Hand geometry recognition systems rely on measurements of the human hand's shape, size, and finger dimensions, offering a simple and cost-effective biometric method. The process involves image acquisition, feature extraction, and classification using neural network models, with high user acceptance due to its non-intrusiveness. Various stages, including contour detection and geometric measurement, are employed to ensure accurate recognition based on extracted features from scanned hand images.

2. Hand Geometry
• Hand geometry recognition systems are based on a number of
measurements taken from the human hand, including its shape,
size of palm, and length and widths of the fingers.
• The technique is very simple relatively easy to use, and
inexpensive.
• Environmental factors such as dry weather or individual anomalies
such as dry skin do not appear to have any negative effects on the
verification accuracy of hand geometry-based systems.
• The hand images can be obtained by using a simple setup
including a web cam, digital camera. However, other biometric
traits require a specialized, high cost scanner to acquire the data.
• The user acceptability for hand geometry based biometrics is very
high as it does not extract detail features of the individual. An
individual's hand does not significantly change after a certain age.

3. Hand Geometry Recognition
• Biometrical Feature Extraction
• Biometrical features, to be used on the training
of the neural network model, were extracted
from the scanned hand images.

4. Hand geometry using GMM
• Typical systems for authentication of individuals consist
of a data acquisition device (a digitalisation device) , a
preprocessing stage (software performing data pre-
processing operations such as the extraction of
features), and the construction of a classifying model
based on this features.
• The features used for the development of the GMM
algorithm were extracted from colour hand images
(both the top and the side view of the hands).
• The edges of the hands are detected from the images
and a morphological analysis is performed, obtaining a
feature vector.

5. Hand geometry using GMM
• A commercial flatbed scanner was used to acquire the hand
images using 150dpi scanning quality.
• The fingers must be clearly separated from each other in
the image in order to obtain a complete hand shape.
• Landmark Extraction and Hand Alignment
• Since there is clear distinction in intensity between the
hand and the background by design, a binary image is
obtained through thresholding and hand boundary is easily
located afterwards .
• Geometrical marks, i.e. the fingertip points and the valley
points between adjacent fingers, are extracted by travelling
along the hand boundary and searching for curvature
extremities

6. Hand Geometry Recognition
• Step 1:Binarization

7. Hand Geometry Recognition
• Step 2 : Hand Contour Detection
• Contour detection is the process of identifying
the edges of a hand from an image which
results in a numerical sequence which
describes the shape of the hand-palm.
• Contour following is a procedure by which one
runs through the hand silhouette by following
the edge of the image.

8. Hand Geometry Recognition
• Step 2.1. Contour Extraction
• The bitmap graphical files are transformed into text
files that contain the contour description.
• The encoding algorithm consists of a chain code. In
chain coding the direction vectors between successive
boundary pixels are encoded.
• Eight directional code can be coded by 3-bit code
words. Once the chain code is obtained, the perimeter
can be easily computed: for each segment, an even
code implies +1 and an odd code +√2 units.
• The start and end points of the fingers and wrist are
found by looking for minimum and maximum values of
the chain code.

9. • Chain codes are made up of
line segments that must lie on
a fixed grid with the given set
of possible directions. The
starting point is given by its
coordinates, the other points
are reached by passing the grid
from to the grid point to grid
point. The derivative
(0:straight, 1:to the left, 2:to
the right) is invariant under
rotation and needs both a
starting point and a direction.
•

10. Hand Geometry Recognition
• Contour Extraction
• where a shape was
drawn and the chain
codes and coordinates
for every contour point
were extracted.
• Chain coding is based on
identifying and storing
the directions from each
pixel to its neighbor pixel
on each contour.

11. Detection of a Hand contour
• There are three stages involved in the
detection of a hand contour.
• The first stage involves looking for the
starting vectorisation point.
• From the valley between the thumb and
the first finger, a vertical line is traced
down the image until it cuts the contour of
the hand.
• From this point, a horizontal line is traced
to find the starting point at the location
where the line and the hand silhouette
cross each other.
• The part of the hand located from this line
downwards is removed, because it is not
useful in the recognition task.
• starting coordinates are assigned to the
pixel position P0.

12. Detection of a Hand contour
• The second stage involves, starting from the
current pixel position Pn−1, the search, in the
clockwise direction starting from (d+3) mod 8, of
the first pixel with a value of “0”. This will be the
new boundary point. Its coordinate values are
then assigned to Pn and the new direction to d.
• The third stage checks if the new ordinate is
equal to the original ordinate, in which case the
detection of contour halts. Otherwise the second
step is repeated.

13. Geometric measurements

14. Geometric measurements
• Location of Measure Points
• Several intermediate steps were taken in order to detect the main
points of the hands from the image data set. The method for the
geometric hand-palm features extraction is quite straightforward.
• From the hand image, the following main points are located: finger
tips, valleys between the fingers and three more points that are
necessary to define the hand geometry precisely.
• Before any further processing can take place, the hand in the
binarised image has to be detected.
• The first two points to be detected are the ones representing the
thumb and the little finger. These points enable the extraction of
most of the geometrical information and are detected based on the
location of the (Xthumb, Ythumb), and the (Xlittle, Ylittle) points
respectively.

15. Geometric measurements

16. Geometric measurements
• A border following algorithm is applied to
locate the boundary of the binary image . For
each boundary point (x, y) , its curvature K is
estimated from:
where y', x', y". and x" is the first- and second-order coordinate changes along y
and x, calculated from the neighboring points of (x, y) . From the calculated
curvature information, nine landmarks are located which are curvature extremities

17. Border tracing algorithm

18. Border tracing algorithm
• These landmarks, instead of the
traditional pegs that often cause
hand deformation are used to
align the palm to vertical
displacement.
• A reference point and a reference
axis are found first.
• The middle finger baseline is
created by connecting the second
and third valley points.

