10/13 Notes
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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)
____________________________________________________________

 #. Sheep - FMR and FNMR are low (unique and well behaved users)
 #. Goat - FNMR is high
 #. Lamb - FMR is high (voices can be mimiced easy, etc...) (not trying to manipulate system)
 #. 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
--------------------------------

 #. Convolve image I with S_x (filter), gives you G_x == I(x)S_x
 #. Convolve image I with S_y (filter), gives you G_Y == I(y)S_y
 #. 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
 #. Divide G_x and G_y into blocks of size N x N (bigger than 1 by 1, smaller than 20 by 20)
 #. 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