Edge Detection and Convolution - Lecture 5 - Week 2

Question 1

What three factors that cause edges to appear in images?

Answer 1

Depth discontinuity
Surface colour discontinuity
Illumination discontinuity

Represented as a rapid change in the image intensity function

Question 2

In the 1D example what kernel is used to get the first derivative?

Answer 2

0, 0, 0, -1, 1, 0, 0, 0

Question 3

In the 1D example what kernel is used to get the second derivative?

Answer 3

0, 0, 0, 1, -2, 1, 0, 0, 0

Question 4

What is the problem with using convolution to get the derivative?

Answer 4

It amplifies noise, which means that the derivative ends up a complete mess

The solution is to smooth first, e.g. with a gaussian kernel

Question 5

Why is d/dx(If) = I(df/dx)

Answer 5

Because differentiation is a convolution and convolutions are associative

Question 6

What is the Prewitt kernel?

Answer 6

Detecting in x-direction (vertical edges)
-1 0 1
-1 0 1
-1 0 1

Detecting in y-direction (horizontal edges)
-1 -1 -1
0 0 0
1 1 1

Question 7

What is the sobel kernel?

Answer 7

Detecting in x-direction (vertical edges)
-1 0 1
-2 0 2
-1 0 1

Detecting in y-direction (horizontal edges)
-1 -2 -1
0 0 0
1 2 1

Apply both filters for I’x and I’y
Edge magnitude |I| = sqrt(I’x^2 + I’y^2) (euclidean distance between pixels)

Edge direction = tan^-1(I’y/I’x)

Question 8

What detector is the most widely used “simple” edge detector?

Answer 8

Sobel

Question 9

In what direction does the image gradient point?

Answer 9

The direction of most rapid increase in intensity

Question 10

How is the edge strength of a pixel calculated?

Answer 10

Using the euclidean distance between its x and y derivative

Question 11

How can some kernels be made more efficient?

Answer 11

If they are decomposable, say for
-1 0 1
-2 0 2
-1 0 1
Can be decomposed to
1
2 -1 0 1
1

Processing a 1xn then a nx1 kernel is computationally cheaper than an nxn one

Question 12

Are gaussian kernels decomposable?

Answer 12

Yes

Question 13

What is gaussian weighting?

Answer 13

Normal distribution
Spread controlled by sigma

G(x,y) = e^-[(x^2+y^2)/2sigma^2]

Question 14

Is scale important in edge detection?

Answer 14

Edge filters enhance noise, edges exist at many different scales, what scales matter depend on application
Need to incorporate scale into edge detection
Gaussian gives scale & smoothing separable filter

Question 15

At what point does the gaussian approximate 0

Answer 15

beyond 3sigma

Question 16

What properties of gaussian are good?

Answer 16

Anti-aliasing
It’s separable

Question 17

Why does scale selection help?

Answer 17

Fine-scale edges may be just “noise” (irrelevant small-scale structure)

Detection of edges at larger scales is more reliable because there is less confusing detail

Location of edges at coarse scale can direct the search for finer-scale edges. Faster and more robust.

Question 18

What is the canny edge detector?

Answer 18

Gaussian smoothing to select scale
Edge Detection
- Differencing convolution or convolve with derivative of Gaussian
- Edge magnitude and direction

Question 19

What is the 2D laplacian kernel?

Answer 19

Second derivative kernel
Negative centre, positive surround

Isotropic response (invariant in regards to direction)
- One filter
- No edge direction
- Indirect edge magnitude

Question 20

What is the laplacian of the gaussian?

Answer 20

Second derivative of the 2D gaussian

Question 21

What is the Marr-Hildreth Edge Detector?

Answer 21

Second derivative of 2D gaussian / laplacian of the gaussian