How Hough Transform works

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  • เผยแพร่เมื่อ 5 ก.พ. 2025

ความคิดเห็น • 222

  • @NguyenDuy-jd6sm
    @NguyenDuy-jd6sm 5 ปีที่แล้ว +81

    YOUR video is gold sir, thank you very much !

    • @tkorting
      @tkorting  5 ปีที่แล้ว +2

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  • @tiagopadua
    @tiagopadua 6 ปีที่แล้ว +28

    The animation is awesome! I have a very visual memory, and this helped me A LOT to understand exactly what's going on. Thank you so much!!!

    • @tkorting
      @tkorting  6 ปีที่แล้ว

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  • @pardhugopalam5064
    @pardhugopalam5064 7 ปีที่แล้ว +1

    Finally! It made sense both visually & mathematically. The animation of it's working is the best part. Thanks for sharing.

    • @tkorting
      @tkorting  7 ปีที่แล้ว

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  • @harikrishnanprabhakaran8902
    @harikrishnanprabhakaran8902 8 ปีที่แล้ว +23

    Thank you very much for the effort you have taken to explain the subject in a simplified manner..

    • @tkorting
      @tkorting  8 ปีที่แล้ว +2

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  • @cricketjanoon
    @cricketjanoon 4 ปีที่แล้ว +1

    A very clear and concise explanation of the Hough Transform.

    • @tkorting
      @tkorting  3 ปีที่แล้ว

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  • @elenamihalas9761
    @elenamihalas9761 8 ปีที่แล้ว +3

    Thank you very much for your explanation. It was exhaustive and very comprehensive. The graphics helped me a lot to understand the entire process. My compliments!

    • @tkorting
      @tkorting  8 ปีที่แล้ว

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  • @kjasghi2364r9sdfnkj
    @kjasghi2364r9sdfnkj 8 ปีที่แล้ว +115

    that animation made perfect sense and know i finally get it but how the hell do i explain that in an exam hahaha

    • @tkorting
      @tkorting  8 ปีที่แล้ว +3

      thanks for your feedback
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      I hope you have managed to explain in your exam ;)
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    • @timborito1540
      @timborito1540 7 ปีที่แล้ว

      same here :D

    • @senjiukanuba5569
      @senjiukanuba5569 6 ปีที่แล้ว +13

      The advantage of having to explain something like this in an exam is that the examiner probably knows already how it works and he just has to see that you understand it too. And he can ask you for clarification where he's unsure if you understood it. :-)

  • @nicholaspeterman9942
    @nicholaspeterman9942 6 ปีที่แล้ว +1

    Well done, literally the best explanation I have found online.

    • @tkorting
      @tkorting  6 ปีที่แล้ว

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  • @blyaticon8190
    @blyaticon8190 3 ปีที่แล้ว +1

    The explanation with the animation was so good. Thank you!

  • @mingchangliu5316
    @mingchangliu5316 5 ปีที่แล้ว +1

    your video is better than some textbooks, thank you sir!

    • @tkorting
      @tkorting  5 ปีที่แล้ว

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  • @arghadeepmazumder2133
    @arghadeepmazumder2133 6 ปีที่แล้ว +7

    This is exactly how the universities should teach. Thank you very very much for this one.

    • @tkorting
      @tkorting  6 ปีที่แล้ว

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  • @That1dude240
    @That1dude240 7 ปีที่แล้ว +1

    Thank you! The visualization makes the workings of the algorithm a lot more clear.

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +That1dude240 thanks for the positive feedback. Please like and share the video and subscribe to my channel.
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  • @tracknes
    @tracknes 8 ปีที่แล้ว +7

    Finally i got it! I had read the same book but now i see what i was doing wrong. Thank you mate.

    • @tkorting
      @tkorting  8 ปีที่แล้ว

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  • @kennethchen427
    @kennethchen427 4 ปีที่แล้ว +1

    Hello! I am currently working on a lane detecting program and I was having trouble understanding the concept of the Hough Line detection algorithm. You explained it very well. That you so much!!!!!!

