School of Computer Science Queen’s University Belfast Practical TULIP lecture next Tues 12th Feb. Wed 13th Feb 11-1 am. Thurs 14th Feb am. Practical notes on Queen’s on-line.

School of Computer Science Queen’s University Belfast CSC312-4 Noise Reduction Paul Miller

School of Computer Science Queen’s University Belfast Image Enhancement Brightness control Contrast enhancement Noise reduction Edge enhancement Zooming

School of Computer Science Queen’s University Belfast Objectives What is noise? How is noise reduction performed? –Low-pass –Median How they can be implemented using neighbourhood operators.

School of Computer Science Queen’s University Belfast Noise Source of noise = CCD chip. Electronic signal fluctuations in detector. Caused by thermal energy. Worse for infra-red sensors.

School of Computer Science Queen’s University Belfast Noise image + noise = ‘grainy’ image

School of Computer Science Queen’s University Belfast Noise Plot of image brightness. Vertical slice through image. Noise is additive. Noise fluctuations are rapid, ie, high frequency.

School of Computer Science Queen’s University Belfast Noise Histogram Plot noise histogram Histogram is called normal or Gaussian Mean(noise)  = 0 Standard deviation  i is the grey level. 22 

School of Computer Science Queen’s University Belfast Noise Histogram  =10  =20  =30

School of Computer Science Queen’s University Belfast Noise Histogram  =10  =20  =30

School of Computer Science Queen’s University Belfast Noise Reduction - Low pass Noise varies above and below uncorrupted image.

School of Computer Science Queen’s University Belfast Noise Reduction - Low pass How do we reduce noise? Consider a uniform 1-d image A and add noise. Focus on a pixel neighbourhood. Central pixel has been increased and neighbouring pixels have decreased. A i-1 A i A i+1 Ci Ci

School of Computer Science Queen’s University Belfast Noise Reduction- Low pass A i-1 A i A i+1 =0 =3 = = = = Ci Ci

School of Computer Science Queen’s University Belfast Noise Reduction - Low pass Averaging ‘smoothes’ the noise fluctuations. Consider the next pixel A i+1 Repeat for remainder of pixels. A i-1 A i A i+1 A i+2 C i+1

School of Computer Science Queen’s University Belfast Low pass Neighbourhood operator All pixels can be averaged by convolving 1-d image A with mask B to give enhanced image C. Weights of B must equal one when added together.

School of Computer Science Queen’s University Belfast Low pass Neighbourhood operator Extend to two dimensions.

School of Computer Science Queen’s University Belfast Noise Reduction - Low pass

School of Computer Science Queen’s University Belfast Noise reduction Low pass Technique relies on high frequency noise fluctuations being ‘blocked’ by filter. Hence, low-pass filter. Fine detail in image may also be smoothed. Balance between keeping image fine detail and reducing noise.

School of Computer Science Queen’s University Belfast Noise reduction - Median Saturn image coarse detail Boat image contains fine detail Noise reduced but fine detail also smoothed

School of Computer Science Queen’s University Belfast Noise Reduction- Median How do we reduce noise without averaging? Consider a uniform 1-d image A and add noise. Focus on a pixel neighbourhood. Non-linear operator? A i-1 A i A i+1 Ci Ci Median filter!

School of Computer Science Queen’s University Belfast Noise Reduction- Median A i-1 A i A i+1 3 = = = = Ci Ci 2 1 = = =

School of Computer Science Queen’s University Belfast Noise reduction - Median Consider a uniform 1-d image A with a step function. Step function corresponds to fine image detail such as an edge. Low-pass filter ‘blurs’ the edge.

School of Computer Science Queen’s University Belfast A i A i+1 A i+2 C i+1 Noise reduction - Median Consider a uniform 1-d image A with a step function. Step function corresponds to fine image detail such as an edge. Median filter does not ‘blur’ the edge. A i-1 A i A i+1 Ci Ci

School of Computer Science Queen’s University Belfast Median Neighbourhood operator All pixels can be replaced by neighbourhood median by convolving 1-d image A with median filter B to give enhanced image C.

School of Computer Science Queen’s University Belfast Median Neighbourhood operator Extend to two dimensions.

School of Computer Science Queen’s University Belfast Noise reduction Original Low-passMedian

School of Computer Science Queen’s University Belfast Noise reduction Low-passMedian Low-pass: fine detail smoothed by averaging Median: fine detail passed by filter

School of Computer Science Queen’s University Belfast Summary What is noise? –Gaussian distribution Noise reduction –first principles Neighbourhood –low-pass –median Averaging pixels corrupted by noise cancels out the noise. Low-pass can blur image. Median can retain fine image detail that may be smoothed by averaging. Conclusion