EE5811-Computer vision-Filter and resample

Information about image

1:common to use one byte per value(0-255)(black-white)

2:a grayscale image as a function(f:from R^2 to R)

For the function,we can apply other operations to the image:

g(x,y)=f(x,y)+20
g(x,y)=f(-x,y) ->Turn with the y axle

3:Characterizing image transformations

Attributes/properties of functional transformation

• Additivity: T(F1+F2)=T(F1)+T(F2)
• Scaling: T(lambdaF)=lambdaT(F)
• Direct consequence:Linearity: T(alphaF1+betaF2)=alphaG1+betaG2
• Shift Invariance:G[I-j]=T(F(I-j))

4:Impulse response(Delta function)

The meaning: Impulse response to the image can be seen the filter as a transfer function(input a vacant picture with a pixel point’s value is one and other 0,then the filter doing the convolution opetarion to this picture ,final, output image is impulse response of this filter.)
At here,H is impulse response/filter/kernel

The example of formula to calculate

properties of convolution

size

(cross)Correlation

Filters

Filtering

• Form a new image whose pixels are a combination of the original pixels

why?

• To get useful information from images
  (extract edges or contours(to understand shape)
• To enhance the image
  (remove noise)
  (to sharpen or to “enhance image”)