    • @tkorting
      @tkorting  3 ปีที่แล้ว

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  • @velotron
    @velotron 8 ปีที่แล้ว +1

    This visualization really helped me understand the Hough Transform. Thanks!

    • @tkorting
      @tkorting  8 ปีที่แล้ว

      +Joseph Sheedy thanks for your feedback,
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  • @keineangabe1804
    @keineangabe1804 5 ปีที่แล้ว +14

    This is amazing. I mean my prof hasn't done it half that good in double the time.
    Just one little detail I had initially trouble with: we do not use y = a*x+b because a is infinite for a line that has 90 degrees.

    • @tkorting
      @tkorting  5 ปีที่แล้ว

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    • @aitorjara100
      @aitorjara100 4 ปีที่แล้ว +1

      A vertical line hasn't a =1 ?

    • @hermeticGreen
      @hermeticGreen 4 ปีที่แล้ว +2

      @@aitorjara100 No it does not. A 45 degree diagonal line has a=1.

    • @aitorjara100
      @aitorjara100 4 ปีที่แล้ว +7

      @@hermeticGreen Jesus.... sorry I don't know what the hell was I thinking when I posted it

    • @hermeticGreen
      @hermeticGreen 4 ปีที่แล้ว +1

      @@aitorjara100 haha no worries

  • @loveformatt
    @loveformatt 6 ปีที่แล้ว +4

    This video was soooooooo useful! I have a paper due tomorrow on Hough Transform, and how it compares to Inverted Gradient Hash Maps.
    This was amazingly helpful. I was on struggle street. Thank you!!

    • @tkorting
      @tkorting  3 ปีที่แล้ว

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  • @sergioorozco7331
    @sergioorozco7331 4 ปีที่แล้ว +3

    What an absolutely great explanation. The visual of iterating over each pixel to find the whitest spots in the Hough Space was particularly helpful. Thank you!

    • @tkorting
      @tkorting  3 ปีที่แล้ว

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  • @farseenabdulsalam6246
    @farseenabdulsalam6246 4 ปีที่แล้ว

    Best explanation and visualization I have ever seen! Thanks so much for this.

  • @momochi536
    @momochi536 6 ปีที่แล้ว +6

    Amazing animation! For me its very hard to fallow only formulas and a lot of words. But that animation made me understand the idea behind all this! Thank you! :D

    • @tkorting
      @tkorting  6 ปีที่แล้ว

      Thanks for your comment.
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      I feel the same as you, so I try hard to create animations for the theories that I suffer a little bit to understand :)
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  • @ibropwns
    @ibropwns 5 ปีที่แล้ว +3

    Such a great explanation in a very short time! Thank you!

    • @tkorting
      @tkorting  5 ปีที่แล้ว +1

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  • @ERICROJO156
    @ERICROJO156 4 ปีที่แล้ว

    the lines in the Hough space are beautiful

  • @pasindujayaweera5575
    @pasindujayaweera5575 8 ปีที่แล้ว +2

    Clean and simple explanation.. Thanks!!!

    • @tkorting
      @tkorting  8 ปีที่แล้ว +1

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  • @andreasschmid2484
    @andreasschmid2484 7 ปีที่แล้ว +3

    Hmm.. i'm studying for a test. I didn't understand my script at all... but now it's pretty simple. Thank you Thales.

    • @tkorting
      @tkorting  7 ปีที่แล้ว

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  • @mohammedfarahmand7809
    @mohammedfarahmand7809 3 ปีที่แล้ว

    Excellent visualization. Thank you very much.

  • @kamilsledziewski6198
    @kamilsledziewski6198 4 ปีที่แล้ว +5

    Great explanation, OpenCV tutorials could definitely point to your videos!

    • @tkorting
      @tkorting  4 ปีที่แล้ว +1

      Thanks a lot. I would live to have your suggestion true.
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  • @郑文浩-p5i
    @郑文浩-p5i 3 ปีที่แล้ว

    wow,this animation is great to help me undertstand the Hough Transform!!!!

