Noise-resilient estimation of optical flow by use of overlapped basis functions

Sridhar Srinivasan; Rama Chellappa

doi:10.1364/JOSAA.16.000493

Journal of the Optical Society of America A
Vol. 16,
Issue 3,
pp. 493-507
(1999)
•https://doi.org/10.1364/JOSAA.16.000493

Noise-resilient estimation of optical flow by use of overlapped basis functions

Sridhar Srinivasan and Rama Chellappa

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Sridhar Srinivasan and Rama Chellappa, "Noise-resilient estimation of optical flow by use of overlapped basis functions," J. Opt. Soc. Am. A 16, 493-507 (1999)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

Conventional techniques for the computation of optical flow from image gradients are used to formulate the problem as a nonlinear optimization that comprises a gradient constraint term and a field smoothness factor. The results of these techniques are often erroneous, highly sensitive to noise and numerical precision, determined sparsely, and computationally expensive. We regularize the gradient constraint equation by modeling optical flow as a linear combination of a set of overlapped basis functions. We develop a theory for estimating model parameters robustly and reliably. We prove that the extended-least-squares solution proposed here is unbiased and robust to small perturbations in the gradient estimates and to mild deviations from the gradient constraint. Our solution is obtained with a numerically stable sparse matrix inversion, which gives a reliable flow-field estimate over the entire frame. To validate our claims, we perform a series of experiments on standard benchmark data sets at a range of noise levels. Overall, our algorithm outperforms by a wide margin the others considered in the comparison. We demonstrate the applicability of our algorithm to image mosaicking and to motion superresolution through experiments on noisy compressed sequences. We conclude that our flow-field model offers greater accuracy and robustness than conventional optical flow techniques in a variety of situations and permits real-time operation.

Full Article | PDF Article

More Like This

Fast two-frame multiscale dense optical flow estimation using discrete wavelet filters

Haiying Liu, Rama Chellappa, and Azriel Rosenfeld
J. Opt. Soc. Am. A 20(8) 1505-1515 (2003)

Measurement of complex optical flow with use of an augmented generalized gradient scheme

P. J. Sobey, M. G. Nagle, Y. V. Venkatesh, and M. V. Srinivasan
J. Opt. Soc. Am. A 11(11) 2787-2798 (1994)

Differential techniques for optical flow

A. Verri, F. Girosi, and V. Torre
J. Opt. Soc. Am. A 7(5) 912-922 (1990)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (12)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (5)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (46)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Algorithm	Ref.	SNR
		∞		30 dB		20 dB		10 dB
		$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$
Horn and Schunck2 (original)	2	4.19	0.50	5.38	4.15	11.48	10.52	36.59	26.11
Horn and Schunck2 (modified)	2	2.48	0.48	4.91	4.95	13.44	12.40	40.93	28.05
Lucas and Kanade5	5	2.47	0.12	2.98	1.31	6.67	3.47	24.76	11.09
Uras et al.4	4	2.59	0.71	7.06	4.72	19.35	16.51	50.92	31.10
Nagel3	3	2.49	0.21	3.33	2.18	8.24	6.29	25.21	20.51
Anandan6	6	30.64	5.37	32.25	6.64	26.50	13.34	21.49	13.74
Singh7 ( $n = w = 2,$ $N = 2$ )	7	2.24	0.02	2.39	0.06	2.82	1.47	10.45	6.73
Singh7 ( $n = w = 2,$ $N = 4$ )	7	91.70	0.09	87.70	4.07	68.28	13.44	57.94	16.60
Proposed		2.46	0.03	2.49	0.22	2.66	0.68	4.75	1.76

