10/25 Notes¶
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 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)