MATLAB Script - Midterm Exam | Computer Vision | CAP 5415, Exams of Computer Science

Download MATLAB Script - Midterm Exam | Computer Vision | CAP 5415 and more Exams Computer Science in PDF only on Docsity! Subhabrata Bhattacharya CAP 5415 MIDTERM 1. In this problem we are required to create an edge detector and train it using the various edge patches we have obtained from the Berkeley Segmentation Database [1]. We begin by creating oriented first and second order derivative of the Gaussian 2D filter for different scales (σ = 1, 2) and orientations measures (θ = π/4, π/2, 3π/4). In addition to these 12 Gaussian filters we also create another filter that is a square matrix of all 1s. Next we convolve each of training image patches (with edges and non-edges) obtained from [1] to generate responses. These responses are stored in a 13 dimensional feature vector. 1 clear all; 2 close all; 3 clc; 4 5 basedir = '/home/subh/courses/cap5415/ps3/edge examples subset/'; 6 etrain = 'EDGE TRAIN/'; 7 netrain = 'NOT EDGE TRAIN/'; 8 9 dirinfo = [basedir etrain]; 10 fmetrain = buildFeatureMatrix (dirinfo, '*.png'); 11 12 dirinfo = [basedir netrain]; 13 fmnetrain = buildFeatureMatrix (dirinfo, '*.png'); 14 15 pts = [fmetrain; fmnetrain]; 16 labels = [fmetrain(:,13); −fmnetrain(: ,13)]; 17 save('PtsLblsWts.mat','pts','labels'); Listing 1: Matlab script for Problem 1 1 function fmatrix = buildFeatureMatrix (dirinfo, files) 2 % This function creates a feature matrix for all files in the training 3 % directory. number of theta and sigma could be increased/decreased to 4 % increase the size of the feature matrix 5 pi = 3.1415; 6 theta = [pi/4 pi/2 3*(pi/4)]; 7 sigma = [1 2]; 8 9 flidx = dir([dirinfo files]); 10 nImg = length(flidx); 11 12 for icnt = 1:nImg 13 flname = [dirinfo flidx(icnt).name]; 14 fvector = computeFeatureVector(flname, theta, sigma); 15 fmatrix(icnt,:) = fvector(:); 16 end 17 return; Listing 2: Matlab script for Building Feature Matrices from the feature vectors 1 function fvector = computeFeatureVector(flname, theta, sigma) 2 % This function computes a feature vector of 12 dimensions for an image 3 % patch. For each scale value and orientation value, the response of the 4 % given image patch to both first and second directional derivative of 5 % Gaussian filters is computed. flname is the absolute path of the file 6 % containing the image patch. 7 8 % img is 13 x 13 matrix 9 img = imread (flname); 10 img = im2double (img); 11 fvector = ones(1,2* length(theta) * length(sigma) +1); 12 % Counting features 13 lcnt = 1; 14 % Create feature vector for each image 15 for jcnt = 1:length(theta) % for 3 theta (orientation) 16 for kcnt = 1:length(sigma) % for 2 sigma (scales) 17 [x y] = meshgrid(−6: 6); % Create a 13 x 13 template 18 19 var = sigma(kcnt)ˆ2; 20 tcos = cos(theta(jcnt)); 1 Subhabrata Bhattacharya CAP 5415 MIDTERM 21 tsin = sin(theta(jcnt)); 22 gfexp = exp(−(x.ˆ2 + y.ˆ2)/(2*var)); 23 24 % Computing the first derivative of Gaussian wrt theta 25 % f1 = (gfexp./var).*(x.*tcos + y.*tsin); 26 f1 = 2.*gfexp.*(x.*tcos + y.*tsin); 27 f1 = f1 /sum(abs(f1(:))); 28 29 % Computing the second derivative of Gaussian wrt theta 30 f2 = (gfexp./var).*((2*(x.ˆ2) − var) + 2*(x.*y)*tcos*tsin +(2*(y.ˆ2) − var)); 31 f2 = f2/ sum(abs(f2(:))); 32 33 % Convolve filters f1 and f2 with each image patch and store it in a 34 % feature vector 35 feat = conv2 (img, f1, 'valid'); 36 fvector(lcnt) = abs(feat(:)); 37 lcnt = lcnt + 1; 38 feat = conv2 (img, f2, 'valid'); 39 fvector(lcnt) = abs(feat(:)); 40 lcnt = lcnt + 1; 41 end 42 end 43 return; Listing 3: Matlab script for Computing Feature Vector from the edge and non edge Patches 2. Here we use the inputs from the previous problem to test our edge detector. The objective of this exercise is to run the edge detection program over a set of image patches that have edge and non-edge pixels. We evaluate how clearly our edge detection program identifies an image and how often the program detects a non-edge portion in an image patch as a patch containing edge. We use a logistic regression function to find out how every filter fairs in determining edges in image patches. Based on each of these filter’s performance in detecting an edge, they are assigned weights by the logistic regression function. A Receiver Operating Characteristic curve is then plotted to visually interpret the rate of detection of an edge in an image patch against that of misinterpretation of a non-edge pixel as an edge pixel in an image patch. 