  • @fatihozturk6521
    @fatihozturk6521 7 ปีที่แล้ว +2

    Thanks Thales. Most informative channel about AI. Please supply +1000 videos! Oh! What a wonderful day!

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Fatih ÖZTÜRK many Thanks For your ositive feedback
      please like and share this video and subscribe to my Channe
      l best regards

  • @sayahsauki
    @sayahsauki 8 ปีที่แล้ว +3

    this help me with my college project.
    thank you sir for sharing.

    • @tkorting
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  • @turkibaghlaf4565
    @turkibaghlaf4565 5 ปีที่แล้ว +1

    great explanation and the visualization helped me a lot. Thank you for this great content

    • @tkorting
      @tkorting  5 ปีที่แล้ว

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  • @jabbathehot8418
    @jabbathehot8418 7 ปีที่แล้ว +1

    Excellent explanation! Thank you very much, sir!

    • @tkorting
      @tkorting  7 ปีที่แล้ว +1

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  • @mannambhavani4266
    @mannambhavani4266 4 ปีที่แล้ว +2

    Wonderfully explained sir, thanks a lot..it was soo helpful.

    • @tkorting
      @tkorting  3 ปีที่แล้ว

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  • @shahinshahkarami2558
    @shahinshahkarami2558 8 ปีที่แล้ว +1

    Thank you so much. Everything is crystal clear now.

    • @tkorting
      @tkorting  8 ปีที่แล้ว

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  • @ani_kani
    @ani_kani 6 ปีที่แล้ว +1

    Thank you for this video! The animation is very helpful and your explanation is easy to follow. You also sound a bit like Javier Bardem!

    • @tkorting
      @tkorting  6 ปีที่แล้ว

      Thanks a lot for your comment. Please like/share/subscribe.
      It is not the first time that people talks about Javier Bardem :) But probably is because I record in the silence of the night.
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  • @gafgfan
    @gafgfan 3 ปีที่แล้ว

    Very very helpful and clear!

  • @dariodemattiesreyes3788
    @dariodemattiesreyes3788 7 ปีที่แล้ว +1

    Excellent explanation. Thanks!

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Dario Dematties Reyes thanks for your feedback. Please like/share the video and subscribe to my channel. Best regards

  • @sallerc
    @sallerc 8 ปีที่แล้ว +1

    Great explanation, the visualization helped a lot.

    • @tkorting
      @tkorting  8 ปีที่แล้ว

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  • @skittles6486
    @skittles6486 6 ปีที่แล้ว +1

    Thank you very much for this wonderful explanation. This was really really helpful for me.

    • @tkorting
      @tkorting  6 ปีที่แล้ว

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  • @wolfisr
    @wolfisr 7 ปีที่แล้ว +1

    ohh, it was a very clear explanation! many thanks and well done!

    • @tkorting
      @tkorting  7 ปีที่แล้ว

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  • @instructorstartonedu110
    @instructorstartonedu110 5 ปีที่แล้ว +1

    That's so clear and thank you!

    • @tkorting
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  • @RawanLaz
    @RawanLaz 7 ปีที่แล้ว +1

    Thanks for the simple explanation :)

    • @tkorting
      @tkorting  7 ปีที่แล้ว

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  • @anoopgeorge6103
    @anoopgeorge6103 5 ปีที่แล้ว +1

    Best video on HT

    • @tkorting
      @tkorting  5 ปีที่แล้ว

      Many thanks for your feedback, please check my new video about circle detection using Hough transform
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  • @johnhendy1281
    @johnhendy1281 5 ปีที่แล้ว +1

    Just purely fantastic.

    • @tkorting
      @tkorting  5 ปีที่แล้ว

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  • @JavierSalazar-i4f
    @JavierSalazar-i4f 4 หลายเดือนก่อน

    Thank you from the sunny Spain

  • @AlexisGaziello
    @AlexisGaziello 7 ปีที่แล้ว +1

    Amazing!! Really clear with animations. Thanks

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Alexis Gaziello thanks for your feedback.
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  • @antonyrizzy
    @antonyrizzy 8 ปีที่แล้ว +1

    Very nice explanation. Thanks!!

