L A Gran

Instituto Columbia SC

Erich theissen 9ª #13 1,31 2013 Edge Detection Techniques: Evaluations and Comparisons

Robotics 2 Mr.victor Salazar

Since different edge detectors work better under different conditions, it would be ideal to have an algorithm that makes use of multiple edge detectors, applying each one when the scene conditions are most ideal for its method of detection. In order tocreate this system, you must first know which edge detectors perform better under which conditions. That is the goal of our project. We tested four edge detectors that use different methods for detecting edges and compared their results under a variety of situations to determine which detector was preferable under different sets of conditions. This data could then be used to create amulti-edge-detector system, which analyzes the scene and runs the edge detector best suited for the current set of data. For one of the edge detectors we considered two different ways of implementation, one using intensity only and the other using color information. The Canny edge detector is widely considered to be the standard edge detection algorithm in the industry. It was first created by John Canny forhis Master’s thesis at MIT in 1983 [2], and still outperforms many of the newer algorithms that have been developed. Canny saw the edge detection problem as a signal processing optimization problem, so he developed an objective function to be optimized [2]. The solution to this problem was a rather complex exponential function, but Canny found several ways to approximate and optimize theedge-searching problem. The steps in the Canny edge detector are as follows: 1. Smooth the image with a two dimensional Gaussian. In most cases the computation of a two dimensional Gaussian is costly, so it is approximated by two one dimensional Gaussians, one in the x direction and the other in the y direction. 2. Take the gradient of the image. This shows changes in intensity, which indicates thepresence of edges. This actually gives two results, the gradient in the x direction and the gradient in the y direction. 3. Non-maximal suppression. Edges will occur at points the where the gradient is at a maximum. Therefore, all points not at a maximum should be suppressed. In order to do this, the magnitude and direction of the gradient is computed at each pixel. Then for each pixel check if themagnitude of the gradient is greater at one pixel's distance away in either the positive or the negative direction perpendicular to the gradient. If the pixel is not greater than both, suppress it. This edge detector is fundamentally different than many of the modern edge detectors derived from Canny’s original. It does not rely on the gradient or Gaussian smoothing. It takes advantage of both localand global thresholding to find edges. Unlike other edge detectors, it converts a window of pixels into a binary pattern based on a local threshold, and then applies masks to determine if an edge exists at a certain point or not. By calculating the threshold on a per pixel basis, the edge detector should be less sensitive to variations in lighting throughout the picture. It does not rely on blurringto reduce noise

in the image. It instead looks at the variance on a local level. The algorithm is as follows: 1. Apply a local threshold to a 3x3 window of the image. Because this is a local threshold, it is recalculated each time the window is moved. The threshold value is calculated as the mean of the 9 intensity values of the pixels in the window minus some small tolerance value. If apixel has an intensity value greater than this threshold, it is set to a 1. If a pixel has an intensity value less than this threshold, it is set to a 0. This gives a binary pattern of the 3x3 window. Another approach to edge detection using color information is simply to extend a traditional intensity based edge detector into the color space. This method seeks to take advantage of the known...