How Hough Transform works

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

Channel: Thales Sehn Körting

Views: 202,844

Keywords: hough, line detection, feature detection, target detection, image processing, image, algorithm, hough transform, digital image processing, gonzalez, woods, dip, ip

Id: 4zHbI-fFIlI

Length: 6min 19sec (379 seconds)

Published: Sat Apr 16 2016