IT472 Digital Image Processing Asim Banerjee Faculty Block #1, Room No. 1109 Extn. # 554

IT472 - Digital Image Processing Edge - Types IT472 - Digital Image Processing

Edge – Derivatives of Intensity Profiles IT472 - Digital Image Processing

IT472 - Digital Image Processing Gradient Operators IT472 - Digital Image Processing

IT472 - Digital Image Processing Gradient Operators IT472 - Digital Image Processing

IT472 - Digital Image Processing Gradient Operators IT472 - Digital Image Processing

Gradient Operators - Application IT472 - Digital Image Processing

Gradient Operators - Application b c d e f g Original image Sobel gradient Spatial Gaussian smoothing function Laplacian mask LoG Thresholded LoG Zero crossings. IT472 - Digital Image Processing

IT472 - Digital Image Processing Edge Detection Steps There are two basic steps of edge detection Detection of short linear edge segments (edgels) Aggregation of edgels into extended edges (maybe parametric description) IT472 - Digital Image Processing

IT472 - Digital Image Processing Any Questions? IT472 - Digital Image Processing

Edgel Detection Methods Difference operators Parametric-model matchers IT472 - Digital Image Processing

Edge is Where Change Occurs Change is measured by derivative in 1D Biggest change, derivative has maximum magnitude Or 2nd derivative is zero. IT472 - Digital Image Processing

IT472 - Digital Image Processing Image Gradient (1/2) The gradient of an image: The gradient points in the direction of most rapid change in intensity The gradient direction is given by: how does this relate to the direction of the edge? IT472 - Digital Image Processing

IT472 - Digital Image Processing Image Gradient (2/2) The edge strength is given by the gradient magnitude IT472 - Digital Image Processing

IT472 - Digital Image Processing The Discrete Gradient How can we differentiate a digital image f[x,y]? Option 1: reconstruct a continuous image, then take gradient Option 2: take discrete derivative (finite difference) How would you implement this as a cross-correlation? IT472 - Digital Image Processing

IT472 - Digital Image Processing The Sobel Operator (1/2) Better approximations of the derivatives exist The Sobel operators below are very commonly used -1 1 -2 2 1 2 -1 -2 IT472 - Digital Image Processing

IT472 - Digital Image Processing The Sobel Operator (2/2) The standard definition of the Sobel operator omits the 1/8 term Doesn’t make a difference for edge detection However, the 1/8 term is needed to get the right gradient value, IT472 - Digital Image Processing

IT472 - Digital Image Processing Gradient Operators (a) Roberts’ cross operator (b) 3x3 Prewitt operator (c) Sobel operator (d) 4x4 Prewitt operator IT472 - Digital Image Processing

IT472 - Digital Image Processing Any Questions? IT472 - Digital Image Processing

IT472 - Digital Image Processing Effects Of Noise (1/2) Consider a single row or column of the image Plotting intensity as a function of position gives a signal Where is the edge? IT472 - Digital Image Processing

IT472 - Digital Image Processing Effects Of Noise (2/2) (a) (b) (c) Original image and its edge output Noise added (zero mean and σ = 0.03) and edge output Noise added (zero mean and σ = 0.09) and edge output IT472 - Digital Image Processing

Solution: Smooth First Where is the edge? Look for peaks in IT472 - Digital Image Processing

Derivative Theorem Of Convolution This saves us one operation: IT472 - Digital Image Processing

Laplacian of Gaussian (LoG) Consider Laplacian of Gaussian operator Where is the edge? Zero-crossings of bottom graph IT472 - Digital Image Processing

2D edge detection filters Laplacian of Gaussian Gaussian derivative of Gaussian is the Laplacian operator: IT472 - Digital Image Processing

Optimal Edge Detection: Canny (1/2) Assume: Linear filtering Additive Gaussian noise Edge detector should have: Good Detection. Filter responds to edge, not noise. Good Localization: detected edge near true edge. Single Response: one per edge. IT472 - Digital Image Processing

Optimal Edge Detection: Canny (2/2) Optimal Detector is approximately Derivative of Gaussian. Detection/Localization trade-off More smoothing improves detection And hurts localization. This is what you might guess from above (detect change) + (remove noise) IT472 - Digital Image Processing

Edge Detection Tutorials An interesting tutorial on edge detection is available at http://www.pages.drexel.edu/~weg22/edge.html An interesting tutorial on Canny edge detector is available at http://www.pages.drexel.edu/~weg22/can_tut.html IT472 - Digital Image Processing

The Canny Edge Detector (1/4) original image (Lena) IT472 - Digital Image Processing

The Canny Edge Detector (2/4) norm of the gradient IT472 - Digital Image Processing

The Canny Edge Detector (3/4) thresholding IT472 - Digital Image Processing

The Canny Edge Detector (4/4) thinning (non-maximum suppression) IT472 - Digital Image Processing

Non-maximum Suppression Check if pixel is local maximum along gradient direction requires checking interpolated pixels p and r IT472 - Digital Image Processing

IT472 - Digital Image Processing Predicting the next edge point Assume the marked point is an edge point. Then we construct the tangent to the edge curve (which is normal to the gradient at that point) and use this to predict the next points (here either r or s). (Forsyth & Ponce) IT472 - Digital Image Processing

IT472 - Digital Image Processing Hysteresis Check that maximum value of gradient value is sufficiently large drop-outs? use hysteresis use a high threshold to start edge curves and a low threshold to continue them. IT472 - Digital Image Processing

Effect of  (Gaussian kernel size) Canny with original The choice of depends on desired behavior large detects large scale edges small detects fine features IT472 - Digital Image Processing

Scale Smoothing Eliminates noise edges. Makes edges smoother. Source (Forsyth & Ponce) Smoothing Eliminates noise edges. Makes edges smoother. Removes fine detail. Figures show gradient magnitude of zebra at two different scales IT472 - Digital Image Processing

IT472 - Digital Image Processing Scale Space (1/5) IT472 - Digital Image Processing

IT472 - Digital Image Processing Scale Space (2/5) fine scale high threshold IT472 - Digital Image Processing

IT472 - Digital Image Processing Scale Space (3/5) coarse scale, high threshold IT472 - Digital Image Processing

IT472 - Digital Image Processing Scale Space (4/5) coarse scale low threshold IT472 - Digital Image Processing

IT472 - Digital Image Processing Scale Space (5/5) larger Gaussian filtered signal first derivative peaks Properties of scale space (with Gaussian smoothing) edge position may shift with increasing scale () two edges may merge with increasing scale an edge may not split into two with increasing scale IT472 - Digital Image Processing

Gaussian - Image filter Laplacian of Gaussian Gaussian delta function IT472 - Digital Image Processing

IT472 - Digital Image Processing Any Questions? IT472 - Digital Image Processing

That’s all for now. We shall continue in the next class. IT472 - Digital Image Processing