Lecture 2

Question 1

Histogram

Answer 1

Defines the frequency of pixels with certain intensity

Question 2

Histogram probability

Answer 2

Sum over L-1(H(i))=N

H(i)/N=P(i)

Question 3

Point operation

Answer 3

Output pixels depends on the corresponding input pixel

Question 4

Contrast stretching

Answer 4

Smaller intensity range of input and map over entire input.

Question 5

Intensity inversion

Answer 5

All light parts become dark, all dark become light

Question 6

Histogram equaliziation

Answer 6

Compute intensity histogram of the image, compute probability function from histogram. Compute cumulative probability function. Apply mapping function. Spread out most frequent intensities. Histogram bins more equal.
Formulas on slide

Question 7

Neighborhood operations

Answer 7

Each pixel depends on a neighborhood of pixels

Question 8

Linear shift invariance

Answer 8

Linearity when multiplying and adding input by scalars gives output multiplied by same scalars and added in same way. Shift in input yields shift output

Question 9

Impulse response

Answer 9

Reaction of any system in response to external change

Question 10

LSI operation

Answer 10

Fully characterized by impulse response. Formula on slides

Question 11

Border solutions

Answer 11

• Zero padding: Extend with 0 border
• Clamping: give extra border pixels same value as the ones they have been placed hrizontally
• Repeating: Repeat the image and put next to each other
• Mirroring: mirror pixels at border

Question 12

Uniform filtering kernel

Answer 12

Take average of all neighbors including own value

Question 13

Prewitt

Answer 13

Symmetry along x or y, equivalent to first derivative.
1 0 -1
1 0 -1
1 0 -1

Question 14

Sobel

Answer 14

Symmetry along x or y. Equal to second derivative
1 0 -1
2 0 -2
1 0 -1

Question 15

Frequency/fourier domain

Answer 15

Deal with the rate at which the pixel values are changing in spatial domain. low frequencies away, high frequencies amplified so sharp contrast

Question 16

Gaussian

Answer 16

Formula on slide
It is seperable and circularly sysmmetric. It has optimal space-frequency localization. Infinitly smooth and scales naturally

Question 17

seperability

Answer 17

Kernels can be seperated in their x and y such that they are easier computable

Question 18

Gradient vector

Answer 18

dinv I(x,y)=[Ix(x,y),Iy(x,y)]^T
Points in direction of steepest intensity increase. Orthogonal to lines of equal intensity.

Question 19

Gaussian regulation

Answer 19

Add information to improve the accuracyy of the image by edge detection

Question 20

Median vs Gaussian

Answer 20

Median for many small sources of noise. Gaussian for large source of noise.

Question 21

Enhancing image

Answer 21

• Reduce noise by combining images

- Deconvoltion: undo the convolution process as much as possible to see underlying image

Question 22

Deconvolution

Answer 22

• inverse image filtering via Fourier domain
• Regularized linear least-square fitting approach
• Improved solutions using iterative deconvolution algorithms -> best