This document discusses Bezier curves and their applications. It begins with an introduction to Bezier curves, including their history and properties. It then describes different types of Bezier curves such as classical, rational, and dynamic Bezier curves. The document reviews several applications of Bezier curves in computer graphics, animation, and font design. Finally, it discusses related work using Bezier curves for tasks such as gait recognition, gesture recognition, and facial expression recognition.

1. Contents
• Introduction
• Types of Bezier curve
• Applications
• Literature Review
• Problem statement
• Conclusion
• References

2. Introduction
Bezier curve were independently introduced by
P.de Casteljau and P.E. Bezier and have been
applied to a wide variety of computer-aided
design application.
“A Bezier curve is a parametric curve frequently
used in Computer graphics and related fields.”

3. Introduction…
• A system that supports users to design curves
must be:
1 Intuitive: We expect that every step.
2 Flexible: The system should provide the users
With more control for designing and editing the
shape of curve.
3 Easy: The way of creating and editing a curve
should be easy.

4. Introduction…
4 Unified Approach: The way representing ,
creating and editing.

5. Polynomial curve
• Quadratic : X(t)=at2 + bt +c (2 nd order)

6. Polynomial curve cont…
• Cubic: X(t)=at3 + bt2 + ct + d
(3rd order)

7. Control Points
• Polynomial coefficients a, b, c, d can be
interpreted as control points.
Where a, b, c, d have x , y ,z components each.

8. control points…
• How many control points?
• Two points define a line (1st order)
• Three points define a quadratic curve (2nd
order)
• Four points define a cubic curve (3rd order)
• k+1 points define a k-order curve

9. Bezier Curve

10. where i = 0, 1, 2, ... , n, and
Types of Bezier Curve
Classical Bezier curve: Classical Bezier curves use
the special case of the Bernstein polynomial
where n = 3.

11. • Now we can mathematically define a degree
three Bezier curve. Let Q(u) be such a curve:

12. Where each B3i(u) term is scaler valued in R
and the control point Pi is vector valued in R3.
In matrix form we can also write:

14. A Bezier curve of degree five

15. A Bezier curve of degree nine

16. • IN general, a Bezier spline of degree k is
defined on n = k + 1 control points, where the
set of control points P = { P0, P1, . . ., Pk} forms
a control polygon with n vertices.

17. Rational Bezier Curve
 The problem with just a regular point is that
there is no info on how to project it.
 The rational form has advantages in that it can
represent a wide range of curves, and surfaces
 Curves could be in the form of circles, ellipses,
parabolas, and hyperbolas; surfaces can be in the
form of spheres, ellipsiods,cylinders, cones,
paraboloids, hyperboloids, and hyperbolic
paraboloids

18. Rational B-Spline
• B-splines are like Bezier curves because they both
use a control polygon to define the curve, and are
helpful due to their control points’ local control of
the resulting shape. The B in B-spline stands for
”basis,” and the basis is specified by the Cox-de
Boor formula for computing the basis function.
• B-spline can be rational or non-rational,
depending on the use of homogeneous
coordinates.

19. Dynamic Bezier curve
• DBC incorporates local information within the
classical BC theory , by variably moving Bezier
points to new parametrically determined
locations between the BC point and CtrPoly ,
with the optimal value of the shifting
parameter (SP) being analytically determined
for a prescribed admissible distortion, using the
Lagrangian multiplier method.

20. Dynamic Bezier curve Cont…

21. Dynamic Bezier curve Algorithm

22. Applications
1 Computer graphics: Bezier curves are widely
used in computer graphics to model smooth
curves .
2 Animation: In animation application ,such as
Adope Flash and synfig,Bezier curves are used to
Outline ,for example movement .
3 Font: TrueType fonts use Bezier splines
composed of quadratic Bezier curves.

