Edge detection Flashcards
What is the edge detection and its relation with the Fourier transform
Generally, for edge detection, we can simply use the Fourier transform of an image where we only keep the high frequencies since we usually notice the sharp edges in borders
what is the convolution?
we have a pixel and a pixel neighbourhood then we apply a weighted sum
except for the Fourier transform, what is the other method that we can use
Another way to do that is by relying on the local derivative in an image
what is the local derivative
simply the difference between the pixel and the neighbour divided by the distance
what is the Laplacian operator
the laplacian derivative relies on the second derivative where we can simply use translate it into a structuring element or in other words convolution with the structuring element
how to compute the gradient of an image
the gradient simply consists of local difference
explain how the gradient can be used to perform edge detection
when we use the amplitude we will notice somehow black image with gradient edges, adding a certain threshold where we keep only higher values then this results in a darker image with visible edges
by using the angles we notice a blurry unclear image and it also reflect the direction of the gradient
for the masked angle
what kind of edges we can detect by using Robert
it allows detecting vertical and horizontal edges
compare briefly Robert, Sobel and prewitts edge detectors
For Sobel detector we have two orthogonal structuring elements then we use them both and perform the square root to later on obtain detected edge on all the sides, the idea is it gives more importance to the central pixel which is not the case to Prewitt
while Robert the edges are quite thin since the structuring element is way thinner and since the pixel is not very centred, the edging is a bit shifted
explain the gradient filter
consists of applying a local difference
what are the other morphological filters
top-hat which is the local maximum - the original image
bottom-hat which is the original image - the local minimum
and they allow detecting either the edge inside or outside border
Explain the use of the laplacian of gaussian
generally linear edges detectors are usually supper sensitive to noise, hence this filter apply initially some smoothing using a gaussian filter (low pass filter),
then using laplacian on the top of it
what type of filters is Laplacian
it reflects the second local derivative, hence it is a high pass filter
explain the Difference of Guassian
Generally we have two gaussian filters with different σ then we simply apply a difference between the two obtained images, this type of filter usually used for edge enhancement
generally, when we detect the 0 crossing in the in profile of each image we d know it is an edge
Explain the Canny edge
in the canny edge,
we define two thresholds, everything higher than the threshold is the border lower than the threshold then we have no border
it is commonly used edge detector :
- we initially apply a smoothing for the noise using a low pass filter
- we apply gradient intensity detection, Sobel
- remove all the edges that are not the local maximum, meaning we look at all the edges and omit the ones that are not local maximum
- double border intensity threshold , we only keep the values that are about a certain value
- weak edge removal, we set a threshold for instance weak border are >= 10% of image maximum
