Linear filters and edge detection

CS223b: COMPUTER VISON Linear Filters and Edge Detection • convolution • shift invariant linear s y stem y • Fourier Transform • Aliasin g and sam p lin g gpg • scale representation •ed g e detection g Reading: Chapters 7, 8, Forsyth & Ponce book [...].. .Linear Filters • Linear filtering: g – Form a new image whose pixels are a weighted sum of original pixel values, values using the same set of weights at each point 1 – Center origin of the kernel F at each pixel location – Multiply weights by corresponding pixels – Set resulting value for each pixel 1 1 1 • Represent the linear weights as an image, F • F i called... Efficient Implementation • Both the BOX filter and the Gaussian filter are separable into two 1D convolutions: – Fi convolve each row with a 1D filter First l h ih fil – Then convolve each column with a 1D filter Differentiation and convolution • Recall, for 2D function, f(x,y): f  f x   , y f x, y   lim     0  x    • This is linear and shift invariant, so must be the result... called convolution 1 1 Convolution 1 1 1 • Image, R, resulting from convolution of F with image H, where u,v range i h over kernel pixels: Rij   H iu, jv Fuv , u,v Warning: the textbook mixes up H and F d Slide credit: David Lowe (UBC) Slide credits for these examples: Bill Freeman, David Jacobs Convolution I 10 11 10 0 0 1 9 10 11 1 0 1 10 9 10 0 2 1 11 10 9 10 9 11 9 10 11 9 99 11 10 9 9 11 . COMPUTER VISON Linear Filters and Edge Detection • convolution • shift invariant linear s y stem y • Fourier Transform • Aliasin g and sam p lin g gpg • scale representation •ed g e detection g Reading:. represented as a matrix of integer values il p i xe l Source: S. Seitz Filters Filters • Linear filtering: • Linear filtering: – Form a new image whose pixels are a weighted sum of original. the ima g es g •Features (edges, corners, blobs…) M dif h i ti M o dif y or en h ance i mage proper ti es - super-resolution, in-painting, de-noising Linear Filters • Linear filterin g : g –