1 clear all; 2 close all; 3 clc; 4 5 basedir = '/home/subh/courses/cap5415/ps3/edge examples subset/'; 6 etest = 'EDGE TEST/'; 7 netest = 'NOT EDGE TEST/'; 8 % Obtain Data for learning 9 load('PtsLblsWts.mat'); 10 11 % Determining the weights by performing logistic regression 12 weights = logisticRegression(pts, labels); 13 save('PtsLblsWts.mat', 'weights'); 14 15 % Determine feature vector from the test images that have edges 16 dirinfo = [basedir etest]; 17 fmetest = buildFeatureMatrix (dirinfo, '*.png'); 18 19 % For non edges 20 dirinfo = [basedir netest]; 21 fmnetest = buildFeatureMatrix (dirinfo, '*.png'); 22 23 % These would be inputs to the function produceROCInputs which would return 24 % the probability of detection and probability of false alarm for each 25 % image patch. 26 icnt = 1; 27 for thd = 0.001: 0.005: 0.99 28 pd(icnt) = produceROCInputs(fmetest, weights/1000, thd); 29 pfa(icnt) = produceROCInputs(fmnetest, weights/1000, thd); 30 icnt = icnt + 1; 31 end 32 33 plot(pfa, pd); 34 title('Receiver Operating Characteristic Curve'); 2 Subhabrata Bhattacharya CAP 5415 MIDTERM 5 sigma = [1 2]; 6 7 % load the image 8 img = im2double(rgb2gray(imread(flname))); 9 [width height] = size(img); 10 11 lcnt = 1; 12 for jcnt = 1:length(theta) % for 3 theta (orientation) 13 for kcnt = 1:length(sigma) % for 2 sigma (scales) 14 [x y] = meshgrid(−6: 6); % Create a 13 x 13 template 15 16 var = sigma(kcnt)ˆ2; 17 tcos = cos(theta(jcnt)); 18 tsin = sin(theta(jcnt)); 19 gfexp = 2*exp(−(x.ˆ2 + y.ˆ2)); 20 21 % Computing the first derivative of Gaussian wrt theta 22 f1 = (gfexp./var).*(x.*tcos + y.*tsin); 23 f1 = f1/sum(abs(f1(:))); 24 25 % Computing the second derivative of Gaussian wrt theta 26 f2 = (gfexp./var).*((2*(x.ˆ2) − var) + 2*(x.*y)*tcos*tsin +(2*(y.ˆ2) − var)); 27 f2 = f2/sum(abs(f2(:))); 28 29 % Convolve filters f1 and f2 with each image patch and store it in a 30 % feature vector 31 feat = conv2 (img, f1, 'same'); 32 resp(:,lcnt) = abs(feat(:)); 33 lcnt = lcnt + 1; 34 feat = conv2 (img, f2, 'same'); 35 resp(:,lcnt) = abs(feat(:)); 36 lcnt = lcnt + 1; 37 end 38 end 39 %feat = conv2 (img, ones(13,13), 'same'); 40 %resp(:,lcnt) = abs(feat(:)); 41 42 [fsize nfilter] = size(resp); 43 44 % Responses generated, now get the edge 45 % Create a blank template for the output 46 tplt = 255*ones(size(img(:))); 47 % Compare likelihood of each filter coming up with an edge across a threshold 48 Sx = zeros(fsize,1); 49 for jcnt =1: nfilter 50 x = resp(:,jcnt); 51 Sx = Sx + weights(jcnt).*x; 52 end 53 p = 1./(1+ exp(−Sx)); 54 for icnt = 1:fsize 55 if (p(icnt,1) ≥ thd) 56 tplt(icnt,1) = 0; 57 end 58 end 59 edgeImg = reshape(tplt, [width height]); 60 return Listing 10: Matlab script for Detecting Edge inside an image 1 function CompareResults(filename, outputname) 2 seg = readSeg(filename); 3 bmap = seg2bmap(seg); 4 bmap = xor(bmap, ones(size(bmap))); 5 figure;imshow(uint8(bmap), []); 6 imwrite(bmap, outputname); 7 return; Listing 11: Matlab script for Displaying a Human Segmented Image 5 Subhabrata Bhattacharya CAP 5415 MIDTERM 4. We need to derive the derivative of log-likelihood of the following expression P [t = k|x] = e −θk.x∑M j=1 e −θj .x The likelihood of all xi in x, being correctly labeled ki in k is given by: N∏ i=1 P [ti = ki|xi] = N∏ i=1 e−θki .xi∑M j=1 e −θj .xi Therefore the Log Likelihood is given by: L = log ( N∏ i=1 P [ti = ki|xi] ) = N∑ i=1 log ( e−θki .xi∑M j=1 e −θj .xi ) (1) The derivative of the Log-likelihood wrt θj,k (which is the kth entry in θj) could be obtained by partially differen- tiating 1 wrt θj,k ∂L ∂θj,k = N∑ i=1 ∂ ∂θj,k log(e−θki .xi)− log( M∑ j=1 e−θj .xi)  = − N∑ i=1 ∂ ∂θj,k log( M∑ j=1 e−θj .xi) = xk N∑ i=1 e−θj .xi∑M j=1 e −θj .xi (xk being the kth value of x) References [1] D. Martin and C. Fowlkes and D. Tal and J. Malik, Database of Human Segmented Natural Images and its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistic Proc. 8th Int’l Conf. Computer Vision, 2001, July, Vol 2 pp 416–423. 6 Subhabrata Bhattacharya CAP 5415 MIDTERM Figure 2: Comparison of Edge Detection Results: Leftmost column is the original image, Rightmost show the result obtained by Human Detection and the central column show the results obtained by the edge detector implemented by us 7