10/13 Notes

Quiz Thursday

• Covers Chapter 1
• Cheat Sheet
• Notes and Book and HW 1

Users / Subjects

Some users overlap (fnmr, fmr) some are very unique (never overlap)

Categories of users (Dottingtons Zoo) (Biometric Menagerie)

1. Sheep - FMR and FNMR are low (unique and well behaved users)
2. Goat - FNMR is high
3. Lamb - FMR is high (voices can be mimiced easy, etc...) (not trying to manipulate system)
4. Wolf - FMR is high (deliberatly manipulates trait to defeat system, i.e voice)

Orientation Field

Level 1 details - also singular points

Method 2 - Gradient Method

Primarily uses Edge Filters

Img(x)S_x = G_x

• convolution operation (conv2 in matlab)
• Img is image
• S_x is filter
• G_x is output matrix

Edge Filters

Sobel Filter

S_x

-1 0 1

-2 0 2

-1 0 1

S_y

1 2 1

0 0 0

-1 -2 -1

Robert’s Cross

R_x

1 0

0 -1

R_y

0 1

-1 0

Prewitt’s Filter

P_x

-1 0 1

-1 0 1

-1 0 1

P_y

1 1 1

0 0 0

-1 -1 -1

Prewitt and Sobel tend to be most used

Canney Edge is good

Will use Sobel for project

Algorithm for Orientation Fields

1. Convolve image I with S_x (filter), gives you G_x == I(x)S_x
2. Convolve image I with S_y (filter), gives you G_Y == I(y)S_y
3. If G_x is high and G_y is low, then vertical edge, if G_y is high and G_x is low, then horizontal edge
4. Divide G_x and G_y into blocks of size N x N (bigger than 1 by 1, smaller than 20 by 20)

5. Estimate the local orientation of each block

   • theta = (1/2) * tan^-1(summation(i = 1 to W, summation(j = 1 to W, 2 * G_x(i, j) * G_y(i, j))) / (summation(i = 1 to W, summation(G_x^2(i, j) - G_y^2(i, j)))))
   • Use atan2 in matlab