Machine Vision

1. Machine Vision ENT 273 Hema C.R. Edge Detection Techniques Lecture 6

2. What is an edge? • Edge is a discontinuity in an image • Edge corresponds to a change in image intensity • An edge is also the border between two different regions

3. C A B Image Intensity Image Intensity Variations • Step • Lines • Junction

4. Edge in Images • The edges of an image hold much information about the image. • The edges tell where objects are, their shape and size, and something about their texture. • An edge is where the intensity of an image moves from a low value to a high value or vice versa. • Edge detection is often the first step in image segmentation.

5. Edge Definitions • Edge Point • A point in an image with co-ordinates [i, j] at the location of a significant local intensity change in the image • Edge Fragment • Corresponds to the i and j co-ordinates of an edge and the edge orientation Ф, which may be the gradient angle • Edge Detector • An algorithm that produces a set of edges from an image • Contour • Is a list of edges or the mathematical curve that models the list of edges. • Edge Linking • Is the process of forming an ordered list of edges from an unordered list • Edge Following • Is the process of searching the image to determine contours

6. Edge Detection • Edge detection is an operation to detect significant local changes in the intensity level in an image • The gradient is a measure of change in a function. • Significant changes in gray values of images can be detected by using a discrete approximation to the gradient

7. Gradient • The gradient is defined as the vector • The vectorG[f(x,y)] points in the direction of the maximum rate of increase of the function f(x,y) • Magnitude of the gradient is given as

8. Steps in Edge Detection • Edge detection algorithms consists of three steps • Filtering • Filtering is commonly used to remove noise, however more filtering might result in weak edges • Enhancement • Enhancement is used to emphasize pixels with significant changes in local intensity values , this is done by computing gradient magnitude • Detection • Methods to detect strong edge points is essential, thresholding provides criterion for detection

9. Convolution • Convolution is a mathematical operation which is fundamental to many common image processing operators. • Convolution provides a way of `multiplying together' two arrays of numbers, generally of different sizes, but of the same dimensionality, to produce a third array of numbers of the same dimensionality. • In image processing convolutions are used to implement operators whose output pixel values are simple linear combinations of certain input pixel values. • One of the input arrays is normally just a grey level image. • The second array is usually much smaller, and is also two dimensional and is known as the kernel.

10. Convolution • Each kernel position corresponds to a single output pixel, the value of which is calculated by multiplying together the kernel value and the underlying image pixel value for each of the cells in the kernel, and then adding all these numbers together. • For example value of bottom right pixel is given by

11. Edge Detectors • First Order Derivatives • Roberts Operator • Sobel Operator • Prewitt Operator • Second Order Derivatives • Laplacian Operator • Canny Edge Detector

12. Roberts Operator • Uses a 2 x 2 neighborhood of current pixel • Magnitude of edge is computed as • Its convolution masks are

13. Sobel Operator • The 3 x 3 Sobel operator acts locally on the image and only detects edges at small scales. • The operator is sensitive to high frequency noise in the image and will generate only local edge data instead of recovering the global structure of a boundary. • Smooth transitions in contrast that occur over too large a spatial scale to fit in the 3x 3 window of the Sobel operator will not be detected.

14. Figure (a) Figure (b) Sobel Operator • If an object with a jagged boundary is present, as shown in Figure (a), the Sobel operator will find the edges at each spike and twist of the perimeter as in Figure (b). • Sobel Convolution mask

15. Prewitt Operator • Prewitt is similar to Sobel with a slightly different mask • This operator does not place any emphasis on the pixels closer to the center of the mask • Prewitt convolution mask

16. Roberts Operator Comparison Sobel Operator Prewitt Operator

17. Drawbacks of First Derivative Operators • Computes first derivatives above a threshold. • Hence too many edge points are detected

18. threshold a b Second Derivative Operators • These operators find points that have local maxima in gradient values and consider them as edge points • A peak in first derivative and • A zero crossing in the second derivative 1st and 2nd derivative of an edge illustrated in one dimension.

19. Second Derivative Operators • Laplacian of Gaussian operator • Canny operator

20. Laplacian of Gaussian operator [LoG] • Combines Gaussian filtering with Laplacian for edge detection • Gaussian filters noise due to very small local peaks in first derivative. • Edge detection criteria is presence of a zero crossing in the second derivative with a corresponding large peak in the first derivative • Laplacian convolution mask is used on the second derivative

21. Illustration of LoG Edge using LoG Original image

22. Canny Operator Canny Edge Detection • Canny proposed a new edge detector that is optimal for step edges corrupted by white noise. • The Canny method one of the most powerful edge-detection method is related to three criteria • The detection criterion • Important edge should not be missed • The localization criterion • Distance between the actual and located position of edge should be minimal • The one response • Minimizes multiple responses to single edge.

23. Comparison between Sobel and Canny operators • It uses two different thresholds (to detect strong and weak edges), and includes the weak edges in the output only if they are connected to strong edges. • This method is therefore less likely than the others to be fooled by noise, and more likely to detect true weak edges. Original Image Sobel Edge Canny Edge

24. Machine Vision Edge Detection Techniques End of Lecture 6