Frequency analysis

Question 1

Gaussian filter

Answer 1

Smooths images by averaging pixel values with a weighted gaussian kernel.
Removes high frequency components leading to a smoother less detailed img

Question 2

Box filter

Answer 2

Smoothens but can introduce edge artifacts
Uniform averaging kernel
can introduce abrupt transitions at edges because it doesnt weight pixel contributions smoothly

Question 3

Frequency Analysis of gaussian and box filter

Answer 3

Both act as low pass filters in the freq domain, suppressing high freq

Question 4

Aliasing

Answer 4

Misrepresentation of high frequency signals as lower frequencies due to insufficient sampling

Question 5

Ensure sampling rate satisfies Nyquist criterion
What is that?

Answer 5

Sampling rate >= 2 x highest frequency

Question 6

Fourier transform

Answer 6

Decomposes signal into sinusoidal components
Key params: Amplitude, frequency, Phase

Question 7

1D fourier transform

Answer 7

Mathematical project of the signal onto sinusoidal basis function
Produces amplitudes and phases of sinusoids at different frequencies

Question 8

2D Fourier transform

Answer 8

Extension of the Fourier transform to analyze images.
Frequency representation:
- Center: low freq (smooth variations, broad patterns)
- Edges of the spectrum: high freq (sharp transitions, details)
eg. trees, and leaves

Question 9

Low-pass filtering technique

Answer 9

Allows low freq to pass, while attenuating high frequencies
effect: smooths images, removes details and noise
good for reducing noise and blurring

Question 10

High-pass filtering technique

Answer 10

Retains high frequencies while suppressing low frequencies
effect: emphasizes edges and fine details
good for edge detection in images, highlighting textures

Question 11

Band-pass filter

Answer 11

Allows only a specific range of frequencies to pass
Effect: isolate patterns at specific scales
Good for detecting periodic patterns such as fabric textures or ripples.

Question 12

Discrete Fourier Transform

Answer 12

Convert discrete signals to their frequency domain representation (digital images)
Freq spectrum is periodic due to discrete nature of input

Question 13

Why aliasing happens

Answer 13

Insufficient sampling leads to high frequencies wrapping around into lower frequencies

Question 14

Visualizing frequency components:
Magnitude
Phase

Answer 14

Magnitude: represents the strength of each frequency component
Dominates overall structure of the freq spectrum

Phase: Encodes positional details and fine structure

Question 15

Frequency in images

Answer 15

Frequency in an image refers to the rate of change in intesity values across the spatial domain