Stanford CS223B Computer Vision, Winter 2005 Lecture 3 Filters and Features (with Matlab) Sebastian Thrun, Stanford Rick Szeliski, Microsoft Hendrik Dahlkamp, Stanford [with slides by D Forsyth, D. Lowe, M. Polleyfeys, C. Rasmussen, G. Loy, D. Jacobs, J. Rehg, A, Hanson, G. Bradski,…]

Assignment 1 FAQ Compiling projects Taking the images cxcored.dll is the debug version of cxcore.dll, can be compiled from cxcore.dsp Use template cvsample.dsp to get paths right Taking the images Assignment change: out-of-focus images no longer needed Don’t print a border around the chessboard

Assignment 1 FAQ Corner finding How to verify results Supply correct parameters e.g. corner_count<>0 Visualize corner ordering How to verify results Backproject scene corners into image Use common sense: etc

Stanford CS223B Computer Vision, Winter 2005 Lecture 3 Filters and Features (with Matlab) Sebastian Thrun, Stanford Rick Szeliski, Microsoft Hendrik Dahlkamp, Stanford [with slides by D Forsyth, D. Lowe, M. Polleyfeys, C. Rasmussen, G. Loy, D. Jacobs, J. Rehg, A, Hanson, G. Bradski,…]

Today’s Goals Features 101 Linear Filters and Edge Detection Canny Edge Detector

Today’s Question What is a feature? What is an image filter? How can we find corners? How can we find edges?

What is a Feature? Local, meaningful, detectable parts of the image

Features in Computer Vision What is a feature? Location of sudden change Why use features? Information content high Invariant to change of view point, illumination Reduces computational burden

(One Type of) Computer Vision Feature 1 Feature 2 : Feature N Image 2 Image 1 Feature 1 Feature 2 : Feature N Computer Vision Algorithm

Where Features Are Used Calibration Image Segmentation Correspondence in multiple images (stereo, structure from motion) Object detection, classification

What Makes For Good Features? Invariance View point (scale, orientation, translation) Lighting condition Object deformations Partial occlusion Other Characteristics Uniqueness Sufficiently many Tuned to the task

Today’s Goals Features 101 Linear Filters and Edge Detection Canny Edge Detector

What Causes an Edge? Depth discontinuity Surface orientation discontinuity Reflectance discontinuity (i.e., change in surface material properties) Illumination discontinuity (e.g., shadow) Slide credit: Christopher Rasmussen

Quiz: How Can We Find Edges?

Edge Finding 101 im = imread('bridge.jpg'); image(im); figure(2); bw = double(rgb2gray(im)); image(bw); gradkernel = [-1 1]; dx = abs(conv2(bw, gradkernel, 'same')); image(dx); colorbar; colormap gray [dx,dy] = gradient(bw); gradmag = sqrt(dx.^2 + dy.^2); image(gradmag); matlab colorbar colormap(gray(255)) colormap(default)

Edge Finding 101 Example of a linear Filter

What is Image Filtering? Modify the pixels in an image based on some function of a local neighborhood of the pixels 10 5 3 4 1 7 7 Some function

Linear Filtering Linear case is simplest and most useful Replace each pixel with a linear combination of its neighbors. The prescription for the linear combination is called the convolution kernel. 10 5 3 4 1 7 0.5 1.0 7 kernel

Linear Filter = Convolution g11 g11 I(i-1,j-1) I(.) g12 + g12 I(i-1,j) I(.) g13 + g13 I(i-1,j+1) + I(.) g21 g21 I(i,j-1) g22 + g22 I(i,j) I(.) I(.) g23 + g23 I(i,j+1) + I(.) g31 g31 I(i+1,j-1) I(.) g32 + g32 I(i+1,j) I(.) g33 + g33 I(i+1,j+1) f (i,j) =

Linear Filter = Convolution

Filtering Examples

Filtering Examples

Filtering Examples

Image Smoothing With Gaussian figure(3); sigma = 3; width = 3 * sigma; support = -width : width; gauss2D = exp( - (support / sigma).^2 / 2); gauss2D = gauss2D / sum(gauss2D); smooth = conv2(conv2(bw, gauss2D, 'same'), gauss2D', 'same'); image(smooth); colormap(gray(255)); gauss3D = gauss2D' * gauss2D; tic ; smooth = conv2(bw,gauss3D, 'same'); toc

Smoothing With Gaussian Averaging Gaussian Slide credit: Marc Pollefeys

Smoothing Reduces Noise The effects of smoothing Each row shows smoothing with gaussians of different width; each column shows different realizations of an image of gaussian noise. Slide credit: Marc Pollefeys

Example of Blurring Image Blurred Image - =

Edge Detection With Smoothed Images figure(4); [dx,dy] = gradient(smooth); gradmag = sqrt(dx.^2 + dy.^2); gmax = max(max(gradmag)); imshow(gradmag); colormap(gray(gmax));

Scale Increased smoothing: Eliminates noise edges. Makes edges smoother and thicker. Removes fine detail.