23. Literature Review
1.Human Gait recognition using Bezier curves ,
2011.
a) Proposed Algorithm : Mean and variance
method.
b) Result : In this Rank1 report the percentage
of subjects in a set that were identified
exactly .Rank5 results report the percentage
of test subject whose actual match in the
reference database.
c) Reference : [1] pratibha mishra.

24. Literature Review Cont…
2. Motion detection with pyramid structure of
background model for intelligent surveillance
system,2012
a) Proposed Method : Bezier curve smoothing
method to reduce the noise for motion detection
based on our proposed adaptive background
model.
b) Result : In comparison , the accuracy rates
produced by similarity and F1 for the MSDE
method were 57.52% or less and 75.11% or less,
respectively.[2]

25. Literature Review Cont…
3. Gesture recognition using Bezier curve for
visualization navigation from registered 3-D
data,2003.
a) Proposed Method : For detecting skin regions to
identify hand involved in virtual object
manipulation the color image is converted to the
SCT color space to reduce lighting artifacts. Skin
pixels are selected with a minimum distance
classifier using mahalanobis distance.
b) Result : Detected the manipulating hand
correctly in 1639 of 1641 images (99.9 %).[3]

26. Literature Review Cont…
4. Smile detection via bezier curve of mouth
interest points,2013.
a) Proposed Method : In this extract points on
the mouth via Shi & Tomasi algorithm.
b) Result : Achieve accuracy up to 85 % on
Genki dataset .[4]

27. Literature Review Cont…
5. Facial Expression recognition based on Co-
ordinate and Bezier curve,2013.
a) Proposed Method : RGB/Skin tone color
algorithm .
b) Result : Once face has been identify then the
face will be converted from RGB image to
binary image . Identification of lips, eyes will be
take place according to the algorithmic
approach. The identification parts will be
converted to binary image and apply bezier
curve to identify the expression.

28. Problem Statement
Conventional biometrics like fingerprint
recognition, iris recognition ,face recognition can
not work well from a large distance. In visual
Surveillance, the distances between the cameras
and the people under surveillance are often large. In
these situation , it is almost impossible to acquire
the detailed conventional biometric information
.Unlike other biometrics, GAIT can be captured
from a distance camera, without drawing the
attention of the observed subject.

29. Objective
Proposed algorithm : This algorithm is based on
Bezier curves. The proposed gait recognition
system consists of three unit:
a) Image processing
b) Feature extraction
c) Gait recognition

30. Figure Proposed algorithm

31. Key Frames Generation
• Determine the key frames of a walking gait by
observing the different phases of a human
walk cycle as
shown in Figure

32. Sequence of selecting Control Points of
bezier curve

33. • We select five control points from every frame
of an individual according to Figure, Here,
first point is selected to locate ankle, next is
selected to locate the toe , next is selected to
indicate the knee, next is selected to indicate
palm and last one is selected to locate
shoulder.

34. Bezier curve
• A bezier curve is represented by the function
• where N is the degree of curve (total number
of control points), Pi = (xi , yi) and Bi , N (t),
for i = 0, 1, . . . , N, are the Bernstein
polynomials of degree N, and t ϵ [0, 1].

35. Conclusion
Dynamic Bezier curve is a efficient method to fit
geographical curves. It make advantages of GAIT
Recognition using bezier curve that it solve
problem of geographical curves.

36. References
[1] Pratibha Mishra ,Human Gait Recognition
Using Bezier Curves 2011.
[2] Shih-Chia Huang , Fan-Chieh Cheng, Motion
detection with pyramid structure of background
model for intelligent surveillance systems 2012.
[3] Min C.Shin , Leonid V. Tsap , Dmitry B.
Goldgof, Gesture recognition using Bezier curves
for visualization navigation from registered 3-D
data 2003.

37. References cont…
[4] Pinky Rai , Manish Dixit , Smile Detection via
Bezier curve of Mouth Interest Points , 2013.
[5] M.Swathi , P.A Ashoka Vardini , T.Bharat
kunar , Facial Expression Recognition Based on
Co-ordinate and Bezier curves , 2013

38. Thank you…