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D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and
Applications[IJARIDEA]
Vol.2, Issue 2,27 April 2017, pg. 78-82
© 2017, IJARIDEA All Rights Reserved
78
Video denoising using Optical flow estimation &
Regularized non-local means
D.Raja Raghunath1
, P V Pavan Kumar2
, CH Mourya Pradeep3
, A.AniletBala4
1,2,3
Department of Electronics and Communication Engineering, SRM University, India
4
Assistant Professor (O.G), Department of Electronics and Communication Engineering,
SRM University, India
rajaraghunath_prasad@srmuniv.edu.in 1
Abstract— A novel video denoising calculation is exhibited. The non-nearby means(NL-implies) perform denoising by
misusing the common excess of examples inside a picture; they play out a weighted normal of pixels whose areas are
near each other. This permits to lessen altogether the clamor while saving the majority of the picture content. the
utilization of movement remuneration by regularized optical stream strategies grants vigorous fix correlation in a
spatiotemporal volume. We present in this paper a variational approach that lessening commotion by Regularized non-
nearby means technique.
Keywords—Image And Video Denoising, Noise Reduction, Non-Local Means, Optical Flow.
I. INTRODUCTION
Video denoising is a noteworthy issue since the procedure comprises of division, recreation,
and so forth where these errands require quality contribution to get coveted yield. Video
denoising is expulsion of clamor from a video flag which is essentially separated into two
sorts (1) spatial video denoising strategy, in this procedure for each edge in the video
commotion decrease is connected exclusively. (2) fleeting video denoising technique, in this
procedure the commotion between edges is decreased and some of the time movement
remuneration might be utilized for abstaining from ghosting relics when consolidating
together pixels from various casings. The spatial-worldly video denoising is the mix of both
spatial and transient denoising which is additionally called as 3D denoising. Diverse video
denoising strategies have been contemplated, among which primary segment investigation
and non-neighborhood models. The vital part investigation is principally utilized for
information lessening. The quantity of primary segments is not exactly or equivalent to
number of perceptions. From [1] calculation of PCA is equivalent to Singular esteem
deterioration (SVD). Since PCA is simply relies on upon diminishment of information where
in this procedure still some measure of commotion residuals are available. We likewise
learned about non-nearby means[2] which brought fix based techniques into picture
denoising. The Non-neighborhood implies process weighted normal of pixels whose
surroundings are close. The aggregate variation(TV) regularization[3] amends the leftover
commotion which is available in the moving structures. The ROF model[4] limits the
aggregate variety in smoothing the reestablished picture by saving edges.
II. RELATED WORKS
Coloma Ballester[18] tells that an alternate model for joint optical stream and impediment
estimation was proposed. The optical stream strategy depends on a TV-L1 approach and
consolidates data that permits to recognize impediments. This data depends on the uniqueness
of the stream and the proposed vitality supports the area of impediments on areas where this
difference is negative. Expecting that blocked pixels are unmistakable in the past casing, the
optical stream on non-impeded pixels is forward assessed while is in reverse evaluated on the
impeded ones. Neighborhood channels are nonlocal picture and motion picture channels
which lessen the commotion by averaging comparative pixels. The primary question of the
paper[2] is to introduce a bound together hypothesis of these channels and dependable criteria
to contrast them with other channel classes. A CCD clamor model will be displayed
supporting the association of neighborhood channels. An arrangement of neighborhood
D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and
Applications[IJARIDEA]
Vol.2, Issue 2,27 April 2017, pg. 78-82
© 2017, IJARIDEA All Rights Reserved
79
channels will be proposed, including established picture and film denoising techniques and
talking about further an as of late presented neighborhood channel, NL-implies.
Jerome boulanger[18] proposed a versatile measurable estimation system in light of the
neighborhood examination of the predisposition difference exchange off was proposed. At
every pixel, the space time neighborhood is adjusted to enhance the execution of the
proposed fix based estimator. The proposed technique is unsupervised and requires no
movement estimation. Here, a calculation for adjusting progressive viewfinder outlines has
been depicted by Andrew adams[14]. Initial, a gauge of between edge interpretation is
figured by adjusting basic projections of edges in two pictures. The gauge is then refined to
register an entire 2D likeness change by adjusting point highlights. This calculation is strong
to commotion, never requires putting away more than one viewfinder outline in memory, and
keeps running at 30 outlines for every second on standard cell phone equipment. [7] proposed
a principle in which the division is the urgent stage in iris acknowledgment. We have utilized
the worldwide limit an incentive for division. In the above calculation we have not
considered the eyelid and eyelashes relics, which corrupt the execution of iris
acknowledgment framework. The framework gives sufficient execution likewise the
outcomes are attractive.
