SUSAN: structure-preserving noise reduction

EE264: Image ProcessingFinal Presentationby Luke Johnson

6/7/2007

SUSAN PrincipleSUSAN Principle Published by Stephen M. Smith and J. Michael Brady (1997)Published by Stephen M. Smith and J. Michael Brady (1997) USANUSAN

Univalue Segment Assimilating NucleusUnivalue Segment Assimilating Nucleus Image is assumed to be made up of featuresImage is assumed to be made up of features Each feature is assumed to be of uniform brightnessEach feature is assumed to be of uniform brightness USAN is defined as the area that corresponds to the feature which USAN is defined as the area that corresponds to the feature which

the center mask pixel is associated withthe center mask pixel is associated with

Shaded area = USAN

SUSAN PrincipleSUSAN Principle

SUSAN – Smallest USANSUSAN – Smallest USAN Used for edge and corner detectionUsed for edge and corner detection Area of USAN is minimized at edges and cornersArea of USAN is minimized at edges and corners No derivatives = better performance on noisy imagesNo derivatives = better performance on noisy images

Noise reductionNoise reduction USAN used as kernel for weighted averagingUSAN used as kernel for weighted averaging Preserves underlying structure of imagePreserves underlying structure of image Non-linearNon-linear

SUSAN denoising algorithmSUSAN denoising algorithm For each image pixel:For each image pixel:

Overlay mask centered at image pixelOverlay mask centered at image pixel Determine USANDetermine USAN Replace image pixel with average of USAN pixelsReplace image pixel with average of USAN pixels

USAN determinationUSAN determination

Binary comparison:Binary comparison:

Gaussian comparison:Gaussian comparison:

t t is the brightness threshold set by the useris the brightness threshold set by the user

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Spatial weightingSpatial weighting

Also assume that pixels spatially nearer to the Also assume that pixels spatially nearer to the nucleus are more likely to be part of the same featurenucleus are more likely to be part of the same feature

Spatial Gaussian weighting:Spatial Gaussian weighting:

σσ is the spatial smoothing factor chosen by the useris the spatial smoothing factor chosen by the user

This means that the weight for each pixel is This means that the weight for each pixel is determined by how “close” it is to the center pixel determined by how “close” it is to the center pixel both in the spatial domain and in the brightness both in the spatial domain and in the brightness domain.domain.

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AveragingAveraging Apply both weighting functions and average:Apply both weighting functions and average:

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Zero-area USANZero-area USAN

Since the center pixel is not counted as part of the Since the center pixel is not counted as part of the USAN, it is possible to have an USAN area of zero or USAN, it is possible to have an USAN area of zero or close to zeroclose to zero

If this is the case then the nucleus is assumed to be If this is the case then the nucleus is assumed to be impulse noise and its value is replaced by the impulse noise and its value is replaced by the median of its eight closest neighborsmedian of its eight closest neighbors

SUSAN filter demonstrationSUSAN filter demonstration

Test image used in Smith (1997) Residual after one pass with SUSAN filter (contrast enhanced)

Gaussian noise added (rms = 15.1) one filter iteration (rms = 3.51)

two iterations (rms = 2.80) residual (contrast enhanced)

with impulse noise (rms = 24.8) two iterations of SUSAN filter (rms = 5.72)

residual 3x3 median filter (rms = 6.81)

Parameter dependenceParameter dependence

σ and t must be optimized for each iteration of the filter

Gaussian noise in natural Gaussian noise in natural imagesimages

with Gaussian noise (rms = 25) SUSAN filter result (rms = 7.99)steering kernel result (rms = 6.66)

Iterative steering Kernel – Takeda, Farsiu, Milanfar (2006)

Compression artifactsCompression artifacts

Poor-quality JPEG (rms = 9.76) SUSAN filter (rms = 8.60) bilateral filter (rms = 8.52)

Bilateral filter – Tomasi (1998)

Film Grain NoiseFilm Grain Noise

image corrupted by film grain noise Results of SUSAN filter Results of bilateral filter

ConclusionsConclusions SUSAN filter works well at reducing noise while preserving the SUSAN filter works well at reducing noise while preserving the

underlying structure of images although it does have difficulty underlying structure of images although it does have difficulty in certain situations. in certain situations.

