REU Week 1 Presented by Christina Peterson

Edge Detection Sobel ◦ Convolve image with derivative masks:  x:  y: ◦ Calculate gradient magnitude ◦ Apply threshold

Edge Detection Marr Hildreth ◦ Apply Laplacian of Gaussian to an image ◦ Find zero crossings  {+,-}, {+, 0, -}, {-, +}, {-, 0, +} ◦ Mark edges  Apply threshold to slope of zero-crossings

Edge Detection Canny ◦ Convolve image with first derivative of gaussian ◦ Find magnitude of gradient and orientation ◦ Apply non-max suppression  For each pixel, check if it is a local max by comparing it to neighbor pixels along normal direction to an edge ◦ Apply hysteria thresholding

Canny Example Original Image Canny Output

Harris Corner Detector Implemented Harris Corner Detector ◦ 1. x and y derivatives  Ix=conv2(double(I), maskx, ‘same’)  Iy=conv2(double(I), masky, ‘same’) ◦ 2. products of derivatives  Ix2=Ix.*Ix  Iy2=Iy.*Iy  Ixy=Ix.*Iy ◦ 3. sums of products of derivatives  Sx2=gauss_filter(Ix2, sigma, kernel_size)  Sy2=gauss_filter(Iy2, sigma, kernel,size)  Sxy=gauss_filter(Ixy, sigma, kernel_size)

Harris Corner Detector ◦ 4. Define matrix H(x,y):  For j=1:columns,  For i=1:rows,  H{ i, j } = [Sx2(i, j) Sxy(i, j); Sxy(i, j) Sy2(i, j) ◦ 5. Response Detector  For j=1:columns,  For i=1:rows,  R( i, j ) = det(H{ i, j } )– k*(trace(H{ i, j }))^2 ◦ 6. Apply threshold to R  Edge: R <  Corner: R > 10000

Harris Corner Detector

Sift Purpose ◦ To identify features of an image regardless of scale and rotation Scale Space ◦ Resize image to half size (octave) ◦ Blur image by adjusting sigma ◦ 4 octaves and 5 blur levels are recommended

Sift Sift Features ◦ Divide image into 4 x 4 windows ◦ Divide each window into 4 x 4 subwindows Calculate magnitude and gradient for each subwindow ◦ Generate a histogram of 8 bins for each 4 x 4 window Each bin represents a gradient orientation 4 x 4 x 8 = 128 dimensions

Sift using Vl_feat

Match candidates by finding patches that have the most similar SIFT descriptor

Optical Flow Lucas Kanade Optical Flow Does not work for areas of large motion ◦ Resolved by Pyramids

Optical Flow

Bag of Features Implemented a Bag of Word classification Divided image into frames Concatenated sift descriptors for each frame Kmeans2 to cluster features Image represented as histogram Used histograms as training data for SVM

Bag of Features Results for 8 frames and 20 clusters: ◦ 9.5% accuracy on test data Conclusions: ◦ Increase frames and clusters to improve accuracy

Research Topics 1. Survey on Multiple Human Tracking by Detection Methods Afshin Dehghan 2. Data Driven Attributes for Action Detection Rui Hou 3. Subspace Clustering via Graph Regularized Sparse Coding Nasim Souly