III. OVERVIEW OF NON-LOCAL MEANS
The variational methods consists in minimizing an energy in order to force certain properties
on the unknown solution. The solution uTV is obtained by minimizing the following energy:
uTV = argmin u − log p(g|u) + λ TV(u) (1)
The term − log p(g|u) is a data fidelity term based on the loglikelihood, that adapts to the
noise statistic.
TV(u) is a regularization term and λ > 0 is the parameter that sets compromise between data
fidelity and smoothness. A regularization parameter if set too low will not allow to recover
flat areas creating staircase effect.
For each pixel i in the image domain Ω the solution of NL-means is :
gj where Zi = (2)
The weights is probability of two noisy pixels belongs to same structure which is
also known as same true grey level.
(3)
Where is kernel decay function, h is a filtering parameter and d a distance function that
measures similarity between patches Pi and pj of size |P| extracted around the pixels i and j
other information about the kernel is referred from [5]. The non-local means algorithm is
robust to different noise statistics and it is widely used and improved. The NL-means perform
well on the flat surface areas.
IV.REGULARIZED NON-LOCAL MEANS
RNL algorithm is proposed which combines both the Total variation Regularization and
Non-local means to reduce staircasing effect as mentioned. The equation for RNL is:
uRNL=argmin- logp(gj|ui)+ λTV(u) (4)
this is also equals to the solution:
uRNL=argmin- logp(uNL)i|ui)+ λTV(u) (5)
D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and
Applications[IJARIDEA]
Vol.2, Issue 2,27 April 2017, pg. 78-82
© 2017, IJARIDEA All Rights Reserved
80
The objective of this calculation is to diminish the uncommon fix impact seen on pictures
and recordings accordingly of the NL-implies calculation. We play out a nearby
regularization of the NL-implies, utilizing a non-neighborhood information devotion term
consolidated with aggregate variety. We propose an instinctive model that is adjusted to
various clamor models and infer a basic determination plot in the general instance of the
exponential family, that incorporates an expansive scope of commotions experienced in
imaging gadgets. In addition, our model offers a characteristic expansion to video denoising.
We utilize the worldly NL-implies with 3-dimensional patches, that we regularize utilizing
our versatile spatial TV regularization. This enables us to ensure transient consistency
without agony from lingering commotion. The principle commitments of our work are the
straightforward model and its instinctive translation, the capacity to manage diverse
commotion insights on account of a general model, and the common augmentation to video
denoising that gives because of the spatio-fleeting patches productive denoising alongside a
superior worldly consistency. A concise usage of the RNL calculation is appeared in
calculation 1.
Algorithm 1 RNL
Parameters: g : input noisy image,
h : filtering parameter
|P| : patch size
N : size and shape of neighbourhood
λ : regularization parameter
Non-local means step- computation of weights
For i∈Ω, j ∈N(i) do
Compute wi,j= φ(-(d(g(Pi),g(Pj)))/(2|P|h^2 ))
end for
return
Z = u = (6)
A. Minimization step:
uRNL=argmin A(ui)- + λTV(u) (7)
return uRNL
on the basis on Non-local means for video denoising. We can adapt the RNL algorithm to
image sequences: the Non-local means step benefits from the temporal information while the
Total Variation regularization is applied spatially to reduce noise.
B. Adaption to video denoising:
Video denoising profits by the transient data all through the edges, gave that the casings
can be placed in correspondence with each other. The NL-implies have been adjusted to
video denoising and they accomplish spatiotemporal sifting without earlier movement
remuneration. Indeed, the creators have even demonstrated that movement pay is counter-
gainful, since it lessens the quantity of hopefuls and it is frequently off base. We take after
the possibility of the NL-implies and adjust our R-NL calculation to video denoising. We
play out the NL-implies utilizing spatio-fleeting pursuit windows, then we apply the versatile
TV regularization spatially on each casing to lessen the lingering commotion. Be that as it
may, Liu et al. advocate in that movement compensationis in actuality fundamental, even in a
D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and
Applications[IJARIDEA]
Vol.2, Issue 2,27 April 2017, pg. 78-82
© 2017, IJARIDEA All Rights Reserved
81
non-neighborhood setting. They coordinate optical stream estimation in the NL-implies
structure with a specific end goal to perform more proficient denoising while at the same time
ensuring better transient soundness. In both NL-means and R-NL, if few edges are utilized
for the inquiry window(which is frequently the case with a specific end goal to bring down
the computational costs), no fleeting normality is ensured.
