Image Restoration - Focus on Noise 12/3/2018

References Gonzales and Wood second edition Jain 12/3/2018

Enhancement - Restoration Subjective Objective Goodness Test Visual – meet the psychophysical aspects of HVS Objective measures Masks Small. Spatial or Frequency domain Large. More frequently driven by freq domain analysis Noise only Smoothing filters Similar to Enhancement approaches Degradation model Intuitive/heuristic analysis Math model. This model is often an approx. 12/3/2018

Overview Measured From [1] Unknown Approximation 12/3/2018

Noise sources Device noise (often thermal) Digitization process Sampling and quantization Transmission Environment 12/3/2018

Noise models White noise: autocorrelation is an impulse Colored noise Usually assume that noise is uncorrelated with the image Gaussian: circuit noise, illumination, environment (thermal) Rayleigh: range imaging Uniform: easy to model Others: exponential, impulse (salt and pepper) 12/3/2018

Sample pdfs From [1] 12/3/2018

Test image 3 distinct gray levels From [1] 12/3/2018

Additive Noise From [1] 12/3/2018 Noise is added to the respective gray levels. Hence the multiple lobe histograms From [1] 12/3/2018

Additive Noise From [1] 12/3/2018

Estimation of Noise Parameters – Periodic Noise Periodic noise – filter in frequency domain. Appears as pair of impulses. The removal can be automated when the impulses are more pronounced. From [1] 12/3/2018

Noise Parameter Estimation – Known Model Noise parameters can be computed by focusing on small sub-image (patch). From [1] 12/3/2018

Mean and S.D. estimation 12/3/2018

Image Restoration – Noise Only Degradation Use Filters: Spatial Filter n(x,y) is unknown. For periodic noise, N(u,v) can be estimated from G(u,v) – spikes at predominant noise frequencies. 12/3/2018

Noise Reduction Filters 12/3/2018

Applying Arithmetic and Geometric Filters From [1] 12/3/2018

More Noise Reduction Filters 12/3/2018

Comparisons of Filters Arithmetic: Smoothing reduces noise. Blurring. Geometric: Smoothing. Less loss of image detail than Arithmetic. Harmonic: Reduces salt noise. No impact on pepper noise. Contraharmonic: Reduces salt and pepper noise. Q>0 reduces pepper noise. Q<0 reduces salt noise. Cannot reduce salt and pepper noise in the same pass. Q = 0 yields Arithmetic Q = -1 yields Harmonic 12/3/2018

Order Statistics Filters 12/3/2018

Multiple applications of the Median Filter From [1] 12/3/2018

Order Statistics Filters - 2 12/3/2018

Adaptive Filter – Reduce Local Noise 12/3/2018

Arithmetic, Geometric and Adaptive Filters From [1] 12/3/2018

Adaptive Median Filter Preserve detail. Smooth non-impulse noise {different from tradition median filter}. Like Adaptive Filter use a window Sxy. The center of the window is replaced by the result Unlike Adaptive Filter, the size of the window is increased. Notation zmin = min gray level in Sxy. zmax = max gray level in Sxy. zmed = median gray level in Sxy. zxy = gray level at coordinate (x,y). Smax = max allowed size of Sxy. 12/3/2018

Adaptive Median Filter Level A: { is zmed an impulse?} while window size is less than Smax do if zmed > zmin AND zmed < zmax, then Go To Level B else increase the window size end while output zxy Level B: { is zxy an impulse?} if zxy > zmin AND zxy < zmax, then output zxy else output zmed Algorithm objectives Remove salt and pepper noise Smooth other noise Reduce distortions, e.g. excessive thinning or thickening of boundaries 12/3/2018

Adaptive Median Filter From [1] 12/3/2018

Periodic Noise Band reject filters Band pass filters Notch filters 12/3/2018