Morphomathematics

Question 1

what are the morphomathematical operations

Answer 1

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

Question 2

what is the image complement

Answer 2

it corresponds to the invert of the image

Question 3

what is the symmetry of an image

Answer 3

it corresponds to the reflection of an image through the origin

Question 4

what is the dilation

Answer 4

the dilation with a structuring element means the intersection with the structuring element should not be empty

Question 5

what is erosion

Answer 5

The erosion with a structuring element means that the structuring element should be contained in the inside

Question 6

mention some important properties of dilation

Answer 6

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

Question 7

mention some important properties of erosion

Answer 7

erosion is not commutative X⊖B≠B⊖X

increasing meaning the size of the structuring element is always included inside the image

Question 8

what is the opening

Answer 8

consist of applying a succession of erosion then dilation, it leads to open the gapes in the image

Question 9

what is the closing

Answer 9

the closing consists of applying a succession of dilation and erosion
leads to closing the gapes present in the shape

Question 10

explain the properties of opening combined operators

Answer 10

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

Question 11

explain the properties of closing combined operators

Answer 11

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

Question 12

explain hit or miss transform

Answer 12

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))

Question 13

explain thining and thickening

Answer 13

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

Question 14

what is the filter that allows increasing or decreasing the brightness of an image?

Answer 14

The min-max filter consists of non-linear filter

Question 15

explain the skeleton extraction and its downside

Answer 15

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

Question 16

explain the distance map

Answer 16

associating to every pixel in the image the closest distance to the background

Question 17

explain the ultimate eroded point

Answer 17

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

Question 18

explain OBject labelling

Answer 18

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

Question 19

what is the is idea behind watershed transform

Answer 19

The main idea consists of detecting the local minimum and building a sort of dams on the local maximum fill those xholes

Question 20

what are the saddle point in the gradient crests

Answer 20

the saddle points reflect the pixel points that are locally maximum on a specific direction and minimum on the other direction

Question 21

what are the different steps of the watershed transform

Answer 21

we start by computing the gradient of the image to enhance the edges
we compute the local minimum to fill in the edges

Question 22

what are the different steps of the watershed transform

Answer 22

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

Question 23

what are the pros and cons of the watershed transform transform

Answer 23

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

Question 24

how to overcome the over-segmentation in the watershed transform

Answer 24

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

Question 25

what is the object labelling

Answer 25

usually performed on a binary, by relying on a structuring element all the connected components of the image are assigned specific label