Line Detection
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The document describes how to detect lines in an image using the Hough transform. It explains that the Hough transform represents lines in a polar coordinate system and works by plotting the curves for each edge point and finding the intersections, which indicate collinear points that make up a line. It then outlines the steps to apply this technique: 1) load an image, 2) optionally convert to grayscale and blur, 3) perform edge detection using Canny, and 4) detect lines using Hough transform by finding intersections above a threshold.
Line Detection
- 1. Individual Assignment 11. Line Detection of an Image MCS3108 – IMAGE PROCESSING AND VISION U. V Vandebona 13440722
- 2. Tools and Techniques Used Java OpenCV HoughLinesP Function Canny Operation Gaussian Smoothing
- 3. Hough Line Transform It is a transformation technique used to detect straight lines. To apply the Transform, first an edge detection pre- processing is desirable.
- 4. Line in an Image expressed as… Cartesian coordinate system Polar coordinate system For Hough Transforms, we will express lines in the Polar system
- 5. How it Works θ r x y Arranging the terms:
- 6. How it Works… In general, for each point (x0, y0) , we can define the family of lines that goes through that point as: Meaning that each pair (rθ,θ ) represents each line that passes by (x0, y0)
- 7. How it Works… If for a given (x0, y0) we plot the family of lines that goes through it, we get a sine wave. For instance, for x0 = 8 and y0 = 6 and we get the following plot (in a plane coordinates with θ and r) We consider only points such that r > 0 and 0 < θ < 2π
- 8. How it Works… We can do the same operation above for all the points in an image. If the curves of two different points intersect in the plane coordinates with θ and r, that means that both points belong to a same line. For instance, following with the example above and drawing the plot for two more points: x1 = 9, y1 = 4 and x2 = 12, y2 = 3, we get:
- 9. The three plots intersect in one single point (0.925, 9.6), these coordinates are the parameters ( θ, r) or the line in which (x0, y0) , (x1, y1) and (x2, y2) lay.
- 10. So it means… A line can be detected by finding the number of intersections between curves. The more curves intersecting means that the line represented by that intersection have more points. In general, we can define a threshold of the minimum number of intersections needed to detect a line.
- 11. Hough Line Transform It keeps track of the intersection between curves of every point in the image. If the number of intersections is above some threshold, then it declares it as a line with the parameters ( θ, rθ) of the intersection point.
- 12. Application 1. Loads an image 2. (Optional) Convert to grayscale 3. (Optional) Blur Image Gaussian Smoothening 4. Edge Detection Canny Operation 5. Line Detection Hough Line Transformation
- 13. Application