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File:Test deux points sur grand axe ellipse.svg

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Français : Une image contient une ellipse (en noir). Pour détecter cette ellipse, on prend un couple de points (pixels) (A1, A2) de l'image et on fait l'hypothèse qu'ils sont sur le grand axe, donc que A1A2 = 2a et que le centre de l'ellipse est le milieu de [A1A2].

Pour tester cette hypothèse, on prend un point M de l'image, ce qui détermine le demi petit-axe b ; ces points sont nécessairement dans le disque grisé. La transformée de Hough se fait donc avec un seul paramètre, b, pour un couple (A1, A2) donné.

Dans le cas présent, chaque cellule b de la matrice d'accumulation ne contient qu'au plus deux occurrences, l'hypothèse « [A1A2] est le grand axe » est donc rejetée.
English: An image shows an ellipse (in black). To detect this ellipse, we take a couple of points (pixels) (A1, A2) in the picture and we assume they are on the major axis, thus A1A2 = 2a and the center of the ellipse is the middle of [A1A2].

To test this hypothesis, we considere a point M in the picture, this sets the half-lenght b of the minor axis; these points are in the grey disk. The Hough transform involves only one parameter, b, for each couple (A1, A2).

In the case shown here, each b cell of the accumulation matrix only holds two occurrences or less, the hypothesis “[A1A2] is the major axis” is thus rejected.
Date
Source Own work, from Y. Xie and Q. Ji, “A New Efficient Ellipse Detection Method”, in International Conference on Pattern Recognition, 2002
Author Cdang


 
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