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Image Pre-Processing

- Image pre-processing (predzpracování obrazu)
- transformations of the input image leading to

noise reduction, image improvement or preparation

of the image for subsequent image analysis - Image pre-processing operations
- Spatial domain
- Point transforms
- Linear filters
- Non-linear filters
- Frequency domain
- Filters in frequency domain

Point Transforms

- Point transform (bodová transformace)
- a pixel by pixel transformation of the image

array in spatial domain - Position-dependent point transform
- g(x,y) t ( f(x,y), x, y)
- t lt 0, NI gt ? lt 0, Nx gt ? lt 0, Ny gt ? lt 0, NI

gt - Compensation for uneven illumination
- Compensation for uneven dark charge of CCD pixels
- Position-independent point transform
- g(x,y) t ( f(x,y))
- t lt 0, NI gt ? lt 0, NI gt
- Change of image brightness t (x) x k
- Change of image contrast t (x) any function

of x, for example - t (x) k x, t (x) k xn, t (x) k

log(x), t (x) k exp(x)

Position-independent Point Transforms

- Look-up table (LUT)
- Usually t (x) is pre-computed, the table of its

values is called look-up-table (LUT). The LUT is

1D array of values. The size of this array is

determined by the bit depth of the image (256

values for 8-bit image, 4096 values for 12-bit

image, etc.). - Intensity histogram
- The best way to choose t (x) is to look at the

intensity histogram of the given image. Intensity

histogram is a 2D plot where x-axis represents

intensity (e.g. 0-255 for 8-bit image) and y-axis

represents the number of pixels in the image

having the corresponding intensity.

Position-independent Point Transforms

- Example of the influence of point transform

(contrast change) on the intensity histogram for

t (x) 4 x

Other Intensity Histogram Examples

- Under- and over-exposed image (pod- a

pre-exponovaný obraz)

Filters

- Filter (filtr)
- a position-independent operator that transforms

the image - Filter in spatial domain (filtr v prostorové

doméne) - spatial operator that produces the output image

array g(x,y)from the input image array f(x,y) - Filter in frequency domain (filtr ve frekvencní

doméne) - frequency operator that produces the output image

spectrum ?(x,y) from the input image spectrum

F(x,y) - Low-pass filter (nízkofrekvencní filtr)
- a filter that keeps low frequencies and

suppresses the high ones - High-pass filter (vysokofrekvencní filtr)
- a filter that keeps high frequencies and

suppresses the low ones

Linear Filters

- Linear filter (lineární filtr)
- spatial linear operator that produces the output

image array g(x,y) from the input image array

f(x,y) in the following way g(x0,y0) is obtained

by a linear combination of pixels of the input

image array f(x,y) within a neighbourhood of

pixel (x0,y0). - nm1 3x3 neighbourhood
- nm2 5x5 neighbourhood
- nm3 7x7 neighbourhood

Linear Filters

- Convolution kernel (konvolucní jádro)
- The function h(a,b) is called convolution kernel.
- The function h(a,b) is usually symmetric

h(a,b) h(-a,b) h(a,-b) h(-a,-b). - The values of the function h(a,b) usually depend

on radius - The function h(a,b) is specified as a matrix H.
- If nm then the matrix H is square.
- g(x,y) F(x,y) H
- F(x,y) matrix of neighbours of pixel (x,y)
- H convolution kernel
- scalar matrix multiplication

(defined in the same way as scalar vector

multiplication)

Linear Filters

- Principle of linear filtering using a 3x3

convolution kernel - The intensity value at position (m,n) is replaced

by the sum of nine numbers, where each number is

obtained by multiplication of the number in

matrix with the intensity value behind this

number. - This process (nine multiplications plus eight

additions) must be performed for each position in

the image, i.e. all values of m and n.

Linear Filters

- Problem with linear image filtering
- Image convolution can be realised by scanning the

convolution mask line by line over the image. At

the shaded pixels the intensity value has already

been replaced by the convolution sum. Thus the

intensity values at the shaded pixels falling

within the filter mask need to be stored in an

extra buffer!

Smoothing Linear Filters

- Smoothing (vyhlazování)
- elimination of high frequencies
- usually performed using averaging (either

weighted or non-weighted) - Example Smoothing using average 3x3 filters
- non-weighted weighted

weighted

Smoothing Linear Filters

- Gaussian filter (Gaussuv filtr)
- the best smoothing filter

Smoothing Linear Filters

- Example of Gaussian filtering with different

values of s - Original s 1
- s 2 s 4

Edge Detection Linear Filters

- Edge detection (detekce hran)
- usually performed using linear filters simulating

1st or 2nd derivative - can be used for edge enhancement or object

boundaries reconstruction - Sobel filter
- approximates the first derivative of the image
- the basic kernels are (1,-1) or (1,0,-1)
- mostly 3x3 kernel is used with the sum of

coefficients equal to 0 - results for several 3x3 kernels can be averaged
- there are 8 possibilities of the following type
- often used after Gaussian filter(so called

derivative of Gaussian DroG)

Edge Detection Linear Filters

- Laplacian filter
- approximates the second derivative of the image
- the basic kernel is (1,-2,1)
- mostly 3x3 kernel is used with the sum of

coefficients equal to 0 - two basic types of 3x3 kernel are used, others

are possible - often used after Gaussian filter(so called

Laplacian of Gaussian LoG Mexican hat filter)

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