    • @tkorting
      @tkorting  8 ปีที่แล้ว

      thanks for your feedback

  • @yingninghe4077
    @yingninghe4077 5 ปีที่แล้ว +1

    thank you sir. very easy to understand.

    • @tkorting
      @tkorting  5 ปีที่แล้ว

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  • @ashRAFKSALIM
    @ashRAFKSALIM 5 ปีที่แล้ว

    So ,it's like we have points on XY plane and when we transform the y=ax+b in b=-ax+y and plot that b=-ax+y in ab plane
    and do it for all the given points of x,y and when we have so many lines in ab plane intersecting a common point we take it and use it as xy and plot a line that will fit maximum number of points ? is that so ?

  • @shawz4308
    @shawz4308 8 ปีที่แล้ว +7

    learned a lot.
    thank you very much.
    It's really good !

    • @tkorting
      @tkorting  8 ปีที่แล้ว

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  • @aminazgol3918
    @aminazgol3918 6 ปีที่แล้ว +1

    thank u very much that was a very easy explanation I really enjoyed it.

    • @tkorting
      @tkorting  5 ปีที่แล้ว

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  • @StickDoesCS
    @StickDoesCS 3 ปีที่แล้ว

    great video! Found it very useful :))

  • @ShahidulIslamcse
    @ShahidulIslamcse 7 ปีที่แล้ว +2

    The explanation is very good. Thanks

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Shahidul Islam thanks for your feedback.
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  • @monikadelekta3344
    @monikadelekta3344 6 ปีที่แล้ว +1

    REALLY helpful!! helped me finally understand the maths behind it!

  • @Danielikesinging
    @Danielikesinging 5 ปีที่แล้ว +1

    Awesome tutorial! Thanks man!

    • @tkorting
      @tkorting  5 ปีที่แล้ว

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  • @nupoortendolkar8295
    @nupoortendolkar8295 7 ปีที่แล้ว +1

    thanks...for the video..it simplified the concept...

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Nupoor Tendolkar thanks for your feedback.
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  • @kathirs1
    @kathirs1 5 ปีที่แล้ว

    Hi, I am not getting the exact idea behind this. So first, we are detecting edges using canny or any algorithms which leaves us with edges in the image. Now, edges can be lines in the image which is what you explained as y = ax +b where a is the slope and b is the intercept of the line. In the fitter space, I will call it as hough space, my question is "How points in the line equation of the edge becomes line in the hough space"?

    • @tkorting
      @tkorting  5 ปีที่แล้ว

      Thanks for your question
      Please subscribe to my channel
      You are right, first detect edges, then use the edges to find lines. Maybe the point that you did not understand is the accumulator (which creates the figure), the more two points intercept in the hough space, the more points are aligned in the original one. This is why the location of the lines are in the maximum points of the hough image.
      Regards

  • @zhemann
    @zhemann 6 ปีที่แล้ว

    At 1:55 how can the green line have a positive slope? Both (Xi, Yi) and (Xj, Yj) have a negative value for a, so in feature space both lines should have a positive slope right? I do believe that your eplanation is correct, however I still have trouble to grasp this transformation. It doesn't make sense to me how the lines are drawn in feature space.

  • @bocao9552
    @bocao9552 6 ปีที่แล้ว +1

    Great visualization.

    • @tkorting
      @tkorting  6 ปีที่แล้ว

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  • @krishnasundar5638
    @krishnasundar5638 5 ปีที่แล้ว

    Can you explain me how the another way
    r = x cos(theta) + y sin(theta) arrived ?
    I assume r is the shortest distance from origin to the line.
    I came across henesse normal form and the shortest distance between points and planes but I still couldn't relate with the above equation. Can you explain it to me how we arrived/derived to the above equation ?
    Edit : found it after some deep diving into basics
    People who wants to know how this equation originated, the term we're looking to search and learn for is "normal form representation of a line"

  • @xiuhongeu4491
    @xiuhongeu4491 7 ปีที่แล้ว +1

    Awesome explaination!

