Skip to main content
SpringerLink
Log in

Direct computation of shape cues using scale-adapted spatial derivative operators

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

This paper addresses the problem of computing cues to the three-dimensional structure of surfaces in the world directly from the local structure of the brightness pattern of either a single monocular image or a binocular image pair.

It is shown that starting from Gaussian derivatives of order up to two at a range of scales in scale-space, local estimates of (i) surface orientation from monocular texture foreshortening, (ii) surface orientation from monocular texture gradients, and (iii) surface orientation from the binocular disparity gradient can be computed without iteration or search, and by using essentially the same basic mechanism.

The methodology is based on a multi-scale descriptor of image structure called the windowed second moment matrix, which is computed with adaptive selection of both scale levels and spatial positions. Notably, this descriptor comprises two scale parameters; a local scale parameter describing the amount of smoothing used in derivative computations, and an integration scale parameter determining over how large a region in space the statistics of regional descriptors is accumulated.

Experimental results for both synthetic and natural images are presented, and the relation with models of biological vision is briefly discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aloimonos Y. 1988. Shape from texture. Biological Cybernetics, 58:345–360.

    Google Scholar 

  • Babaud J., Witkin A.P., Baudin M., and Duda R.O. 1986. Uniqueness of the Gaussian kernel for scale-space filtering. IEEE Trans. Pattern Anal. and Machine Intell., 8(1):26–33.

    Google Scholar 

  • Bergen J. and Adelson E. 1988. Early vision and texture perception. Nature, 333:363–364.

    Google Scholar 

  • Bigün J., Granlund G.H., and Wiklund J. 1991. Multidimensional orientation estimation with applications to texture analysis and optical flow. IEEE Trans. Pattern Anal. and Machine Intell., 13(8):775–790.

    Google Scholar 

  • Bijl P. and Koenderink J.J. 1993. Visibility of elliptical Gaussian blobs. Vision Research, 33(2):243–255.

    Google Scholar 

  • Blake A. and Marinos C. 1990a. Shape from texture: Estimation, isotropy and moments. J. of Artificial Intelligence, 45:323–380.

    Google Scholar 

  • Blake, A. and Marinos, C. 1990b. Shape from texture: The homogeneity hypothesis. In Proc. 3rd Int. Conf. on Computer Vision, Osaka, Japan, pp. 350–353, IEEE Computer Society Press.

  • Blakemore C. 1970. A new kind of stereoscopic vision. Vision Research, 10:1181–1200.

    Google Scholar 

  • Blostein D. and Ahuja N. 1989a. A multiscale region detector. Computer Vision, Graphics, and Image Processing, 45:22–41.

    Google Scholar 

  • Blostein D. and Ahuja N. 1989b. Shape from texture: Integrating texture element extraction and surface estimation. IEEE Trans. Pattern Anal. and Machine Intell., 11(12):1233–1251.

    Google Scholar 

  • Brown L.G. and Shvaytser H. 1990. Surface orientation from projective foreshortening of isotropic texture autocorrelation. IEEE Trans. Pattern Anal. and Machine Intell., 12(6):584–588.

    Google Scholar 

  • Caelli T. 1985. Three processing characteristics of visual texture segmentation. Spatial Vision, 1:19–30.

    Google Scholar 

  • Casadei, S., Mitter, S., and Perona, P. 1992. Boundary detection in piecewise homogeneous images. In G. Sandini (ed.), Proc. 2nd European Conf. on Computer Vision, volume 588 of Lecture Notes in Computer Science, Springer-Verlag, pp. 174–183.

  • Davis L., Janos L., and Dunn S. 1983. Efficient recovery of shape from texture. IEEE Trans. Pattern Anal. and Machine Intell., 5(5):485–492.

    Google Scholar 

  • Field D.J. 1987. Relations between the statistics of natural images and the response properties of cortical cells. J. of the Optical Society of America, 4:2379–2394.

    Google Scholar 

  • Florack L.M.J., ter Haar Romeny B.M., Koenderink J.J., and Viergever M.A. 1992. Scale and the differential structure of images. Image and Vision Computing, 10(6):376–388.

    Google Scholar 

  • Förstner, M.A. and Gülch, E. 1987. A fast operator for detection and precise location of distinct points, corners and centers of circular features. In Proc. Intercommission Workshop of the Int. Soc. for Photogrammetry and Remote Sensing, Interlaken, Switzerland.

  • Gårding, J. 1991. Shape from Surface Markings. Ph.D. Thesis, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm.

  • Gårding J. 1992. Shape from texture for smooth curved surfaces in perspective projection. J. of Mathematical Imaging and Vision, 2:329–352.

    Google Scholar 

  • Gårding J. 1993. Shape from texture and contour by weak isotropy. J. Of Artificial Intelligence, 64(2):243–297.

    Google Scholar 

  • Gårding, J. and Lindeberg, T. 1994. Direct estimation of local surface shape in a fixating binocular vision system. Technical Report ISRN KTH/NA/P-94/08-SE, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology. Shortened version in J.-O. Eklundh (ed.), Proc. 3rd European Conf. on Computer Vision, Stockholm, Sweden, volume 800 of Lecture Notes in Computer Science, Springer-Verlag, pp. 365–376.

  • Gibson J. 1950. The Perception of the Visual World, Houghton Mifflin, Boston.

    Google Scholar 

  • Jones, D.G. and Malik, J. 1992. Determining three-dimensional shape from orientation and spatial frequency disparities. In Proc. 2nd European Conf. on Computer Vision, Santa Margherita Ligure, Italy, pp. 661–669.

