10/25 Notes
===========

Grading Schedule
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Quiz 1 back : 10/27

HW 1 back: 11/1

Project 1 Back: 11/3

Assignment Schedule
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HW 2: 10/25 - 11/1

Project 2: 11/1 - 11/15

HW 3: 11/22 - 12/1

Orientation Field
-----------------

Each point has a number that represents a degree of orientation (0 - 360)

2 approches to extract orientation Field
 * FFT Method
 * Gradient Method
    * Implementing for project 2

Level 2 Extraction steps
------------------------

Image -> Orientation Field -> Image Enhancement (use Gabor Filter) -> Binarization(highlight dark and light pixels) -> 
Ridge Thinning -> Minutiae Extraction -> Post Processing

Singular Points
---------------

2 Types
 * Core
 * Delta

If all orientation of cells point the same way, it's a *non-Singular point*

If substantial change in angle, then it's a *Core Point*

If multiple radical angle divergence, it's a *delta point*

If you find 2 loops, it's a *whorl core point*


Poincare Index
--------------

In counterclockwise direction

Orientation Field = theta = [0, pi)

PI = (1 / pi) Summation[i = 0 to 7](Orientation Field[(i + 1) % 8] - Orientation Field[i])


Corrected PI = (1 / pi) Summation[i = 0 to 7](delta(Orientation Field[(i + 1) % 8] - Orientation Field[i]))

delta(theta) =
 * theta - pi if theta > pi / 2
 * theta if -pi / 2 <= theta <= pi/2
 * pi + theta if theta < -pi / 2

after delta, PI = one of 4 numbers
 * if 0 -> Non SP (not interesting)
 * if 1 -> loop
 * if -1 -> delta
 * if 2 -> Whorl (because sum of 2 loops)

Classification
--------------

if no interesting points -> plain arch

if core right above delta or vice versa -> tented arch

if core northwest to delta -> left loop

if core northeast to delta -> right loop

if 2 cores in center (very close to each other) and 2 delta points -> whorl

if 2 cores in center (farther apart) and 2 deltas -> twin loop

Point Pattern Matching
-----------------------

Minutiae Point
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(x, y, theta)

so we get location and orientation in tuple

Minutiae Matching
-----------------

What geometric transformation aligns 2 Minutiae point maps?

Max score = total amount of points that could be aligned

How do we go about this?

Transformation called *Affine Transformation*

Affine Transformation
---------------------
 * Rotation
 * Translation

So we use a combo of these 2 to find orientation

If we have a set of points and another image with another set of points, what is the rotation
and Translation of image such that we get max possible matching between image points?

(See next class for more info)