1) The document discusses curvelet transformation and its application to object tracking. Curvelet transformation is a multiscale directional transform that can efficiently represent objects with curved edges using only a small number of coefficients. 2) It describes the stages of curvelet transformation including sub-band decomposition, smooth partitioning, renormalization, and ridgelet analysis. It also discusses the fast discrete curvelet transform implementation using unequally spaced fast Fourier transforms. 3) The proposed algorithm calculates the curvelet coefficients of frames to track objects based on the difference in curvelet energy between frames. Preliminary results on sample video frames are shown to demonstrate the calculation of curvelet coefficients.

1. Curvelet Transformation Based
Object Tracking
Project Guide: Project Members :
Mr.Roshan Singh Apurv Singh (0806313008)
Asst. Professor Arvind Yadav(0806313009)
CEA Dept. Yogesh Maurya(0806313058)
GLAITM Shobhit Bajpayee(2906313002)
Vipin Kumar (0806313051)

2. Curvelet Transform
 It was developed by Candès and Donoho
in 1999.
 It is a multiscale directional transform.
 Uses energy of curvelet.
 It designed to handle curves using only a
small number of coefficients
 Do not require extra parameter.

3. Curvelet Transform
vs
Wavelet Transform
Wavelet Transform cannot describe curve
discontinuities
Curvelet Transform is a new multi-scale
representation

4. Stages of Curvelet Transform
1. Sub-band decomposition:-
We define P0 (low pass filters) and ds , s>=0(high
filters). The image f is filtered into subbands using
Atrous algorithm as
f  (P0 f, d1f, d2f,…)

5. 2.Smooth Partitioning
Each subband is smoothly windowed into “squares”
of appropriate scale as
hQ = wQ .ds f
where wQ is a nonnegative smooth function
localized around a grid of dyadic squares defined
as

6. 3. Renormalization
 Renormalization is centering each dyadic
square to the unit square [0,1][0,1] as
gQ =(1/ TQ) hQ
For each Q, the operator TQ is defined as
( TQf)(x1, x2) = 2s f (2sx1 -k1, 2sx2- k2)

7. 4.Ridgelet analysis
 Each square is analyzed in the orthonormal
ridgelet
 system. This is a system of basis elements
making
 an orthonormal basis for L(R2):
 (Q) = gQ,

8. FAST DISCRETE CURVLET
TRANSFORM
There is two distinct implementation for curvlet
transform
the wrapping-based transform
 unequally-spaced fast Fourier transform
(USFFT).

9. PROPOSED ALGORITHM
Step1:
 compute the energy of curvelet coefficients of
the square box
Step2:
 for frame_no = 2 to last do compute the
curvelet coefficients of the frame

10. Cont…..
Step3:
 Make a bounding box with centroid
(Cnew 1, Cnew 2).
Step4:
 Compute the difference of energy di,j of curvelet
coefficient of bounding box, with E.
Step5:
Mark the object in current frame with bounding box
with centeroid (C1,C2) and energy of bounding box
E.

11. WORK DONE SO FAR
 Reading a noise free video(.avi) in matla b
a=mmreader(„video1.avi‟);
b=read(a,100);
imshow(b).
 Dividing video into frames.
for i=1 : 50
(:,:,:,i)=read(a,i);
end
for i=20: 30
figure, imshow(b(:,:,:,i));
end

12. Cont….
 Calculation of curvlet coefficient

13. EXPERIMENTAL RESULT
 FRAME SEQUENCE
1 5 9
13 17 21

14. CURVLET COEFFICIENT
Curvlet coefficint for Frame10 (cell 1)CU

15. Cont…
Curvlet coefficint for Frame20 (cell 1)CU

16. REFERENCES
 New Tight Frames of Curvelets and Optimal
Representations of Objects with Piecewise C2
Singularities‟,Comm. Pure Appl. Math. 57 (2004) 219-
266.
 „Fast Discrete Curvelet Transforms‟, Multiscale Model.
Simul. 5(2006), no. 3, 861-899.
 S. Nigam and A. Khare, “Curvelet Transform Based
Object Tracking,” Proceedings of IEEE International
Conference on Computer and Communication
Technologies, Allahabad, 17-19 September 2010, pp. 230-
235