Algorithm	Ref.	SNR
		∞		30 dB		20 dB		10 dB
		$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$
Horn and Schunck2 (original)	2	45.08	10.50	56.31	23.71	60.51	26.21	60.56	27.30
Horn and Schunck2 (modified)	2	32.18	11.57	36.20	13.90	42.95	21.61	47.31	24.85
Uras et al.4	4	—	—	32.57	35.16	34.16	38.19	40.05	36.47
Nagel3	3	33.73	12.93	35.80	13.95	41.85	21.21	47.36	24.61
Anandan6	6	31.46	18.31	41.72	22.73	42.46	23.78	50.86	29.21
Singh7 (step 2, $n = w = 2,$ $N = 2$ )	7	38.83	14.66	43.93	23.24	43.70	21.43	45.58	18.27
Singh7 (step 2, $n = w = 2,$ $N = 4$ )	7	37.63	15.24	47.80	31.74	47.75	29.66	49.52	27.02
Proposed		20.71	22.11	20.81	22.07	26.41	22.44	34.07	23.21

Algorithm	Ref.	SNR
		∞		30 dB		20 dB		10 dB
		$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$
Horn and Schunck2 (original)	2	38.72	27.67	50.06	30.28	57.39	30.38	63.54	29.67
Horn and Schunck2 (modified)	2	2.02	2.27	6.38	8.05	17.15	19.65	32.30	27.08
Uras et al.4	4	0.62	0.52	3.58	7.11	8.95	17.03	20.00	23.60
Nagel3	3	2.44	3.06	7.46	8.89	18.85	20.67	33.38	28.07
Anandan6	6	4.54	3.10	6.88	5.51	14.03	12.55	29.20	24.81
Singh7 (step 1, $n = 2,$ $w = 2$ )	7	1.64	2.44	15.32	30.96	44.87	45.03	75.01	41.71
Singh7 (step 2, $n = 2,$ $w = 2$ )	7	1.18	2.40	6.54	10.93	27.01	24.72	61.86	22.54
Proposed		0.61	0.26	0.78	0.40	2.62	1.59	16.07	10.98

Algorithm	Ref.	SNR
		∞		30 dB		20 dB		10 dB
		$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$
Horn and Schunck2 (original)	2	12.02	11.72	31.36	23.40	42.01	25.59	49.48	25.84
Horn and Schunck2 (modified)	2	2.55	3.67	6.70	7.37	13.64	14.43	25.16	20.83
Uras et al.4	4	4.64	3.48	6.58	4.35	10.14	12.62	18.33	17.82
Nagel3	3	2.94	3.23	7.31	7.46	15.48	16.07	27.11	21.33
Anandan6	6	7.64	4.96	21.56	15.28	31.32	19.67	45.45	24.06
Singh7 (step 1, $n = 2,$ $w = 2$ )	7	17.66	14.25	31.87	27.22	52.50	31.88	71.27	28.38
Singh7 (step 2, $n = 2,$ $w = 2$ )	7	3.29	8.60	14.40	12.92	22.35	17.04	42.89	21.89
Proposed		2.94	1.64	3.23	1.98	4.28	3.54	11.69	7.67

Algorithm	Ref.	SNR
		∞		30 dB		20 dB		10 dB
		$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$	$\bar{∊}$	$\bar{σ}$
Horn and Schunck2 (original)	2	31.69	31.18	42.22	31.69	50.79	30.40	58.04	29.42
Horn and Schunck2 (modified)	2	9.78	16.19	12.92	16.32	19.64	19.77	37.03	28.01
Uras et al.4	4	8.94	15.61	11.87	15.57	16.18	18.34	31.50	28.59
Nagel3	3	10.22	16.51	13.80	16.89	20.74	19.80	38.86	28.43
Anandan6	6	13.36	15.64	17.33	14.75	24.87	19.37	42.46	27.57
Singh7 (step 1, $n = 2,$ $w = 2$ )	7	44.84	23.91	44.56	24.23	47.39	26.36	56.17	31.16
Singh7 (step 2, $n = 2,$ $w = 2$ )	7	42.06	23.52	39.74	22.09	38.03	20.97	43.59	21.84
Proposed		8.94	10.63	9.48	10.32	13.14	12.06	24.75	19.03

Abstract

Cited By

Figures (12)

Tables (5)

Equations (46)

Journal of the Optical Society of America A