19. • The mid-point of this baseline is used as the
reference point of the palm rotation, and the
axis from the reference point to the middle
finger landmark is selected as the reference
axis.
• A rotation angle is thus calculated from the
orientation of the reference axis :

20. • The reference axis is aligned to be upward
vertical in order to align the hand image with
the database template to the same
orientation, and finger-wise correspondence
between the input image and the template is
established, using the rotation equation:

21. Geometric measurements
• Feature Selection :
• Salient features are necessary for the robust recognition of
hand geometry. The lengths of the five fingers (L, to L5), the
widths of the four fingers (except the thumb) at two locations
(W, to Ws), and the shape of the three middle fingertip
regions (S, to S3) will be used for recognition.
• Finger baselines: four finger baseline between finger valley
points are located on the hand boundary.
• Because the middle-finger is the only finger which does not
have large spatial variations of its valley points for different
placement of the hands, the middle-finger baseline is formed
by connecting the second and third (count from the left)
valley points.

22. Geometric measurements
• The ring finger has two valley points (third and fourth) as well.
However, since the relative heights of these two valley points
are more sensitive to hand placement, it is unstable to use
these two valley points to reference axis.
• The baselines for the thumb, the index finger, the ring finger,
and the little finger are formed in the same fashion. It is
assumed that the two end points of each baseline have the
same distance from the respective fingertip point. Using one
of the respective points as one of the end points (first valley
point for thumb, second for index, third for ring, and fourth
for pinky), we locate the other end point by searching for the
point which has the same distance from the fingertip at the
another side of the boundary of the finger. The baselines are
formed afterwards by connecting pairs of end points.

23. Geometric measurements
• Finger lengths: For each finger, the fingertip point
and the middle point of its baseline determine its
finger length Li, i=1,2,3,4.
• Finger widths: For each finger except the thumb,
the first finger width Wi, i=l, 3, 5, 7, is the width
at the middle point of the finger length, and the
second finger width Wj, j=2,4, 6, 8, is the width at
one-eighth way (with respective to the finger
length) from the fingertip.

24. Geometric measurements
• Fingertip regions: For the index, middle, and ring fingers,
the top one-eighth portion of the fingers are defined as the
fingertip regions. Each fingertip region is represented by a
set of ordered boundary points (between 50 to 90). The
bottoms of the fingertip regions are coincident with WZ,
Wd, and W6 respectively. Similar to the palm alignment,
the fingertip regions are also aligned by the method .
• The middle point of the bottom line is found as the
reference point and the axis between middle point and the
fingertip top point is the reference axis. As long as the
rotation angle is found, the fingertip regions are aligned.
The coordinates of the fingertip points are recorded, and
re-sampling may be required in order to match the testing
image fingertip points and the template fingertip points

25. • Hierarchical Recognition :
• The extracted hand features are put into two groups.
• Group #1 consists of the 13 finger lengths and widths
of all fingers, and group #2 consists of the 3 fingertip
regions.
• A sequential recognition scheme is adopted, using
these two groups of features. Group #I: A Gaussian
mixture model (GMM), based upon statistical modeling
and neural networks is used to obtain the characteristic
parameters for the group #1 features of each person:
where ci is the weighting coefficient of each of the
Gaussian model, pi is the mean vector of the each
model, C, is the covariance matrix of each model,
M is the number of the models, and L is the
dimension of the feature vectors.

26. • The GMM is trained by the training images of
each person, and the characteristic parameters
are acquired for each user in terms of Ci , pi, and
L, of size lx M . The probability p(2 1 u) of an
input test image 2 belongs to class u can
• If the image is determined to pass a preset
threshold of the GMM probability estimation of
the template the image is further processed with
the group #2 features in the following step.

27. • Group #2: The mean distributions of the group #2
features, the point distributions of the three
fingertip regions, are used as the fingertip
templates for each user in the database. The
number of points on the input fingertip region S,
and on the corresponding template I;, must be
the same, and linear re-sampling of St is needed
if the two are different but the difference is
within an acceptable range (10% in our
implementation). If the difference is greater than
lo%, it is rejected.

29. • For all the fingertip points of the three
fingertips, we calculate the percentage of
failure points. If the percentage is higher than
another threshold (say, l0%), we declare that
the input hand image does not correspond to
the template and should be rejected.
Otherwise, it is recognized as the valid user
represented by the template.

30. Neural Network Model
• A multi-layer perceptron (MLP) was developed as a
discriminative two class classifier.
• The output or target values were coded according to
the type of person that the input pattern belonged to.
When the input pattern belonged to a genuine person,
the output was given a value of 1. When the input
pattern represented an impostor person, the output
was fixed to −1. Figure 9 shows the architecture of the
neural network. This architecture contains 10 input
units, a single hidden layer with a total of 40 hidden
neurons.

32. • The neural network was trained using the gradient descent
algorithm with momentum and weight/bias learning
functions. Contrary to other neural network algorithms
such as the RDP ([18,19]), the MLP suffers from over
learning and local minima.
• Therefore, the neural network was trained for 2,500 and
10,000 epochs using regularisation which involves a
modification on the error function to avoid over learning.
Also, a multi-start algorithm was also applied to avoid local
minima. The mean, standard deviation, and the best results
obtained after 50 random different initialisations are
presented.
• The input signals were normalised within a [−1, 1] range for
each input component.