Fig.1. Denoising process of video which converted into frames of the rnl process
The figure shows the sigma value of noisy video and PSNR value of the denoised image.
V. CONCLUSION
The proposed demonstrate offers effective regularization of the Non-nearby means over the
PCA denoising which just relies on upon the information decrease. The versatile
regularization gave a decent trade off between diminishment of remaining commotion and by
saving the surfaces The model has an instinctive elucidation and a quick execution with
straight many-sided quality for the exponential family, and it could be adjusted to various
issue utilizing other regularization terms. We have displayed this model as a regularization of
the NL-implies yet the reasoning of this technique could apply to any non-nearby utilitarian,
for example, the enhanced adaptations of the NL-implies or even BM3D.
REFERENCES
[1] T. Brox and J. Malik, “Large displacement optical flow: Descriptor matching in variational motion
estimation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 3, pp. 500–513, Mar. 2011.
[2] A. Buades B. Coll J.-M. Morel "A non-local algorithm for image denoising"Proc. IEEE Comput. Soc.
Conf. Comput. Vis. Pattern Recognit. vol. 2 pp. 60-65 Jun. 2005.
[3] A. Chambolle "An algorithm for total variation minimization and applications" Math. Imag. Visvol. 20 no.
1 pp. 89-97 2004.
[4] L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D,
vol. 60(1):259-268, 1992.
[5] A. Buades, B. Coll, and J.-M. Morel, “A review of image denoising algorithms, with a new one,”
Multiscale Modeling and Simulation, vol. 4(2), pp. 490–530, Sep 2005.
[6] S. Roth and M. J. Black, “On the spatial statistics of optical flow,” inProc. ICCV, vol. 1. Oct. 2005, pp.
42–49.
[7] Christo Ananth,"Iris Recognition Using Active Contours",International Journal of Advanced Research in
Innovative Discoveries in Engineering and Applications[IJARIDEA],Volume 2,Issue 1,February
2017,pp:27-32.
[8] X. Zhang, M. Burger, X. Bresson, and S. Osher, “Bregmanizednonlocalregularization for deconvolution
and sparse reconstruction,” SIAM J.Imag. Sci., vol. 3, no. 3, pp. 253–276, 2010.
[9] K. J. Lee, D. Kwon, I. D. Yun, and S. U. Lee, “Optical flow estimationwith adaptive convolution kernel
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[10] M. Werlberger, T. Pock, and H. Bischof, “Motion estimation withnon-local total variation regularization,”
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D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and
Applications[IJARIDEA]
Vol.2, Issue 2,27 April 2017, pg. 78-82
© 2017, IJARIDEA All Rights Reserved
82
[11] X. Shen and Y. Wu, “Sparsity model for robust optical flow estimationat motion discontinuities,” in Proc.
IEEE Conf. CVPR, Jun. 2010,pp. 2456–2463.
[12] K. Jia, X. Wang, and X. Tang, “Optical flow estimation using learnedsparse model,” in Proc. IEEE ICCV,
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[13] Z. Chen, J. Wang, and Y. Wu, “Decomposing and regularizingsparse/non-sparse components for motion
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[14] A. Adams, N. Gelfand, and K. Pulli, “Viewfinder alignment,” Comput. Graph. Forum, vol. 27, pp. 597–
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displacements,” Int. J. Comput. Vis., vol. 39, no. 1, pp. 41–56, Aug. 2000.