    • @tkorting
      @tkorting  7 ปีที่แล้ว

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    • @xiuhongeu4491
      @xiuhongeu4491 7 ปีที่แล้ว

      Thales Sehn Körting sure thing! Done that!

  • @tiagopadua
    @tiagopadua 6 ปีที่แล้ว

    So, I have a question. On the Generalised Hough Transform, the difference is that we don't compare with line equations. Instead we compare with the target form/path - for every rotation and scale possible. Is that it? If so, it looks very heavy to calculate that.

    • @tkorting
      @tkorting  6 ปีที่แล้ว

      If I understood your question, yes you need to compute several values to find the lines. That's why we create the matrix, and use the maximum values on the matrix to point to lines. It is expensive computationally.
      Regards

  • @aIIeIujah
    @aIIeIujah 8 ปีที่แล้ว +1

    Quite informative. Thank you!

    • @tkorting
      @tkorting  8 ปีที่แล้ว +1

      +Menard Hernandez Thanks for your feedback
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  • @AlCaponi
    @AlCaponi 8 ปีที่แล้ว

    Best explenation ever! Thank you!

    • @tkorting
      @tkorting  8 ปีที่แล้ว

      +Angelo Conconi Thanks for your feedback
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  • @DurBarak
    @DurBarak 7 ปีที่แล้ว +1

    Great explanation, thanks for making this video.

    • @tkorting
      @tkorting  3 ปีที่แล้ว

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  • @chikanehimemiya3389
    @chikanehimemiya3389 5 ปีที่แล้ว

    muy bello y todo, pero la transformada para círculos?

    • @tkorting
      @tkorting  5 ปีที่แล้ว

      Please subscribe to my channel. My last video is about circle detection.
      Regards

  • @ratangles820
    @ratangles820 8 ปีที่แล้ว +4

    Thankyouu!! Shared with my mates! :D

    • @tkorting
      @tkorting  8 ปีที่แล้ว +2

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    • @javierdelarica6290
      @javierdelarica6290 8 ปีที่แล้ว

      Yo soy tu mate ;D

  • @tugbaozkal
    @tugbaozkal 6 ปีที่แล้ว +1

    Really good and useful video :) thank you

    • @tkorting
      @tkorting  6 ปีที่แล้ว

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  • @muonneutrino
    @muonneutrino 8 ปีที่แล้ว

    How do you know where the lines start and stop? I mean, you have detected that there is a line with r=xcos30 + ysin30. Fine. Now there are some 4 sections that lay on same line (i.e. there are gaps). How do you know where are the boundaries?

    • @tkorting
      @tkorting  8 ปีที่แล้ว

      Hi Gregory, thanks for your feedback. Please like/share and subscribe.
      To discover the start/end points, recall that we applied the Hough transform in the image of edges (1 for edge, 0 for no edge). So with the line equation, you can iterate over x, and find the first and last y with edges. It is a basic suggestion.
      Regards

  • @timborito1540
    @timborito1540 7 ปีที่แล้ว +1

    Thank you SO MUCH!

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Peter Petersen thanks for your feedback
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  • @ao9779
    @ao9779 7 ปีที่แล้ว +1

    Amazing video 🤘🏻

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +F V thanks for your feedback.
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  • @sarvagyagupta4573
    @sarvagyagupta4573 8 ปีที่แล้ว

    This is one good explanation. I just have one question. Why is a point in xy plane a line in ab plane and not any other shape? Same thing or a circle?
    Please let me know.

    • @tkorting
      @tkorting  8 ปีที่แล้ว +1

      Dear friend, thanks for your feedback. Please like/share the video and subscribe.
      Recall that the shapes we showed are for the conversion from xy space to the line equation using radius and angle (2:56). The variation of radius and angle produces the shapes.
      A point in xy plane is not a line in ab plane. Indeed two points in xy plane that should form a line, are represented by a single point in ab plane. If more groups of points in xy plane are part of the same line, then the point will bright more in the resultant image.
      Regards

  • @roynealrayess6690
    @roynealrayess6690 7 ปีที่แล้ว +1

    thanks a bunch! :) awesome animation!

