Edge Detection and Convolution - Lecture 5 - Week 2 Flashcards
What three factors that cause edges to appear in images?
Depth discontinuity
Surface colour discontinuity
Illumination discontinuity
Represented as a rapid change in the image intensity function
In the 1D example what kernel is used to get the first derivative?
0, 0, 0, -1, 1, 0, 0, 0
In the 1D example what kernel is used to get the second derivative?
0, 0, 0, 1, -2, 1, 0, 0, 0
What is the problem with using convolution to get the derivative?
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
Why is d/dx(If) = I(df/dx)
Because differentiation is a convolution and convolutions are associative
What is the Prewitt kernel?
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
What is the sobel kernel?
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)
What detector is the most widely used “simple” edge detector?
Sobel
In what direction does the image gradient point?
The direction of most rapid increase in intensity
How is the edge strength of a pixel calculated?
Using the euclidean distance between its x and y derivative
How can some kernels be made more efficient?
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
Are gaussian kernels decomposable?
Yes
What is gaussian weighting?
Normal distribution
Spread controlled by sigma
G(x,y) = e^-[(x^2+y^2)/2sigma^2]
Is scale important in edge detection?
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
At what point does the gaussian approximate 0
beyond 3sigma
What properties of gaussian are good?
Anti-aliasing
It’s separable
Why does scale selection help?
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.
What is the canny edge detector?
Gaussian smoothing to select scale
Edge Detection
- Differencing convolution or convolve with derivative of Gaussian
- Edge magnitude and direction
What is the 2D laplacian kernel?
Second derivative kernel
Negative centre, positive surround
Isotropic response (invariant in regards to direction)
- One filter
- No edge direction
- Indirect edge magnitude
What is the laplacian of the gaussian?
Second derivative of the 2D gaussian
What is the Marr-Hildreth Edge Detector?
Second derivative of 2D gaussian / laplacian of the gaussian
