Morphomathematics Flashcards
what are the morphomathematical operations
they are types of function that modifies the shape of images, they are considered as postprocessing step, and can only be applied on binary images
what is the image complement
it corresponds to the invert of the image
what is the symmetry of an image
it corresponds to the reflection of an image through the origin
what is the dilation
the dilation with a structuring element means the intersection with the structuring element should not be empty
what is erosion
The erosion with a structuring element means that the structuring element should be contained in the inside
mention some important properties of dilation
commutative, meaning if we dilate the object by a structuring element is equivalent to dilating the structuring element by the object
associative X⊕(B⊕C)=(X⊕B)⊕C
mention some important properties of erosion
erosion is not commutative X⊖B≠B⊖X
increasing meaning the size of the structuring element is always included inside the image
what is the opening
consist of applying a succession of erosion then dilation, it leads to open the gapes in the image
what is the closing
the closing consists of applying a succession of dilation and erosion
leads to closing the gapes present in the shape
explain the properties of opening combined operators
anti-extensive, meaning the result of the opening is enclosed inside the original image
idempotent, meaning you apply opening several times and it won’t change a thing
explain the properties of closing combined operators
extensive, meaning the image is contained inside the results of the closing
idempotent, meaning you apply opening several times and it won’t change a thing
explain hit or miss transform
consist of a combination of structuring elements, to encode both of them we use a matrix ,
where 1s belonging to a structuring element
0s belonging to the others
and points means it belongs to neither of them (the don’t care part),
the idea is to hit a certain pattern where 1 are inside the object and 0s are background
logical_and(erosion(X,B1),erosion(1-X,B2))
explain thining and thickening
for thining it simply consists of removing the result of hit or miss transform from the original image
while thickening consist of using hit or miss transform and merging it with the original image
what is the filter that allows increasing or decreasing the brightness of an image?
The min-max filter consists of non-linear filter
explain the skeleton extraction and its downside
the skeleton extraction consists of a special case of thinning and it relies on a specific structuring element, the downside is that we will notice some extensions on the side, a good option for that is using pruning, over-pruning leads to lose some parts
explain the distance map
associating to every pixel in the image the closest distance to the background
explain the ultimate eroded point
Corresponding to the last pixel that is surviving after a long series of erosion, to perform that we can either use erosion
or simply use the distance map, then use the local Maximum
explain OBject labelling
consist of transforming a binary image into a label image where every pixel has an integer value and each integer value correspond to a certain number and its shared by a certain pixel sharing the same connected component
what is the is idea behind watershed transform
The main idea consists of detecting the local minimum and building a sort of dams on the local maximum fill those xholes
what are the saddle point in the gradient crests
the saddle points reflect the pixel points that are locally maximum on a specific direction and minimum on the other direction
what are the different steps of the watershed transform
we start by computing the gradient of the image to enhance the edges
we compute the local minimum to fill in the edges
what are the different steps of the watershed transform
we start by computing the gradient of the image to enhance the edges
we compute the local minimum to fill in the edges
and to finally fill the basin accordingly, generally we add adam on each local maximum.
we rely on region-based segmentation when performing the watershed basin
what are the pros and cons of the watershed transform transform
the pros it is sensitive to borders and produces closed borders while the cons produces and lot of local minimum and prone to over segmentation
how to overcome the over-segmentation in the watershed transform
through preprocessing we initially replace each region with the average value that what we call the mosaic image, then the gradient is computed to get the edges, finally, we perform a threshold to get rid of the non-needed edge
We generally use the marker image, the question to ask is how to obtain a good marker image, this might be obtained relying either a local minim or local maximum then use an object labelling
