithmetic mean filter – Primarily used on images with Gaussian noise – Retains image detail better than the arithmetic mean 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 26 Mean Filters: Harmonic mean filter Harmonic mean filter – Another variation of the arithmetic mean filter – Useful for images with Gaussian or salt noise – Black pixels (pepper noise) are not filtered 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 27 Arithmetic and geometric mean filters (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 28 Mean Filters: Harmonic mean filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 29 Mean Filters: Harmonic mean filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 30 Mean Filters: Contra-harmonic mean filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 31 Classification of contra-harmonic filter applications 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 32 Contra-harmonic mean filter (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 33 Contra-harmonic mean filter (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 34 Rank / Order / Order Statistics Filters – Known as Rank filters, Order filters OR Order Statistics filters – Operate on a neighborhood around a reference pixel by ordering (ranking) the pixel values and then performing an operation on those ordered values to obtain the new value for the reference pixel – They perform very well in the presence of salt and pepper noise but are more computationally expensive as compared to mean filters 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 35 Rank / Order Statistics Filters: Median filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 36 Rank / Order Statistics Filters: Median filter – Most popular and useful of the rank filters. – It works by selecting the middle pixel value from the ordered set of values within the m × n neighborhood (W) around the reference pixel. • If mn is an even number, the arithmetic average of the two values closest to the middle of the ordered set is used instead. – Many variants, extensions, and optimized implementations in the literature. 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 37 Median filter (Example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 38 Rank / Order Statistics Filters: Max and Min filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 39 Rank / Order Statistics Filters: Max and Min filter – Max filter also known as 100th percentile filter – Min filter also known as zeroth percentile filter – Max filter helps in removing pepper noise – Min filter helps in removing salt noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 40 Max and Min filter (Example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 41 Rank / Order Statistics Filters: Midpoint filter – Calculates the average of the highest and lowest pixel values within a window – What would it do with salt and pepper noise ? 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 42 Midpoint filter (Example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 43