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Video denoising using Optical flow estimation & Regularized non-local means

  • 1. D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and Applications[IJARIDEA] Vol.2, Issue 2,27 April 2017, pg. 78-82 © 2017, IJARIDEA All Rights Reserved 78 Video denoising using Optical flow estimation & Regularized non-local means D.Raja Raghunath1 , P V Pavan Kumar2 , CH Mourya Pradeep3 , A.AniletBala4 1,2,3 Department of Electronics and Communication Engineering, SRM University, India 4 Assistant Professor (O.G), Department of Electronics and Communication Engineering, SRM University, India rajaraghunath_prasad@srmuniv.edu.in 1 Abstract— A novel video denoising calculation is exhibited. The non-nearby means(NL-implies) perform denoising by misusing the common excess of examples inside a picture; they play out a weighted normal of pixels whose areas are near each other. This permits to lessen altogether the clamor while saving the majority of the picture content. the utilization of movement remuneration by regularized optical stream strategies grants vigorous fix correlation in a spatiotemporal volume. We present in this paper a variational approach that lessening commotion by Regularized non- nearby means technique. Keywords—Image And Video Denoising, Noise Reduction, Non-Local Means, Optical Flow. I. INTRODUCTION Video denoising is a noteworthy issue since the procedure comprises of division, recreation, and so forth where these errands require quality contribution to get coveted yield. Video denoising is expulsion of clamor from a video flag which is essentially separated into two sorts (1) spatial video denoising strategy, in this procedure for each edge in the video commotion decrease is connected exclusively. (2) fleeting video denoising technique, in this procedure the commotion between edges is decreased and some of the time movement remuneration might be utilized for abstaining from ghosting relics when consolidating together pixels from various casings. The spatial-worldly video denoising is the mix of both spatial and transient denoising which is additionally called as 3D denoising. Diverse video denoising strategies have been contemplated, among which primary segment investigation and non-neighborhood models. The vital part investigation is principally utilized for information lessening. The quantity of primary segments is not exactly or equivalent to number of perceptions. From [1] calculation of PCA is equivalent to Singular esteem deterioration (SVD). Since PCA is simply relies on upon diminishment of information where in this procedure still some measure of commotion residuals are available. We likewise learned about non-nearby means[2] which brought fix based techniques into picture denoising. The Non-neighborhood implies process weighted normal of pixels whose surroundings are close. The aggregate variation(TV) regularization[3] amends the leftover commotion which is available in the moving structures. The ROF model[4] limits the aggregate variety in smoothing the reestablished picture by saving edges. II. RELATED WORKS Coloma Ballester[18] tells that an alternate model for joint optical stream and impediment estimation was proposed. The optical stream strategy depends on a TV-L1 approach and consolidates data that permits to recognize impediments. This data depends on the uniqueness of the stream and the proposed vitality supports the area of impediments on areas where this difference is negative. Expecting that blocked pixels are unmistakable in the past casing, the optical stream on non-impeded pixels is forward assessed while is in reverse evaluated on the impeded ones. Neighborhood channels are nonlocal picture and motion picture channels which lessen the commotion by averaging comparative pixels. The primary question of the paper[2] is to introduce a bound together hypothesis of these channels and dependable criteria to contrast them with other channel classes. A CCD clamor model will be displayed supporting the association of neighborhood channels. An arrangement of neighborhood
  • 2. D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and Applications[IJARIDEA] Vol.2, Issue 2,27 April 2017, pg. 78-82 © 2017, IJARIDEA All Rights Reserved 79 channels will be proposed, including established picture and film denoising techniques and talking about further an as of late presented neighborhood channel, NL-implies. Jerome boulanger[18] proposed a versatile measurable estimation system in light of the neighborhood examination of the predisposition difference exchange off was proposed. At every pixel, the space time neighborhood is adjusted to enhance the execution of the proposed fix based estimator. The proposed technique is unsupervised and requires no movement estimation. Here, a calculation for adjusting progressive viewfinder outlines has been depicted by Andrew adams[14]. Initial, a gauge of between edge interpretation is figured by adjusting