    • @tkorting
      @tkorting  3 ปีที่แล้ว

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  • @febbone
    @febbone 5 ปีที่แล้ว +1

    Now I know what I don't understand! Good video

    • @tkorting
      @tkorting  5 ปีที่แล้ว

      Thanks for your feedback
      Please subscribe to my channel
      Regards

  • @BluePandora1
    @BluePandora1 4 ปีที่แล้ว

    Eu amo os seus videos que sao muito claros e didaticos. Voce eh do Parana ?

    • @tkorting
      @tkorting  4 ปีที่แล้ว

      Muito obrigado pelo retorno! Sou gaúcho morando no estado de SP. Inscreva-se no canal.
      Um abraço

  • @ajayshastry5427
    @ajayshastry5427 3 ปีที่แล้ว +2

    very nice

  • @AmitSharma-po1zb
    @AmitSharma-po1zb 6 ปีที่แล้ว

    Hi,
    I am getting this error in OpenCV probablistic hough lines.
    please help to resolve :-
    ---> for x1, y1, x2, y2 in lines[0]:
    cv2.line(image, (x1,y1), (x2,y2),(0,255,0), 3)
    ValueError: not enough values to unpack (expected 4, got 2)

  • @salmaabdelmonem7482
    @salmaabdelmonem7482 7 ปีที่แล้ว +1

    nice explanation thanks !

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Salma Eg thanks a lot for your positive feedback
      Please like and share the video and subscribe to my channel
      Regards

  • @muhibullah4201
    @muhibullah4201 7 ปีที่แล้ว +1

    thank u for your explinatio , did u work on matlab ? I need some help in that

    • @tkorting
      @tkorting  7 ปีที่แล้ว +1

      +muhib ullah thanks for your feedback
      I used octave which is similar to Matlab.
      please subscribe to my channel, like/share the video
      regards

    • @muhibullah4201
      @muhibullah4201 7 ปีที่แล้ว

      Thales Sehn Körting sir I am using matlab , the hough function returns rho ,theta and H matrix ,as u expalined i understood what are rho and theta but what is H ?if u please elaborate it

  • @lewisb8634
    @lewisb8634 8 ปีที่แล้ว +1

    Great video, thank-you for uploading! :)

    • @tkorting
      @tkorting  8 ปีที่แล้ว +1

      thanks for your feedback
      please like/share the video and subscribe
      regards

  • @Matematica_Aplicada
    @Matematica_Aplicada 5 ปีที่แล้ว +2

    Thales o video é muito bom. Bem explicado. Faça um em português também. Há uma carência muito grande de videos neste nível em nossa língua.

    • @tkorting
      @tkorting  5 ปีที่แล้ว

      Muito obrigado pelo comentário, por gentileza inscreva-se no canal.
      Existe o canal do Hemerson Pistori com bastante conteúdo em português.
      Um abraço

  • @amralmatni6586
    @amralmatni6586 4 ปีที่แล้ว

    Great video, thank you

    • @tkorting
      @tkorting  3 ปีที่แล้ว

      Thanks for the feedback, please subscribe to my channel

  • @malleshkumar5187
    @malleshkumar5187 7 ปีที่แล้ว +1

    thank you vary much sir may i know line detection

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      +Mallesh Kumar thanks for your feedback. Please like/share the video and subscribe to my channel. I will put your suggestion in my videos wish list.
      Regards

  • @jhonnatangamav4349
    @jhonnatangamav4349 8 ปีที่แล้ว

    Great video! Thank you for the explanation! :D

    • @tkorting
      @tkorting  8 ปีที่แล้ว

      thanks a lot for your feedback.
      Please subscribe to my channel and share this video with your peers.
      Regards

  • @russellbarnes7732
    @russellbarnes7732 10 หลายเดือนก่อน

    Can anyone tell me if there is equipment out there that utilizes this principle?

