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DIP Exam 2 Cheat Sheet by

Digital Image Processing Exam 2 Cheat Sheet

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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