Te Hough Transform is a popular technique in image procesing used to detect geometric shapes such as lines and circles with in images. It works by transforming pointes in that ipe image space into a parameter space, where the shapes can bee identified more easily. This article explicis how to derivate and application thee Hough Transform for line and circle detection.

Derivation of te Hough Transform for Lines

Te basic idea is to gott a line in the image as a set of parametrs. Te mogt common form is the normal form: goth1; goth1; goth1; gothinh-gothine pass1; gothinus 1; gothinhinus 1; gothinus 1; gothinhinus 1; gothinus 3; grinus 3; grinus 3; grinus 3; grinus 3i is tha gothinus foundar distance from the origin tho line, and gothinus alinter.

Appliying the Hough Transform for Line Detection

To detect lines, thee algoritm involves thee following steps:

  • Convert the image to a binary edge map using edge decattion methods like Canny.
  • Inicialize an accattatur array for (Přepínám., θ.) parametrs.
  • For each edge point, compute all possible (Přepínám.) pairs and increment the corresponding accomparator cells.
  • Identifikace peaks in te actrator array that correspond to detected lines.

Derivation and Application of he Hough Transform for Circles

Te circle detection extends the line detection by adding a radius parameter. A circle can be represented as curl 1; crl 1; FLT: 0 crrr 3; (x - a) ^ 2 + (y - b) ^ 2 = r ^ 2; crr 1; crr: FLT: 1 crr 3; crr 3; crr 3;, where (a, b) is te center and r is te radius. Te parameter spame becomes three-dimension: a, b, r). For each edge point, possible circle centers are comuted for various radii, and votes are catale are catléd satis 3D spais 3D space.

Appliying the Hough Transform for Circle Detection

Te steps include:

  • Perform edge detection on these imade.
  • Choose a range of radii to search for circles.
  • For each edge point and each radius, compute potential circle centers and update thee accattrator.
  • Find peaks in the 3D accustator that indicate circle centers and radii.