filtering, edge detection

image noise definition

any entity in image that is not interesting for the purpose of the main computation

gaussian noise

additive noise , no correlation between pixels

impulsive noise

individual noisy pixels, intensity differs significantly from true intensity and neighborhood

mean filter

averaging in a local neighborhood of pixels

not good for salt and pepper noise

blures edges, cannot show periodic patterns

convolution

flipping of the filter at both axes

negative sings of the indices h(-i,-j)

main steps of convolution

1. flipping of the filter
2. multiplication of the vilter values with image intensity values
3. summation of the mutiplication results

gaussian filter

2D gaussian filter so transition from filtr mask values to surrounding zero values is not so abrupt

Discretization of gaussian filter

1. choose the standard deviation for the gaussian
2. choose the size N of filter mask
3. compute the discrete values of the filtr mask

non linear filters

median filter

pixels in NxN neigborhood are sorted and median value assigned to middle pixel

no bluring

edge detection steps

1. noise reduction
2. edge enhancement
3. edge detection
4. edge localization

image gradient

orthogona to the edge direction → direction of steepest slope of the intensity function

magnitude → maxiumum rat eof increase

image gradient for continuous and discrete functions

prewitt derivative operators

differende between the columns adjecent to the central column (same for rows)

difference between correlation and convolution mask

convolution incluedes flipping along x- and y-axes

sobel derivative operators

elements closest to the central point are weighted twice

edge detection with gradient operators stepwise

for each pixel


1. compute the image gradient


2. cmpute the gradient magnitude
3. compare magnitude to threshold
4. refine the edge postion by non-maximum suppression