basic projections of edges in two pictures. The gauge is then refined to register an entire 2D likeness change by adjusting point highlights. This calculation is strong to commotion, never requires putting away more than one viewfinder outline in memory, and keeps running at 30 outlines for every second on standard cell phone equipment. [7] proposed a principle in which the division is the urgent stage in iris acknowledgment. We have utilized the worldwide limit an incentive for division. In the above calculation we have not considered the eyelid and eyelashes relics, which corrupt the execution of iris acknowledgment framework. The framework gives sufficient execution likewise the outcomes are attractive. III. OVERVIEW OF NON-LOCAL MEANS The variational methods consists in minimizing an energy in order to force certain properties on the unknown solution. The solution uTV is obtained by minimizing the following energy: uTV = argmin u − log p(g|u) + λ TV(u) (1) The term − log p(g|u) is a data fidelity term based on the loglikelihood, that adapts to the noise statistic. TV(u) is a regularization term and λ > 0 is the parameter that sets compromise between data fidelity and smoothness. A regularization parameter if set too low will not allow to recover flat areas creating staircase effect. For each pixel i in the image domain Ω the solution of NL-means is : gj where Zi = (2) The weights is probability of two noisy pixels belongs to same structure which is also known as same true grey level. (3) Where is kernel decay function, h is a filtering parameter and d a distance function that measures similarity between patches Pi and pj of size |P| extracted around the pixels i and j other information about the kernel is referred from [5]. The non-local means algorithm is robust to different noise statistics and it is widely used and improved. The NL-means perform well on the flat surface areas. IV.REGULARIZED NON-LOCAL MEANS RNL algorithm is proposed which combines both the Total variation Regularization and Non-local means to reduce staircasing effect as mentioned. The equation for RNL is: uRNL=argmin- logp(gj|ui)+ λTV(u) (4) this is also equals to the solution: uRNL=argmin- logp(uNL)i|ui)+ λTV(u) (5)
  • 3. D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and Applications[IJARIDEA] Vol.2, Issue 2,27 April 2017, pg. 78-82 © 2017, IJARIDEA All Rights Reserved 80 The objective of this calculation is to diminish the uncommon fix impact seen on pictures and recordings accordingly of the NL-implies calculation. We play out a nearby regularization of the NL-implies, utilizing a non-neighborhood information devotion term consolidated with aggregate variety. We propose an instinctive model that is adjusted to various clamor models and infer a basic determination plot in the general instance of the exponential family, that incorporates an expansive scope of commotions experienced in imaging gadgets. In addition, our model offers a characteristic expansion to video denoising. We utilize the worldly NL-implies with 3-dimensional patches, that we regularize utilizing our versatile spatial TV regularization. This enables us to ensure transient consistency without agony from lingering commotion. The principle commitments of our work are the straightforward model and its instinctive translation, the capacity to manage diverse commotion insights on account of a general model, and the common augmentation to video denoising that gives because of the spatio-fleeting patches productive denoising alongside a superior worldly consistency. A concise usage of the RNL calculation is appeared in calculation 1. Algorithm 1 RNL Parameters: g : input noisy image, h : filtering parameter |P| : patch size N : size and shape of neighbourhood λ : regularization parameter Non-local means step- computation of weights For i∈Ω, j ∈N(i) do Compute wi,j= φ(-(d(g(Pi),g(Pj)))/(2|P|h^2 )) end for return Z = u = (6) A. Minimization step: uRNL=argmin A(ui)- + λTV(u) (7) return uRNL on the basis on Non-local means for video denoising. We can adapt the RNL algorithm to image sequences: the Non-local means step benefits from the temporal information while the Total Variation regularization is applied spatially to reduce noise. B. Adaption to video denoising: Video denoising profits by the transient data all through the edges, gave that the casings can be placed in correspondence with each other. The NL-implies have been adjusted to video denoising and they accomplish spatiotemporal sifting without earlier movement remuneration. Indeed, the creators have even demonstrated that movement pay is counter- gainful, since it lessens the quantity of hopefuls and it is frequently off base. We take after the possibility of the NL-implies and adjust our R-NL calculation to video denoising. We play out the NL-implies utilizing spatio-fleeting pursuit windows, then we apply the versatile TV regularization spatially on each casing to lessen the lingering commotion. Be that as it may, Liu et al. advocate in that movement compensationis in actuality fundamental, even in a
