nach oben

Erschienen in:

2016 | OriginalPaper | Buchkapitel

Focal Flow: Measuring Distance and Velocity with Defocus and Differential Motion

verfasst von : Emma Alexander, Qi Guo, Sanjeev Koppal, Steven Gortler, Todd Zickler

Erschienen in: Computer Vision – ECCV 2016

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We present the focal flow sensor. It is an unactuated, monocular camera that simultaneously exploits defocus and differential motion to measure a depth map and a 3D scene velocity field. It does so using an optical-flow-like, per-pixel linear constraint that relates image derivatives to depth and velocity. We derive this constraint, prove its invariance to scene texture, and prove that it is exactly satisfied only when the sensor’s blur kernels are Gaussian. We analyze the inherent sensitivity of the ideal focal flow sensor, and we build and test a prototype. Experiments produce useful depth and velocity information for a broader set of aperture configurations, including a simple lens with a pillbox aperture.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Colorful Image Colorization

Nächstes Kapitel An Evaluation of Computational Imaging Techniques for Heterogeneous Inverse Scattering

Proof. From optical flow, \(k *P_t = k *(-u_1P_x-u_2P_y-u_3(xP_x+yP_y))\). Because \(k *xP_x = x(k *P_x) - (xk *P_x) = x(k *P_x) - (k+xk_x) *P\), then \(k *P_t = -u_1I_x-u_2I_y-u_3(xI_x+yI_y)+u_3(2k+xk_x+yk_y)*P\). Likewise, \(k_t *P = k_\sigma \dot{\sigma } *P \propto \) \( (2k+rk_r) *P\). \(\square \)

Proof. Because w is a function of time (and not spatial frequency), \(\hat{m}\) a function of spatial frequency (and not time), and \(\hat{\kappa }\) a function of the time-frequency product \(\sigma \hat{r}\), this equation takes the form \(h_0(xy) = e^{f(x)g(y)}\) or \(h(xy) = \ln h_0 = f(x)g(y)\). Considering \(x=1\) and \(y=1\) in turn, we see that \(g \propto h \propto f\), so that \(f(x)f(y) \propto f(xy)\). Differentiating by x and considering the case \(x=1\) results in the differential equation \(f(y) \propto yf'(y)\), with general solution \(f(y) \propto y^{n}\), equivalently \(y^{2n}\), \(n \in \mathbb {C}\). Realness of v implies \(n\in \mathbb {R}\). Differentiating \(\int _0^{\hat{r}} \frac{\hat{m}(s')}{s'}ds' \propto \hat{r}^{2n}\) yields \(\hat{m} \propto \hat{r}^{2n}\). \(\square \)

Proof. From the Fourier Slice Theorem [32, 33], denoting by \(\mathcal {F}_1\) the 1D Fourier transform, we have \(\mathcal {F}_1\left[ \int \kappa (x,y) dy \right] = \hat{\kappa }(\omega _x, 0 ) = e^{-|\omega _x|^{2n}}\). This function is not positive definite for \(n \ge 2\) (which can be seen by taking \(C(n) = \sum \sum z_i z_j e^{-|x_i-x_j|^{2n}}\) for \(z=[1,-2,1]\) and \(x = [-.1^{2n},0,.1^{2n}]\), and noting that both C(2) and \(\frac{dC}{dn}\) are negative), so by Bochner’s theorem it cannot be the (1D) Fourier transform of a finite positive Borel measure. The only property of such a measure that \(\int \kappa \) could lack is non-negativity, so the existence of negative values of \(\kappa \) follows immediately. \(\square \)

Raghavendra, C.S., Sivalingam, K.M., Znati, T.: Wireless Sensor Networks. Springer, Heidelberg (2006)MATH

Humber, J.S., Hyslop, A., Chinn, M.: Experimental validation of wide-field integration methods for autonomous navigation. In: Intelligent Robots and Systems (IROS) (2007)

Duhamel, P.E.J., Perez-Arancibia, C.O., Barrows, G.L., Wood, R.J.: Biologically inspired optical-flow sensing for altitude control of flapping-wing microrobots. IEEE/ASME Trans. Mechatron. 18(2), 556–568 (2013)CrossRef

Floreano, D., Zufferey, J.C., Srinivasan, M.V., Ellington, C.: Flying Insects and Robots. Springer, Heidelberg (2009)

Koppal, S.J., Gkioulekas, I., Zickler, T., Barrows, G.L.: Wide-angle micro sensors for vision on a tight budget. In: Computer Vision and Pattern Recognition (CVPR) (2011)

Horn, B.K., Fang, Y., Masaki, I.: Time to contact relative to a planar surface. In: Intelligent Vehicles Symposium (IV) (2007)

Horn, B.K., Schunck, B.G.: Determining optical flow. In: 1981 Technical Symposium East, International Society for Optics and Photonics (1981)

Lee, D.N.: A theory of visual control of braking based on information about time-to-collision. Perception 5, 437–59 (1976)CrossRef

Horn, B.K., Fang, Y., Masaki, I.: Hierarchical framework for direct gradient-based time-to-contact estimation. In: Intelligent Vehicles Symposium (IV) (2009)

10.

