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DIP Exam 2 Cheat Sheet

A cheat sheet in English by samclane

Digital Image Processing Exam 2 Cheat Sheet

Transform Discrete Digital 2d Processing Image Fourier Dft Dip
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Complex Unit Circle

Complex Unit Circle

Discrete Fourier Transform

Discrete Fourier Transform

Sinc Definition

Sinc Definition

2D DFT Definition

2D DFT Definition

2D Continuous Fourier Transform

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

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

DFT Table

DFT Table

Fourier Series Definition

Fourier Series Definition

Convol­ution Theorem

Convolution Theorem
Space convol­ution = frequency multip­lic­ation

2D Convol­ution

2D Convolution

Spatial Shift Theorem

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

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

Laplacian in Freq. Domain

Impulse Train Definition

Impulse Train Definition

Convol­ution Definition

Convolution Definition

2D Sampling

2D Sampling

Frequency Shift Theorem

Frequency Shift Theorem

Center DC

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

Power Spectrum

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

DC Component

Gaussian Filter

Gaussian Filter

Unsharp, Highboost, High-E­mphasis

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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