Analysis Of The Hough Transform

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*Lunagariya, Jaydeep
CECS-553 Machine Vision
Spring 2014
Project Description
Many computer vision applications provide vast knowledge about the line in an image. Manually extraction of the line information from an image can be very exhausting and time-consuming; especially there are many lines in the image. An automatic method is desirable, but it is not as trivial as edge detection since if any, one has to detect which edge points belongs to which line. The Hough-transform is more preferable to make this separation possible and is the method I have used in my program for line detection.
In this project, issues regarding the Hough Transform for line detection are considered. The first several sections deal with theory regarding the Hough transform, then the final section discusses an implementation of the Hough transform for line detection and gives resulted images. The program, images, and figures for this project are implemented using the Matlab.
Project Background: Theory of the Hough Transform
The Hough transform (HT) is a powerful global method for detecting edges. It transforms between the Cartesian space and a parameter space in which a straight line (or other boundary formulation) can be defined. Line detection using Hough Transform is point‐line duality. Let’s assume the case where we have straight lines in an image. We first note that for every point (x_i,y_i) in that image, all the straight lines passing through that point satisfy Eq. (1) for varying values of line slope and intercept (m, c) , see Fig 1. y_i = mx_i + c Eq. (1)
Fig 1: Lines through a point in the Fig 2: The (m, c) domain.
Cartesian domain.
Now if we reverse our variables and look instead at the values of (m, c) as a function of the image poin...

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... Input Image (B2bomber.bmp) Fig 7: Converted Gray Image
Compute the threshold value of an input image.
The histogram of an input image is computed for selection of threshold value of a converted gray image. MATLABs ‘imhist(…)’ is the function that is used generate histogram. The appropriate threshold value has been selected, which is, then, applied to an image to threshold itself. Fig 8 and Fig 9 show an example of such images.

Fig 8: Histogram of the Gray Image Fig 9: Image after Thresholding
Apply edge detection to a selected image using different gradient kernels (Sobel, Prewitt, and Roberts), or other methods such as: Canny or zero crossings.
The MATALBs ‘edge(… )’ function is used to detect edges in the input image with various options for an argument (e.g. ‘Sobel’, ‘Canny’, ‘Prewitt’, ‘zerocross’). An example of detected edges is shown in Fig 10.

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