Mathematical Theory
To best explain our algorithm, we first need to explain some of the key mathematical tools that we used.
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Through our research, we discovered that there are three key features that are found in almost every lane detection system. These include:
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Gaussian Blur
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Hough Transform
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A gradient intensity calculator (Roberts, Sobel, Prewitt)
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Gaussian Blur
The Gaussian Blur is a method of blurring and smoothing an image by convolving that image with a Gaussian function. This acts as a low-pass filter, and reduces noise by eliminating higher frequency components.
Images from Wikipedia.com
Hough Transform
The Hough Transform is a transform used to eliminate noise in an image. Often times in images there may be a line detectable by the human eye, but up close there may be imperfections, such as missing pixels, that can affect the ability to accurately detect lanes.
The Hough Transform approximates these lines by first representing the lines as a parametric representations and then using a voting algorithm to decide which line is the line of best fit. This can be seen in the images below where the r and theta values for all possible lines at each point and evaluated and compared. The most similar r and theta would be the output line of the transform.
Image from Wikipedia.com
Roberts, Sobel, and Prewitt
Roberts, Sobel, and Prewitt are all gradient intensity calculators. Each one of these has a different kernel, which can be seen below. These kernels are convolved with the original image. In our work we tried all three filters and found that for our purposes the Roberts was the most effective in our algorithms.
