lecture14 - EECS 442 Computer vision Introduction to Image...

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EECS 442 – Computer vision Introduction to Image Filters Reading: [FP] Chapters: 7,8 Some slides of this lectures are courtesy of prof F. Li, prof S. Lazebnik, and various other lecturers • Convolution • Blurring •Sharpen ing • Multi-scale representation • Aliasing and sampling
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P = [x,y,z] From the 3D to 2D Image 3D world p = [x,y] •Let’s now focus on 2D •Extract building blocks
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Extract useful building blocks
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• We can think of an image as a function, f, from R 2 to R: f ( x, y ) gives the intensity at position ( x, y ) – Defined over a rectangle, with a finite range: f : [ a , b ] x [ c , d ] Æ [0,255] • A color image: (, ) rxy fx y g x y bxy = Source: S. Seitz Images as functions
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Images as functions Source: S. Seitz x y f(x,y)
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• Images are usually digital (discrete): – Sample the 2D space on a regular grid • The image can now be represented as a matrix of integer values 62 79 23 119 120 105 4 0 10 10 9 62 12 78 34 0 10 58 197 46 46 0 0 48 176 135 5 188 191 68 0 49 2 1 1 29 26 37 0 77 0 89 144 147 187 102 62 208 255 252 0 166 123 62 0 31 166 63 127 17 1 0 99 30 Source: S. Seitz pixel Images as functions
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Filters • Linear filtering: – Form a new image whose pixels are a weighted sum of original pixel values – use the same set of weights at each point Goal: Extract useful information from the images •Features (edges, corners, blobs…)
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•Le t f be the image andg be the kernel. The output of convolving f with g is denoted by f * g. Convolution ] l n , k m [ g ] l , k [ f ] n , m )[ g f ( l , k = f Source: F. Durand • Convention: kernel is “flipped” • MATLAB: conv2 vs. filter2 (also imfilter)
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Box filter • Kernel k with positive entries, that sum to 1. • Notice: all weights are equal 1 1 1 1 1 1 1 1 1 Slide credit: David Lowe (UBC) ] , [ g
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 09 0 0 0 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 9 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Source: S. Seitz Box filter ] l n , k m [ g ] l , k [ f ] n , m )[ g f ( l , k =
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 09 0 0 0 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 9 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 0 90 0 90 90 90 90 90 90 90 90 Source: S. Seitz Box filter ] l n , k m [ g ] l , k [ f ] n , m )[ g f ( l , k =
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 09 0 0 0 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 9 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 02 0 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 0 90 0 90 90 90 90 90 90 90 90 Source: S. Seitz Box filter ] l n , k m [ g ] l , k [ f ] n , m )[ g f ( l , k =
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 09 0 0 0 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 9 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 0 2 03 0 0 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 0 90 0 90 90 90 90 90 90 90 90 Source: S. Seitz Box filter ] l n , k m [ g ] l , k [ f ] n , m )[ g f ( l , k =
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0 1 02 03 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Source: S. Seitz Box filter ] l n , k m [ g ] l , k [ f ] n , m )[ g f ( l , k =
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 90 0 90 90 90 0 0 0 0 0 90 90 90 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 20 30 30 30 20 10 0 20 40 60 60 60 40 20 0 30 60 90 90 90 60 30 0 30 50 80 80 90 60 30 0 30 50 80 80 90 60 30 0 20 30 50 50 60 40 20 10 20 30 30 30 30 20 10 10 10 10 0 0 0 0 0 Source: S. Seitz Box filter ] l n , k m [ g ] l , k [ f ] n , m )[ g f ( l , k =
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Box filter • Replaces each pixel with an average of its neigh- borhood . • Achieve smoothing effect (remove sharp features) 1 1 1 1 1 1 1 1 1 Slide credit: David Lowe (UBC) ] , [ g
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Example: Smoothing with a box filter
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• Weight contributions of neighboring pixels by nearness • Constant factor at front makes volume sum to 1 (can be ignored, as we should normalize weights to sum to 1 in any case).
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This note was uploaded on 10/26/2010 for the course EECS 442 taught by Professor Savarese during the Fall '09 term at University of Michigan.

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lecture14 - EECS 442 Computer vision Introduction to Image...

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