What is different between Euclidean distance and the Geodesic distance?












2












$begingroup$


We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said





Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance





This is example



enter image description here










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    2












    $begingroup$


    We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said





    Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance





    This is example



    enter image description here










    share|improve this question







    New contributor




    Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







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      2












      2








      2





      $begingroup$


      We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said





      Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance





      This is example



      enter image description here










      share|improve this question







      New contributor




      Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said





      Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance





      This is example



      enter image description here







      image-processing






      share|improve this question







      New contributor




      Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question







      New contributor




      Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question






      New contributor




      Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 8 hours ago









      Moon LeeMoon Lee

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      New contributor




      Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Moon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






















          1 Answer
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          $begingroup$

          Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.



          That's why the distances at the bottom left of the figure are so different.



          Example of difference






          share|improve this answer











          $endgroup$













          • $begingroup$
            Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
            $endgroup$
            – Moon Lee
            8 hours ago










          • $begingroup$
            @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
            $endgroup$
            – Peter K.
            7 hours ago










          • $begingroup$
            K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
            $endgroup$
            – Moon Lee
            7 hours ago










          • $begingroup$
            @MoonLee: See this answer on SO for some information about how to implement it.
            $endgroup$
            – Peter K.
            7 hours ago











          Your Answer





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          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          5












          $begingroup$

          Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.



          That's why the distances at the bottom left of the figure are so different.



          Example of difference






          share|improve this answer











          $endgroup$













          • $begingroup$
            Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
            $endgroup$
            – Moon Lee
            8 hours ago










          • $begingroup$
            @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
            $endgroup$
            – Peter K.
            7 hours ago










          • $begingroup$
            K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
            $endgroup$
            – Moon Lee
            7 hours ago










          • $begingroup$
            @MoonLee: See this answer on SO for some information about how to implement it.
            $endgroup$
            – Peter K.
            7 hours ago
















          5












          $begingroup$

          Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.



          That's why the distances at the bottom left of the figure are so different.



          Example of difference






          share|improve this answer











          $endgroup$













          • $begingroup$
            Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
            $endgroup$
            – Moon Lee
            8 hours ago










          • $begingroup$
            @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
            $endgroup$
            – Peter K.
            7 hours ago










          • $begingroup$
            K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
            $endgroup$
            – Moon Lee
            7 hours ago










          • $begingroup$
            @MoonLee: See this answer on SO for some information about how to implement it.
            $endgroup$
            – Peter K.
            7 hours ago














          5












          5








          5





          $begingroup$

          Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.



          That's why the distances at the bottom left of the figure are so different.



          Example of difference






          share|improve this answer











          $endgroup$



          Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.



          That's why the distances at the bottom left of the figure are so different.



          Example of difference







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 8 hours ago

























          answered 8 hours ago









          Peter K.Peter K.

          17k83060




          17k83060












          • $begingroup$
            Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
            $endgroup$
            – Moon Lee
            8 hours ago










          • $begingroup$
            @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
            $endgroup$
            – Peter K.
            7 hours ago










          • $begingroup$
            K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
            $endgroup$
            – Moon Lee
            7 hours ago










          • $begingroup$
            @MoonLee: See this answer on SO for some information about how to implement it.
            $endgroup$
            – Peter K.
            7 hours ago


















          • $begingroup$
            Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
            $endgroup$
            – Moon Lee
            8 hours ago










          • $begingroup$
            @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
            $endgroup$
            – Peter K.
            7 hours ago










          • $begingroup$
            K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
            $endgroup$
            – Moon Lee
            7 hours ago










          • $begingroup$
            @MoonLee: See this answer on SO for some information about how to implement it.
            $endgroup$
            – Peter K.
            7 hours ago
















          $begingroup$
          Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
          $endgroup$
          – Moon Lee
          8 hours ago




          $begingroup$
          Great explanation. I cannot upvote your answer because i have not enough score. Could you show to me some math function of geodesic distance? Does it related to gradient image eq. 2? researchgate.net/publication/…
          $endgroup$
          – Moon Lee
          8 hours ago












          $begingroup$
          @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
          $endgroup$
          – Peter K.
          7 hours ago




          $begingroup$
          @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance.
          $endgroup$
          – Peter K.
          7 hours ago












          $begingroup$
          K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
          $endgroup$
          – Moon Lee
          7 hours ago




          $begingroup$
          K: I have implemented it but it does not looks likes geodesic distance. It takes image information in count.
          $endgroup$
          – Moon Lee
          7 hours ago












          $begingroup$
          @MoonLee: See this answer on SO for some information about how to implement it.
          $endgroup$
          – Peter K.
          7 hours ago




          $begingroup$
          @MoonLee: See this answer on SO for some information about how to implement it.
          $endgroup$
          – Peter K.
          7 hours ago










          Moon Lee is a new contributor. Be nice, and check out our Code of Conduct.










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          Moon Lee is a new contributor. Be nice, and check out our Code of Conduct.
















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