Grossmann, P.: Depth from focus. Pattern Recogn. Lett. 5(1), 63–69 (1987)CrossRef

11.

Pentland, A.P.: A new sense for depth of field. Pattern Anal. Mach. Intell. 9(4), 523–531 (1987)CrossRef

12.

Subbarao, M., Surya, G.: Depth from defocus: a spatial domain approach. Int. J. Comput. Vis. 13(3), 271–294 (1994)CrossRef

13.

Rajagopalan, A., Chaudhuri, S.: Optimal selection of camera parameters for recovery of depth from defocused images. In: Computer Vision and Pattern Recognition (CVPR) (1997)

14.

Watanabe, M., Nayar, S.K.: Rational filters for passive depth from defocus. Int. J. Comput. Vis. 27(3), 203–225 (1998)CrossRef

15.

Zhou, C., Lin, S., Nayar, S.: Coded aperture pairs for depth from defocus. In: International Conference on Computer Vision (ICCV) (2009)

16.

Levin, A.: Analyzing depth from coded aperture sets. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part I. LNCS, vol. 6311, pp. 214–227. Springer, Heidelberg (2010)CrossRef

17.

Zhou, C., Lin, S., Nayar, S.K.: Coded aperture pairs for depth from defocus and defocus deblurring. Int. J. Comput. Vis. 93(1), 53–72 (2011)CrossRef

18.

Levin, A., Fergus, R., Durand, F., Freeman, W.T.: Image and depth from a conventional camera with a coded aperture. In: ACM Transactions on Graphics (TOG) (2007)

19.

Veeraraghavan, A., Raskar, R., Agrawal, A., Mohan, A., Tumblin, J.: Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing. In: ACM Transactions on Graphics (TOG) (2007)

20.

Chakrabarti, A., Zickler, T.: Depth and deblurring from a spectrally-varying depth-of-field. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 648–661. Springer, Heidelberg (2012)

21.

Farid, H., Simoncelli, E.P.: Range estimation by optical differentiation. J. Opt. Soc. Am. A 15(7), 1777–1786 (1998)CrossRef

22.

Myles, Z., da Vitoria Lobo, N.: Recovering affine motion and defocus blur simultaneously. Pattern Anal. Mach. Intell. 20(6), 652–658 (1998)CrossRef

23.

Favaro, P., Burger, M., Soatto, S.: Scene and motion reconstruction from defocused and motion-blurred images via anisotropic diffusion. In: Pajdla, T., Matas, J.G. (eds.) ECCV 2004. LNCS, vol. 3021, pp. 257–269. Springer, Heidelberg (2004)CrossRef

24.

Lin, H.Y., Chang, C.H.: Depth from motion and defocus blur. Opt. Eng. 45(12), 127201–127201 (2006)CrossRef

25.

Seitz, S.M., Baker, S.: Filter flow. In: International Conference on Computer Vision (ICCV) (2009)

26.

Paramanand, C., Rajagopalan, A.N.: Depth from motion and optical blur with an unscented Kalman filter. IEEE Trans. Image Process. 21(5), 2798–2811 (2012)MathSciNetCrossRef

27.

Sellent, A., Favaro, P.: Coded aperture flow. In: Jiang, X., Hornegger, J., Koch, R. (eds.) GCPR 2014. LNCS, vol. 8753, pp. 582–592. Springer, Heidelberg (2014)

28.

Rajagopalan, A., Chaudhuri, S., Mudenagudi, U.: Depth estimation and image restoration using defocused stereo pairs. Pattern Anal. Mach. Intell. 26(11), 1521–1525 (2004)CrossRef

29.

Tao, M., Hadap, S., Malik, J., Ramamoorthi, R.: Depth from combining defocus and correspondence using light-field cameras. In: International Conference on Computer Vision (ICCV) (2013)

30.

Rudin, W.: Functional Analysis. McGraw-Hill, New York (1991)MATH

31.

Alexander, E., Guo, Q., Koppal, S., Gortler, S., Zickler, T.: Focal flow: supporting material. Technical report TR-01-16, School of Engineering and Applied Science, Harvard University (2016)

32.

Bracewell, R.N.: Strip integration in radio astronomy. Aust. J. Phys. 9(2), 198–217 (1956)MathSciNetCrossRefMATH

33.

Ng, R.: Fourier slice photography. In: ACM Transactions on Graphics (TOG) (2005)

34.

Schechner, Y.Y., Kiryati, N.: Depth from defocus vs. stereo: how different really are they? Int. J. Comput. Vis. 39(2), 141–162 (2000)CrossRefMATH

35.

Tai, Y.W., Brown, M.S.: Single image defocus map estimation using local contrast prior. In: International Conference on Image Processing (ICIP) (2009)

Titel: Focal Flow: Measuring Distance and Velocity with Defocus and Differential Motion
verfasst von: Emma Alexander
Qi Guo
Sanjeev Koppal
Steven Gortler
Todd Zickler
Verlag: Springer International Publishing
Buch: Computer Vision – ECCV 2016
Print ISBN: 978-3-319-46486-2

Electronic ISBN: 978-3-319-46487-9

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-46487-9_41

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"