Basics of Linear Hough Transform
- 2. Introduction • The Hough transform is a feature Extraction technique used in image analysis, computer vision and digital image processing . • It is a technique to isolate the curves of a given shapes in a given image. • Classical Hough Transform can locate regular curves like straight lines, circles, parabolas, ellipses, etc.
- 3. • Every edge pixel Is a point that votes for all shapes that passes through it. • This voting procedure is carried out in a Parameter space. • Parameter space is a K-dimensional Histogram.
- 4. Hough Transform for Straight line A straight line can be mathematically represented as: Y = ax + b Where, a is slope and b is a intercept
- 5. Image Space Parameter space Y = ax + b b = -ax + y
- 6. Point Line Line Point Image Space Parameter space
- 8. Line Detection Algorithm • Step-1:- Quantize the parameter space • Step-2:- Create accumulator array • Step-3:- Set all value by zero • Step-4:- For each edge in (xi, yi), P(a, b) = P (a, b) + 1 If (a, b) lies on line: -mxi + yi • Step-5:- Find local maxima in P(a, b) xi, yi Image space P (a, b) Maxima xi, yi
- 9. Applications • Detection of lines • Fill the edges • Linking the edge points • To Find out Points are collinear • Find aligned points in image that create lines
- 12. • We get our (a, b) = (1, 1) • Our line of equation is y = ax + b • By substitute values we will get, y = x + 1 This line in collinear that has values (1,2), (2,3), (3,4), (4,5) on it. Hence all the points lies on the same line they are called collinear.
- 13. Problem in Hough Transform • For the line of equation Y = ax + b The slope a lies between – ∞ ≤ 𝑎 ≤ +∞ Which creates problem in the case of quantizing vertical line. It ends up with massive amount of data and large accumulator to store it. In that case this representation fails completely.
- 14. Solution • There is one more representation that can be used 𝑥𝑠𝑖𝑛𝜃 + 𝑦𝑐𝑜𝑠𝜃 + 𝜌 = 0 here 𝜃 is finite: 0 ≤ 𝜃 ≤ 𝜋 𝜌 is a finite
- 15. Advantages of Hough Transform • Tolerant to the gaps in the edges • Not affected by noise • Not affected by occlusion in image Ending..