Contents

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

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.”

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 usersWith more control for designing and editing the shape of curve.3 Easy: The way of creating and editing a curve should be easy.

Introduction…

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

Polynomial curve

• Quadratic : X(t)=at2 + bt +c (2 nd order)

Polynomial curve cont…

• Cubic: X(t)=at3 + bt2 + ct + d (3rd order)

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.

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

Bezier Curve

where i = 0, 1, 2, ... , n, and

Types of Bezier CurveClassical Bezier curve: Classical Bezier curves use the special case of the Bernstein polynomial where n = 3.

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

Where each B3i(u) term is scaler valued in Rand the control point Pi is vector valued in R3.

In matrix form we can also write:

A Bezier curve of degree five

A Bezier curve of degree nine

• 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.

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

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.

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.

Dynamic Bezier curve Cont…

Dynamic Bezier curve Algorithm

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.

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.

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]

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]

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]

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.

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.

Objective

Proposed algorithm : This algorithm is based on Bezier curves. The proposed gait recognition system consists of three unit: a) Image processingb) Feature extractionc) Gait recognition

Figure Proposed algorithm

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

Sequence of selecting Control Points of bezier curve

• 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.

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].

Conclusion

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

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.

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

Thank you…