# Hough Transform In Image Processing

Hough transform: a way of finding edge points in an image that lie along a straight line or curve.

### Introduction of Hugh Transform

- The Hough transform (HT) can be used to detect lines, circles or other parametric curves
- It was introduced in 1962 (Hough 1962) and first used to find lines in images a decade later (Duda 1972).
- The goal is to find the location of lines in images.
- This problem could be solved by e g Morphology and a linear • This problem could be solved by e.g. Morphology and a linear structuring element, or by correlation.
- Hough transform can detect lines, circles and other structures if their parametric equation is known.
- It can give robust detection under noise and partial occlusion • It can give robust detection under noise and partial occlusion.

## Haugh Transform Algorithm

- Consider one valid edge point (xi,yi) in xy-plane & the equation of line passing through it can be,

- As it is a point, infinite lines will be passing through it given by above equation & different values of a & b.
- We can write this equation as,

which gives us a line in ab-plane(parameter plane) passing through fixed pair (xi,yi).

- Next, we will consider 2nd valid edge point (xj,yj) and find out equation in parameter plane. It will be,

- If these 2 points lies on a st line in xy-plane, then the two lines in parameter plane will intersect at point(a’,b’) where, a’ is slope and b’ is intercept of line passing through 2 points (xi,yi) and (xj,yj) in xy-plane.