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DIP Exam 2 Cheat Sheet by

Digital Image Processing Exam 2 Cheat Sheet
transform     discrete     digital     2d     processing     image     fourier     dft     dip

Complex Unit Circle

Discrete Fourier Transform

Sinc Definition

2D DFT Definition

2D Continuous Fourier Transform

Wrap Around Error

Solved by zero padding
If f(x) and h(x) are A and B samples respec­tively, pad f(x) and h(x) with zeros so both have length P>=­A+B-1
If not zero, creates discon­tinuity called "­fre­quency leakag­e", equivalent to convolving with sinc() function
Reduced by multip­lying with function that tapers smoothly to zero (windowing or apodizing)

Butter­worth Lowpass Filter

D0 is cutoff freq and D(u,v) is distri­bution of (u,v) from centered origin. n is order

DFT Table

 

Fourier Series Definition

Convol­ution Theorem

Space convol­ution = frequency multip­lic­ation

2D Convol­ution

Spatial Shift Theorem

Spatial transform only affects FT phase

Conjugate Symetry

F*(u,v) = F(-u, -v) (Conjugate Symmetry)
F*(-u,-v) = -F(u,v) (Conjugate Asymmetry)

Fourier Spectrum and Phase Angle

Steps for Filtering

1 + 2. Given f(x,y) is MxN, zero pad to 2Mx2N (PxQ)
3. Multiply by (-1)x+y to center
4. Take DFT of f(x,y) to get F(u,v)
5. Generate symmetric filter H(u,v) of size PxQ
6. Get processed image gp(x,y­)={­rea­l[­F­-1­{G(­u,v)}} * (-1)x+y

Laplacian in Freq. Domain

 

Impulse Train Definition

Convol­ution Definition

2D Sampling

Frequency Shift Theorem

Center DC

To shift F(0,0) (DC Component) to center, multiply by (-1)­x+y

Power Spectrum

Total power of image is just sum of P(u,v) over P-1,Q-1

a = 100[do­ublesum P(u,v)/Pt]

DC Component

Gaussian Filter

Unsharp, Highboost, High-E­mphasis

gmask(x,y) = f(x,y) - flp(x,y)
g(x,y) = f(x,y) + k*gmas­k(x,y)
k=1, unsharp
k>1, highboost

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