  • Jones J. and Palmer L. 1987a. An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. J. of Neurophysiology, 58:1233–1258.

    Google Scholar 

  • Jones J. and Palmer L. 1987b. The two-dimensional spatial structure of simple receptive fields in cat striate cortex. J. of Neurophysiology, 58:1187–1211.

    Google Scholar 

  • Julesz B. 1981. Textons, the elements of perception and their interactions. Nature, 290:91–97.

    Google Scholar 

  • Kanatani K. 1984. Detection of surface orientation and motion from texture by a stereological technique. J. of Artificial Intelligence, 23:213–237.

    Google Scholar 

  • Kanatani K. and Chou T.C. 1989. Shape from texture: General principle. J. of Artificial Intelligence, 38:1–48.

    Google Scholar 

  • Koenderink J.J. 1984. The structure of images. Biological Cybernetics, 50: 363–370.

    Google Scholar 

  • Koenderink J.J. and van Doorn A.J. 1976. Geometry of binocular vision and a model for stereopsis. Biological Cybernetics, 21:29–35.

    Google Scholar 

  • Koenderink J.J. and van Doorn A.J. 1990. Receptive field families. Biological Cybernetics, 63:291–298.

    Google Scholar 

  • Koenderink J.J. and van Doorn A.J. 1992. Generic neighborhood operators. IEEE Trans. Pattern Anal. and Machine Intell., 14(6):597–605.

    Google Scholar 

  • Lindeberg T. 1990. Scale-space for discrete signals. IEEE Trans. Pattern Analysis and Machine Intell., 12(3):234–254.

    Google Scholar 

  • Lindeberg T. 1993a. Detecting salient blod-like image structures and their scales with a scale-space primal sketch: A method for focus-of-attention. International Journal of Computer Vision, 11(3):283–318.

    Google Scholar 

  • Lindeberg T. 1993b. Discrete derivative approximations with scale-space properties: A basis for low-level feature extraction. J. of Mathematical Imaging and Vision, 3(4):349–376.

    Google Scholar 

  • Lindeberg, T. 1993c. On scale selection for differential operators. In K.A. Høgdra, B. Braathen, and K.H. (eds.), Proc. 8th Scandinavian Conference on Image Analysis, Norwegian Society for Image Processing and Pattern Recognition, Tromsø, Norway, pp. 857–866.

  • Lindeberg T. 1994a. Scale-Space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science, Kluwer Academic Publishers: Dordrecht, Netherlands.

    Google Scholar 

  • Lindeberg, T. 1994b. Scale selection for differential operators. Technical Report ISRN KTH/NA/P-94/03-SE, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology. (Submitted).

  • Lindeberg T. and Gårding J. 1993. Shape from texture from a multi-scale perspective. Technical Report ISRN KTH/NA/P--93/03--SE, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm. Shortened version in H.-H. Nagel (ed.), Proc. 4th International Conference on Computer Vision, IEEE Computer Society Press: Berlin, Germany, pp. 683–691.

    Google Scholar 

  • Lindeberg, T. and Gårding, J. 1994. Shape-adapted smoothing in estimation of 3-D depth cues from affine distortions of local 2-D brightness structure. In J.-O. Eklundh (ed.), Proc. 3rd European Conf. on Computer Vision, Stockholm, Sweden, volume 800 of Lecture Notes in Computer Science, Springer-Verlag, pp. 389–400.

  • Malik J. and Perona P. 1990. Preattentive texture discrimination with early vision mechanisms. J. of the Optical Society of America, 7:923–932.

    Google Scholar 

  • Mardia K.V. 1972. Statistics of Directional Data. Academic Press: London.

    Google Scholar 

  • Marr D. 1982. Vision. W.H. Freeman: New York.

    Google Scholar 

  • Marr D.C. 1976. Early processing of visual information. Phil. Trans. Royal Soc (B), 27S:483–524.

    Google Scholar 

  • O'Neill B. 1966. Elementary Differential Geometry. Academic Press: Orlando, Florida.

    Google Scholar 

  • Pentland A.P. 1986. Shading into texture. J. of Artificial Intelligence, 29:147–170.

    Google Scholar 

  • Pollard S.B., Mayhew J.E.W., and Frisby J.P. 1985. PMF: A stereo correspondence algorithm using a disparity gradient limit. Perception, 14:449–470.

    Google Scholar 

  • Rao A.R. and Schunk B.G. 1991. Computing oriented texture fields. CVGIP: Graphical Models and Image Processing, 53(2):157–185.

    Google Scholar 

  • Rogers B. and Cagenello R. 1989. Orientation and curvature disparities in the perception of three-dimensional surfaces. Investigative Opthalmology and Visual Science, 30:262.

    Google Scholar 

  • Stone, J.V. 1990. Shape from texture: Textural invariance and the problem of scale in perspective images of surfaces. In Proc. British Machine Vision Conference, Oxford, England, pp. 181–186.

  • Super, B.J. and Bovik, A.C. 1992. Shape-from-texture by waveletbased measurement of local spectral moments. In Proc. IEEE Comp. Soc. Conf. on Computer Vision and Pattern Recognition, Champaign, Illinois, pp. 296–301.

  • Turner M. 1986. Texture discrimination by Gabor functions. Biological Cybernetics, 55:71–82.

    Google Scholar 

  • Tyler C. and Sutter E. 1979. Depth from spatial frequency difference: An old kind of stereopsis? Vision Research, 19:859–865.

    Google Scholar 

  • