Week 2 - Image Features: Edges

Question 1

Why are Edges important

Answer 1

They are key for image detection
occur at boundaries, shadows, changes in texture or colour erc
Human brain quickly recognises them

Question 2

What are edges

Answer 2

Boundaries between physically distinct regions

Discontinuities in intensity values
A place of rapid change in the image intensity function
‘Extrema of the derivative’

Question 3

What is edge location in terms of differentiation

Answer 3

Equivalent to differentiating the intensity function I(x)
dI / dx

Question 4

What are 2 main techniques for edge detection

Answer 4

Smoothing convolution
Differentiation

Question 5

What is the difference between using weighted and non weighted kernel averaging

Answer 5

eg 111 and 121
weighted averaging creates better smoothing

Question 6

What is a simple kernel for finding the 1st and 2nd derivative

Answer 6

In this context, differentiation is a type of convolution
(-1, 0 ,1)
(1, -2, 1)

Question 7

What are three discontinuities that cause edges

Answer 7

depth
illumination
surface colour

Question 8

What is the effect if noise of edge detection

Answer 8

It hides the edges as it creates many pixel value changes
Differentiating noise creates a complicated image

Question 9

How do we remove noise for edge detection

Answer 9

Smooth the image first
Then look for the peaks in d/dx (I * f)

Question 10

What is the associative property of convolution

Answer 10

the order in which you convolve multiple functions does not change the final result
(f∗g)∗h=f∗(g∗h)

Question 11

What operations can be performed just via choice of kernel

Answer 11

first derivative
second derivative
smoothing
local average
weighted avergae

Question 12

What is the Prewitt Kernel

Answer 12

It is two kernels: for detecting vertical or horizontal edges

Question 13

What is the prewitt kernel in x direction

Answer 13

-1 0 1
-1 0 1
-1 0 1
Detects vertical edges

Question 14

What is the prewitt kernel in y direction

Answer 14

-1-1-1
000
111
Detects horizontal edges

Question 15

What is the sobel kernel

Answer 15

Also made up of two kernels
The smoothing is weighted towards the centre
(weighted average along the edge)

Question 16

What is the sobel in x-direction

Answer 16

-1 0 1
-2 0 2
-1 0 1
Detecting vertical edges

Question 17

What is the sobel in y-direction

Answer 17

-1-2-1
0 0 0
1 2 1
Detects horizontal edges

Question 18

What sort of image does the sobel and prewitt operators result in

Answer 18

A transformed grey-level image
Derivate of the image in the _direction

Question 19

How do you calculate Edge magnitude

Answer 19

|I’| = √ I’x^2 + I’y^2

Question 20

How do you calculate edge orientation

Answer 20

Φ = tan-1 I’y / I’x

Question 21

What are gradient images

Answer 21

Grayscale images showing gradient magnitude at each pixel

Question 22

What is the gradient of the image

Answer 22

Measure of change in image function in the x and y direction
gradient = magnitude
||∇I||= √(dI/dx)^2 + (dI/dy)^2

Gradient direction = tan-1(gradient y/ gradient x)

Question 23

What are decomposable kernels

Answer 23

eg 3x3 into 3x1 and 1x3
It is cheaper
gets the same result
operations are faster

Eg 21x21 -> 1x21 and 21x1 -> 42 multiplications
instead of 441 at each image point

2n rather than n^2

Question 24

Why is scale important to edge detection

Answer 24

Edges can vary in size, thickness and be more prominent depending on the scale
Need to incorporate scale into edge detection
Gaussian filter is often to introduce scale information

detection at larger scales is more reliable
Location of edges at coarse scale can direct the search for finer-scale edges

Question 25

What is the 1D Gaussian

Answer 25

Represents the distribution of values along one dimension
Gaussian weighting schemes are controlled by σ

Question 26

What is Anti-aliasing

Answer 26

High-frequency details or fine features in an image exceed the resolution (appear blurred)
caused due to undersampling and inadequate representation

Question 27

What is the canny operator

Answer 27

The first derivative of the Gaussian
- differentiate the smoothing kernel
σ determines the scale (x axis on graph of derivative)
smaller σ, sharper edges, less smoothing

Question 28

What does the canny operator mean we no longer have to do

Answer 28

• suppress non maxima of derivative (thinning)
• track using hysteresis thresholds

Question 29

What is suppression of non maxima

Answer 29

aims to reduce the width of detected edges by retaining only the local maxima (or peaks) in the gradient magnitude image along the direction of the gradient (only retains the maxima in the region)

Question 30

How do you find the peak of thick edges

Answer 30

The second derivative gives a precise localisation, where the crossing of x axis occurs

Question 31

What is the 2D Laplacian Kernel

Answer 31

Second derivative filter
After convolution, edge positions will be at zero crossing
The sum of all values should be zero - no scaling
Negative centre, positive surround or vice versa
Isotropic response
eg
1 -2 1
-2-4-2
1 -2 1
or
1 1 1
1-81
1 1 1

Question 32

What is dx notation equal to

Answer 32

d/dx

Question 33

What does an isotropic filter mean

Answer 33

Gives the same response to edges in any direction
one filter
no edge direction (can be bad to lose this info)
indirect edge magnitude

Question 34

What is the Laplacian of Gaussian

Answer 34

The second derivative of the 2D Gaussian
Gives a “Mexican hat” (can be up or down)
Also called Marr-Hildretch edge detector

Instead of just Laplacian, we still have orientation and smoothing
does not create thick edges
σ again determines the scale (broader or narrower kernel)

Question 35

How does size of σ affect gaussian distribution

Answer 35

Larger σ -> broader distribution
Smaller σ -> narrower distribution

Question 36

How do gaussian filters introduce scale information

Answer 36

Blur image with gaussian with different levels of σ
desired amount of smoothing can be used based off these levels