Lecture 7 Spatial filtering

Image denoising Additive noise model: Noise usually assumed to be uncorrelated

Image averaging for noise removal Examples of noise added to the same image Averaging 10, 50 and 128 noisy images

Spatial filtering Linear Space Invariant filters. 1D convolution:

Discrete Convolution 1D Discrete case: 2D discrete case: Length of output: If x is of length M and h is of length L, then y is of length M+L-1

Discrete Convolution

How to handle image borders No data to convolve!

Zero Padding Original image Impulse response array Area with 0s

Do not process border pixels Input image Impulse response array Output image

Smoothing spatial filters Used for noise removal/blurring an image. h1 h2 Usual average Weighted average

Averaging filter Noisy image 3x3 averaging mask (h1) output Note: The smoothing effect removes the noise, but also blurs the image Notice the black frame on the image boundary

Averaging filter 3x3 averaging mask (h1) output Note: Less blur in the center image Larger black frame in the third image More blur in the third image

Averaging filters to remove details Test Image contains details of different resolution Note: Some small squares disappear. Noisy rectangles are blurred to remove noise Vertical bars details are mixed up.