The Edge Normal

Displaying the Edge Normal figure(5); hold on; image(smooth); colormap(gray(255)); [m,n] = size(gradmag); edges = (gradmag > 0.3 * gmax); inds = find(edges); [posx,posy] = meshgrid(1:n,1:m); posx2=posx(inds); posy2=posy(inds); gm2= gradmag(inds); sintheta = dx(inds) ./ gm2; costheta = - dy(inds) ./ gm2; quiver(posx2,posy2, gm2 .* sintheta / 10, -gm2 .* costheta / 10,0); hold off;

Separable Kernels

Combining Kernels / Convolutions 0.0030 0.0133 0.0219 0.0133 0.0030 0.0133 0.0596 0.0983 0.0596 0.0133 0.0219 0.0983 0.1621 0.0983 0.0219

Effect of Smoothing Radius 1 pixel 3 pixels 7 pixels

Robert’s Cross Operator 1 0 0 -1 0 1 -1 0 + S = [ I(x, y) - I(x+1, y+1) ]2 + [ I(x, y+1) - I(x+1, y) ]2 or S = | I(x, y) - I(x+1, y+1) | + | I(x, y+1) - I(x+1, y) |

Sobel Operator -1 -2 -1 0 0 0 1 2 1 -1 0 1 -2 0 2 S1= S2 = -1 -2 -1 0 0 0 1 2 1 -1 0 1 -2 0 2 S1= S2 = Edge Magnitude = Edge Direction = S1 + S1 2 tan-1 S1 S2

The Sobel Kernel, Explained Sobel kernel is separable! Averaging done parallel to edge

Sobel Edge Detector figure(6) edge(bw, 'sobel')

Robinson Compass Masks -1 0 1 -2 0 2 0 1 2 -1 0 1 -2 -1 0 1 2 1 0 0 0 -1 -2 -1 2 1 0 1 0 -1 0 -1 -2 2 0 -2 1 1 -1 -1 0 -1

Claim Your Own Kernel! Frei & Chen

Comparison (by Allan Hanson) Analysis based on a step edge inclined at an angle q (relative to y-axis) through center of window. Robinson/Sobel: true edge contrast less than 1.6% different from that computed by the operator. Error in edge direction Robinson/Sobel: less than 1.5 degrees error Prewitt: less than 7.5 degrees error Summary Typically, 3 x 3 gradient operators perform better than 2 x 2. Prewitt2 and Sobel perform better than any of the other 3x3 gradient estimation operators. In low signal to noise ratio situations, gradient estimation operators of size larger than 3 x 3 have improved performance. In large masks, weighting by distance from the central pixel is beneficial.

Today’s Goals Features 101 Linear Filters and Edge Detection Canny Edge Detector

Canny Edge Detector figure(7) edge(bw, 'canny')

Canny Edge Detection Steps: Apply derivative of Gaussian Non-maximum suppression Thin multi-pixel wide “ridges” down to single pixel width Linking and thresholding Low, high edge-strength thresholds Accept all edges over low threshold that are connected to edge over high threshold

Non-Maximum Supression Non-maximum suppression: Select the single maximum point across the width of an edge.

Linking to the Next Edge Point Assume the marked point is an edge point. Take the normal to the gradient at that point and use this to predict continuation points (either r or s).

Edge Hysteresis Hysteresis: A lag or momentum factor Idea: Maintain two thresholds khigh and klow Use khigh to find strong edges to start edge chain Use klow to find weak edges which continue edge chain Typical ratio of thresholds is roughly khigh / klow = 2

Canny Edge Detection (Example) gap is gone Strong + connected weak edges Original image Strong edges only Weak edges courtesy of G. Loy

Canny Edge Detection (Example) Using Matlab with default thresholds

Application: Road Finding (add roadrunner video here)

Corner Effects

Today’s Goals Features 101 Linear Filters and Edge Detection Canny Edge Detector