Mark's Topics

Question 1

Fourier Transform

Answer 1

Allows us to understand frequency of a signal. Integration of the signal * sine wave

Question 2

Discrete Fourier Transform

Answer 2

FT applied to N points. Finds out how many sine waves are in the signal, gives us understanding of it.

Question 3

High, Critical, Low sampling

Answer 3

High Sampling is good, captures most detail. Critical sampling is just about good, captures just enough detail. Low sampling is bad, doesn’t capture enough detail, results in aliasing.

Question 4

Nyquist Sampling Theory

Answer 4

Critical Frequency = 2* Max frequency of signal

Question 5

2D Discrete Fourier Transform

Answer 5

For NxN Image. Results in 2D signal (like a wave at sea). Implemented using Fast Fourier Transform (by noticing symmetry in results of original FT).

Question 6

Properties in FT

Answer 6

Vertical bars lead to horizontal bars in transform. Shift Invariant. Rotation will give rotated frequency. Scaling will give scaled frequencies.

Question 7

Histogram

Answer 7

Describes how grey levels occupy an image.

Question 8

Point Operations

Answer 8

A (mathematical) function maps old pixels to new one. (Point by Point)

Question 9

Intensity Normalisation

Answer 9

Distributes grey levels in the image linearly between completely black and completely white. Used for normalisation in algorithms. Use a scaling factor s=white(255)/(MaxBrightness-MinBrightness)

Question 10

Histogram Equalisation

Answer 10

Tunes brightness of image to suit our eye. Distributes grey levels in a non linear way. Gives flat historgram.

Question 11

Thresholding (+Advanced)

Answer 11

Reduces image to black and white. Points Above value = white. Points below value = black. Advanced (optimal) Thresh decides what value to choose.

Question 12

Group Operations Aims

Answer 12

Improve quality of image by removing noise or rubbish in the image.

Question 13

Template Convolution

Answer 13

Process regions of points in original image to get a single new point in new image. Sum of all points in template multiplied by a weighting.

Question 14

Direct Averaging

Answer 14

For 3x3 template, weighting = 1/9. 5x5, w=1/25. More averaging = Bigger border + less noise + feature blur. Optimal size depends on amount of noise.

Question 15

Gaussian Averaging

Answer 15

Most likely to match noise, weighting comes from a Gaussian Function. Slower than direct averaging, but better noise reduction for same blurring.

Question 16

Median filter

Answer 16

Takes centre point of a ranked list derived from the template. Good for black and white noise, retains edges within images, ranking makes it slow.

Question 17

Edge Detection

Answer 17

Fucking Edge Detection. Important in Vision. Detect low level features which are grouped together to find high level features.

Question 18

Edge Detection methods

Answer 18

Determine contrast and intensity change using {MATHS}

Question 19

First Order Approximation (Edge Detection)

Answer 19

f’(x)=Px+1,y - Px,y. Equivalent to convolving matrix with image. Matrix=[{2,-1},{-1,0}]. Where 2 is original pixel

Question 20

Matrix Convolution with image (E/D)

Answer 20

For each pixel in original image, new value for the pixel is sum of all nearby pixels multiplied by equivalent value in matrix.

Question 21

Improved First Order Approximation (E/D)

Answer 21

Use Taylor Series to approxmiate. Two matrices {1, 0,-1} (horiz), and [1, 0, -1] (vert)

Question 22

Reducing noise due to differentiation (E/D)

Answer 22

Include averaging. Difference horizontally and average vertically using Mx=[{-1,0,1},{-1,0,1},{-1,0,1}]. Difference vertically and average horizontally using My=[{1,1,1},{0,0,0},{-1,-1,-1}]

Question 23

Prewitt Operator

Answer 23

Edge direction = tan^-1 (My/Mx). Has direct averaging

Question 24

Sobel Operator

Answer 24

Standard basic operator. Using Gaussian Filtering. Optimal differencing in one direction + Optimal averaging in the other. Cheap, averaging blurs the image

Question 25

Sobel Operator matrices

Answer 25

Mx=[{-1,0,1},{-2,0,2},{-1,0,1}] My=[{1,2,1},{0,0,0},{-1,-2,-1}]

Question 26

Canny Edge Detection

Answer 26

Optimal Edge Detector: Good localisation, low noise, no multiple response. Use an approximate template created by: Gaussian Smoothing,Sobel Operator, Non-Max-suppression, hysteresis thresholding. Gives thin edges in right place.

Question 27

Hysteresis Threshold Function

Answer 27

Upper and lower switching threshold. Only switch down when below a lower threshold. Only switch up when above upper threshold. Noise tolerance between upper and lower thresh.

Question 28

Second Order Detection

Answer 28

Differentiate First order detection. Gives ‘zero crossing’ at edges. Detect all zero crossings. M=[{0,1,0},{1,-4,1},{0,1,0}]

Question 29

Marr-Hildreth

Answer 29

Adds smoothing to Second Order edge detection. Gives connected edge points. Slow as templates can be slow. Solution = use FT.

Question 30

Shape Extraction using Template matching

Answer 30

Match template to an image. Store evidence in accumulator array. Maximum of evidence is the location of the shape. Slow but optimal. Can handle noise and occlusion.

Question 31

Hough Transform for Lines.

Answer 31

For line y=mx+c, plot c=-xm+y in accumulator space. Each point on original line represents a gradient, maps to a line in accumulator space. Can read off intercept and gradient of accumulator space

Question 32

Hough Transform for Lines code

Answer 32

Search all of x & y

• If value is greater than a threshold
• -Loop all values of gradient
• –Apply c=-xm + y to find c. Add point to accumulator

Question 33

Hough Transform for Circles

Answer 33

Using (x-x0)^2 + (y-y0)^2 = r^2. Need to loop all values of radius instead of gradient. If radius is unknown, add radius to accumulator space and loop through set of radius values. Search for max in accumulator

Question 34

Hough Transform for Ellipses

Answer 34

((x-x0)^2)/a^2 + ((y-y0)^2)/b^2 = 1. Add rotation to accumulator space. Giving 5D accumulator (x0,y0,a,b,rotation). VERY SLOW

Question 35

Generalised Hough Transform

Answer 35

For arbitrary shapes, lookup table R-table. Take centre of arbitrary shape. Form R-Table storing distance and angle of each point from the centre. Edge direction is index to distance of centre point. Every element R-table votes for correct centre (may also vote incorrectly)

Question 36

Generalised Hough Transform code

Answer 36

Loop all image points
-If point is greater than a threshold
--Get edge direction Thi(x,y). Lookup d and Theta for Thi(x,y). Vote at centre d,Theta(Thi)
#Scale d for bigger/smaller shapes. 
#Add rotation to Theta if rotated.