Linear filters like averaging and Gaussian filters can remove grain noise by averaging pixel values in a neighborhood. Median filters are better at removing outliers without reducing sharpness by setting a pixel to the median value in its neighborhood. The document demonstrates applying averaging and median filters in Matlab to remove noise, and using morphological opening to estimate and subtract a background illumination to rectify it.

1. Matlab:Image Restoration Techniques

2. Removing Noise By Linear FilteringLinear filters, such as averaging or Gaussian filters can be used to remove certain types of noise. An averaging filter is useful for removing grain noise from a photograph. Because each pixel gets set to the average of the pixels in its neighborhood, local variations caused by grain are reduced.

3. Removing Noise By Median FilteringWith median filtering, the value of an output pixel is determined by the median of the neighborhood pixels, rather than the mean. The median is much less sensitive than the mean to extreme values (called outliers). Median filtering is therefore better able to remove these outliers without reducing the sharpness of the image.

4. Applying the averaging filter>>I=imread('img.bmp'); >> I=I(:,:,1);>> imshow(I);>>K = filter2(fspecial('average',3),I)/255;>>figure, imshow(K)

5. Applying the median filter>>I=imread('img.bmp'); >> I=I(:,:,1);>> imshow(I);>> L = medfilt2(I,[3 3]);>>figure, imshow(L)

6. Rectifying background illuminationStep 1: Read ImageStep 2: Use Morphological Opening to Estimate the BackgroundStep 3: View the Background Approximation as a SurfaceStep 4: Subtract the Background Image from the Original Image

7. Rectifying background illuminationStep1: Read ImageI = imread('rice.png'); imshow(I)

8. Rectifying background illuminationStep 2: Use Morphological Opening to Estimate the Background>>background = imopen(I,strel('disk',15));>>figure, surf(double(background(1:8:end,1:8:end))),zlim([0 255]); set(gca,'ydir','reverse');Step 3: View the Background Approximation as a SurfaceRectifying background illuminationStep 2: Use Morphological Opening to Estimate the BackgroundStep 3: View the Background Approximation as a SurfaceRectifying background illuminationStep 4: Subtract the Background Image from the Original ImageI2 = I - background; imshow(I2)