Hello, my name is Thales Sehn Körting and I am going to present how the Hough transform works
The basics of hough Transform is to find aligned points in images that create lines
Suppose that we have this input image here
And then we'll apply some edge extraction algorithm and obtain some images like these
which highlights the main edges of the images and we apply the Hough transform in order to detect
points in images that create these lines here highlighted in colors and how hough transform works
Let's consider this x and y plane and here we provide a very simple
line in Red The Basic equation of this line
can be describe it in terms of y and x and now so the parameters a and b
In this case the parameters a and b are used to
define the angulation of this line here. This line we have lots of
combination of values of x and y
and we have a fixed value a and b. Here we define the parameters of
this line now. Let's invert and consider not the plane xy
but the plane a and b. So we are going to create the plane a and b
which can be called the feature space and in this feature space this point here
x i and y i defines a lot of possibilities here and also the other point
x j and y j
considering different
parameters of a and b to find this line in this feature
parameters, so if we
Intersect these two lines here in the feature space we are going to define this point a and b
where these two Lines here match
and is exactly in this feature
Combination of a and b which is this red line is [defined] [in] the region of space x and y?
The hough Transform is based
Exactly on this feature space here
So if we have these two points here detected as edges in our edge image
so it will define one point here if you have lots of
Points here, you're defining a line all the points will match
Exactly in this point and as long as this combination of points or cure lots of time
This means that we have aligned [defined] it in this feature space
Another way to consider this feature space is to consider not the a and B parameters
but the Data and also Row
parameters which also Define a line equation
But in terms of Angle the theta Angle and also our radius defined by this row value
so we're a
Write the equation in terms of x times cosine of theta plus y times sin [of] theta
Equal to Rho the radius here
So they have transformed basically do this
So they have transform can be viewed in terms of algorithms like this we have
An algorithm that stays looking for all the points looking for edge images
and when it finds some edge point it starts to iterate over all the
Possible [Theta] in Row Values and
Define exactly the occurrences of
These points here in these feature space as long as this line
occurs here, and it [founds] a
Correspondence terms of other points here
it will sum in terms of these space here and
We can see that here. We have zero for all the values
minus Theta from this side, plus Theta from this side
minus row for this side and plus row for this side you can [see] that as long as the
Algorithm runs it will discover different combinations now
It will it is highlighting this
possibility of a line here and define it by all these points in the end
We will see peaks in terms of values in these
which is they have space and all the
Widest points will Define the detected lines in the input image
in the end of the Hough transform
Algorithm
we have to
Look in this image for the pigs which according to this scale is defined by the widest points
So here we have a pig here another pig here another pig these pigs
stands for the detected Lines in the half space
We have just one example here
Which is this pig based on lots of points detected here in this and this pig?
Stands for exactly this line here detected. It's easy to note that in this case
We have 1 2 3 [&] 4 lines
possible to be detected in this feature space which is
represented by 1 2 3 and now 4, the 4th peak in terms of
Detected points in the half space and the algorithm goes up to the end of the image
The main reference that I have used is the well-known
Digital Image Processing book written by
Gonzalez and Woods
So thanks for your attention, and this is how the Hough Transform works