  • 4. D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and Applications[IJARIDEA] Vol.2, Issue 2,27 April 2017, pg. 78-82 © 2017, IJARIDEA All Rights Reserved 81 non-neighborhood setting. They coordinate optical stream estimation in the NL-implies structure with a specific end goal to perform more proficient denoising while at the same time ensuring better transient soundness. In both NL-means and R-NL, if few edges are utilized for the inquiry window(which is frequently the case with a specific end goal to bring down the computational costs), no fleeting normality is ensured. Fig.1. Denoising process of video which converted into frames of the rnl process The figure shows the sigma value of noisy video and PSNR value of the denoised image. V. CONCLUSION The proposed demonstrate offers effective regularization of the Non-nearby means over the PCA denoising which just relies on upon the information decrease. The versatile regularization gave a decent trade off between diminishment of remaining commotion and by saving the surfaces The model has an instinctive elucidation and a quick execution with straight many-sided quality for the exponential family, and it could be adjusted to various issue utilizing other regularization terms. We have displayed this model as a regularization of the NL-implies yet the reasoning of this technique could apply to any non-nearby utilitarian, for example, the enhanced adaptations of the NL-implies or even BM3D. REFERENCES [1] T. Brox and J. Malik, “Large displacement optical flow: Descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, no. 3, pp. 500–513, Mar. 2011. [2] A. Buades B. Coll J.-M. Morel "A non-local algorithm for image denoising"Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. vol. 2 pp. 60-65 Jun. 2005. [3] A. Chambolle "An algorithm for total variation minimization and applications" Math. Imag. Visvol. 20 no. 1 pp. 89-97 2004. [4] L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D, vol. 60(1):259-268, 1992. [5] A. Buades, B. Coll, and J.-M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Modeling and Simulation, vol. 4(2), pp. 490–530, Sep 2005. [6] S. Roth and M. J. Black, “On the spatial statistics of optical flow,” inProc. ICCV, vol. 1. Oct. 2005, pp. 42–49. [7] Christo Ananth,"Iris Recognition Using Active Contours",International Journal of Advanced Research in Innovative Discoveries in Engineering and Applications[IJARIDEA],Volume 2,Issue 1,February 2017,pp:27-32. [8] X. Zhang, M. Burger, X. Bresson, and S. Osher, “Bregmanizednonlocalregularization for deconvolution and sparse reconstruction,” SIAM J.Imag. Sci., vol. 3, no. 3, pp. 253–276, 2010. [9] K. J. Lee, D. Kwon, I. D. Yun, and S. U. Lee, “Optical flow estimationwith adaptive convolution kernel prior on discrete framework,” in Proc.IEEE Conf. CVPR, Jun. 2010, pp. 2504–2511. [10] M. Werlberger, T. Pock, and H. Bischof, “Motion estimation withnon-local total variation regularization,” in Proc. IEEE Conf. CVPR,Jun. 2010, pp. 2464–2471.
  • 5. D.Raja Raghunath et al., International Journal of Advanced Research in Innovative Discoveries in Engineering and Applications[IJARIDEA] Vol.2, Issue 2,27 April 2017, pg. 78-82 © 2017, IJARIDEA All Rights Reserved 82 [11] X. Shen and Y. Wu, “Sparsity model for robust optical flow estimationat motion discontinuities,” in Proc. IEEE Conf. CVPR, Jun. 2010,pp. 2456–2463. [12] K. Jia, X. Wang, and X. Tang, “Optical flow estimation using learnedsparse model,” in Proc. IEEE ICCV, Nov. 2011, pp. 2391–2398. [13] Z. Chen, J. Wang, and Y. Wu, “Decomposing and regularizingsparse/non-sparse components for motion field estimation,” in Proc.IEEE Conf. CVPR, Jun. 2012, pp. 1776–1783. [14] A. Adams, N. Gelfand, and K. Pulli, “Viewfinder alignment,” Comput. Graph. Forum, vol. 27, pp. 597– 606, Apr. 2008. [15] L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion. II,” SIAM J. Numer. Anal., vol. 29, no. 3, pp. 845–866, 1992. [16] L. Alvarez, J. Weickert, and J. Sánchez, “Reliable estimation of dense optical flow fields with large displacements,” Int. J. Comput. Vis., vol. 39, no. 1, pp. 41–56, Aug. 2000. [17] A. Ayvaci, M. Raptis, and S. Soatto, “Occlusion detection and motion estimation with convex optimization,” in Proc. Adv. Neural Inf. Process. Syst., 2010, pp. 100–108. [18] C. Ballester, L. Garrido, V. Lazcano, and V. Caselles, A TV-L1 Optical Flow Method With Occlusion Detection (Lecture Notes in Computer Science), vol. 7476. Berlin, Germany: Springer-Verlag, 2012, pp. 31–40. [19] J. Boulanger, C. Kervrann, and P. Bouthemy, “Space-time adaptation for patch-based image sequence restoration,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 6, pp. 1096–1102, Jun. 2007. [20] [20] T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, “High accuracy optical flow estimation based on a theory for warping,” in Proc. 8thEur. Conf. Comput. Vis., 2004, pp. 25–36.