    • @13lack_Rose
      @13lack_Rose 2 หลายเดือนก่อน

      lane detection systems

  • @durgeshvikramyadav6921
    @durgeshvikramyadav6921 4 ปีที่แล้ว +1

    Awesome video, please improve audio quality. Thank you

    • @tkorting
      @tkorting  3 ปีที่แล้ว

      Thanks for the feedback, please subscribe to my channel
      You are right about the sound quality. Thanks

  • @Almostafa-ge5qq
    @Almostafa-ge5qq 7 ปีที่แล้ว +1

    Very nice explanation. Thanks. can you give me matlab code to impleminte it ?

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      Thanks for your feedback, please like/share the video and subscribe to my channel.
      please email me (tkorting at gmail) and I send you the code (in octave) regards

  • @abdullahyahya2471
    @abdullahyahya2471 8 ปีที่แล้ว

    I could not find Hough Transform in 3rd edition ... Please reply ... Which edition of the book you used ?

    • @tkorting
      @tkorting  8 ปีที่แล้ว

      thanks for your feedback,
      please like/share and subscribe.
      I have used the 1st edition (in portuguese) from 2000, but to cite in the video, I had to find an english version.
      Regards

  • @zahradehghanitafti7125
    @zahradehghanitafti7125 2 ปีที่แล้ว

    Thank you so much

  • @pamp3657
    @pamp3657 ปีที่แล้ว +1

    muito very bueno 👍

  • @wfpnknw32
    @wfpnknw32 6 ปีที่แล้ว +2

    amazing video, also incredible voice, you sound like javier bardem in skyfall

    • @tkorting
      @tkorting  3 ปีที่แล้ว

      Thanks for the comment, please subscribe to my channel

  • @abhilashvadali457
    @abhilashvadali457 4 ปีที่แล้ว

    You are awesome 💯. thank you so much sir.

  • @xmchughs
    @xmchughs 8 ปีที่แล้ว +1

    Thank you

    • @tkorting
      @tkorting  8 ปีที่แล้ว

      thanks for your feedback
      please like/share the video and subscribe
      regards

  • @bestgamesmagazine8393
    @bestgamesmagazine8393 6 ปีที่แล้ว +1

    great thanks

    • @tkorting
      @tkorting  6 ปีที่แล้ว

      Thanks for the feedback.
      Please subscribe to my channel.
      Regards

  • @samsricatjaidee405
    @samsricatjaidee405 2 ปีที่แล้ว

    Thank you.

  • @UltraDicasBR
    @UltraDicasBR 6 ปีที่แล้ว +1

    Muito bom! Este video me ajudou muito com o meu Master project. A animação ajudou muito na intuição do algoritimo.
    Matheus ~ Sheffield

    • @tkorting
      @tkorting  6 ปีที่แล้ว

      Muito obrigado pelo feedback.
      Não se esqueça de se inscrever no canal.
      Um abraço

  • @chatterjeesrijeet
    @chatterjeesrijeet 6 ปีที่แล้ว +1

    Thanks a lot

    • @tkorting
      @tkorting  6 ปีที่แล้ว

      Many thanks for your positive feedback
      Please like/share/subscribe.
      Regards

  • @rohanmathurful
    @rohanmathurful 4 ปีที่แล้ว +1

    Lovely sir Lovely.

    • @tkorting
      @tkorting  3 ปีที่แล้ว

      Thanks for the feedback, please subscribe to my channel

  • @jamesa862
    @jamesa862 3 ปีที่แล้ว

    Very good video, I like and comment

  • @zukahara9029
    @zukahara9029 6 ปีที่แล้ว +1

    Thanks!

    • @tkorting
      @tkorting  6 ปีที่แล้ว

      Thanks for your feedback.
      Please like and share the video and subscribe to my channel.
      Regards

  • @vamshikrishnavakadani184
    @vamshikrishnavakadani184 7 ปีที่แล้ว +1

    Thank you!
    Can I have the transcript of this please

    • @tkorting
      @tkorting  7 ปีที่แล้ว

      Thanks for your feedback.
      Please like/share the video and subscribe ;)
      If you want to reuse my presentation, follow the link
      prezi.com/73sdixc--qtt/?
      Regards