The need to adjust three different parameters (spatial The need to adjust three different parameters (spatial smoothing, brightness threshold, number of iterations) makes smoothing, brightness threshold, number of iterations) makes it a very time consuming method to use. Some way of it a very time consuming method to use. Some way of automatically calculating these parameters would be useful. automatically calculating these parameters would be useful.

More recent denoising algorithms have surpassed SUSAN in More recent denoising algorithms have surpassed SUSAN in performance however many of them use the same general performance however many of them use the same general ideas as the SUSAN filterideas as the SUSAN filter

ReferencesReferences Paris, S. and F. Durand, “A Fast Approximation of the Bilateral Filter using a Signal Processing Paris, S. and F. Durand, “A Fast Approximation of the Bilateral Filter using a Signal Processing

Approach”,Approach”, ECCV ECCV, 2006)., 2006).

Portilla, J., V Strela, M Wainwright, and E P Simoncelli, “Image Denoising using Scale Mixtures Portilla, J., V Strela, M Wainwright, and E P Simoncelli, “Image Denoising using Scale Mixtures of Gaussians in the Wavelet Domain”, of Gaussians in the Wavelet Domain”, IEEE Transactions on Image ProcessingIEEE Transactions on Image Processing. vol 12, no. 11, . vol 12, no. 11, pp. 1338-1351, November 2003. pp. 1338-1351, November 2003.

Rudin, L., S. Osher, and E. Fatemi, “Nonlinear Total Variation based noise removal Rudin, L., S. Osher, and E. Fatemi, “Nonlinear Total Variation based noise removal algorithms", algorithms", Physica DPhysica D, 60 259-268, 1992., 60 259-268, 1992.

Smith, Stephen M. and J. Michael Brady, “SUSAN -- A New Approach to Low Level Image Smith, Stephen M. and J. Michael Brady, “SUSAN -- A New Approach to Low Level Image Processing”, Processing”, International Journal of Computer VisionInternational Journal of Computer Vision, 1997., 1997.

Takeda, H., "Takeda, H., "Kernel Regression for Image Processing and ReconstructionKernel Regression for Image Processing and Reconstruction",", M.S. Thesis M.S. Thesis, , Electrical Engineering, UC Santa Cruz, March 2006.Electrical Engineering, UC Santa Cruz, March 2006.

Takeda, H., S. Farsiu, and P. Milanfar, "Takeda, H., S. Farsiu, and P. Milanfar, "Kernel Regression for Image Processing and ReconstructionKernel Regression for Image Processing and Reconstruction", ", IEEE Transactions on Image IEEE Transactions on Image ProcessingProcessing, Vol. 16, No. 2, pp. 349-366, February 2007., Vol. 16, No. 2, pp. 349-366, February 2007.

Takeda, H., S. Farsiu, and P. Milanfar, "Takeda, H., S. Farsiu, and P. Milanfar, "Robust Kernel Regression for Restoration and Robust Kernel Regression for Restoration and ReconstuctionReconstuction of Images from Sparse Noisy Data of Images from Sparse Noisy Data", ", Proceedings of the International Proceedings of the International Conference on Image Processing (ICIP)Conference on Image Processing (ICIP), Atlanta, GA, October 2006., Atlanta, GA, October 2006.

Tomasi, C. and R. Manduchi, "Bilateral Filtering for Gray and Color Images", Tomasi, C. and R. Manduchi, "Bilateral Filtering for Gray and Color Images", Proceedings of Proceedings of the 1998 IEEE International Conference on Computer Visionthe 1998 IEEE International Conference on Computer Vision, Bombay, India., Bombay, India.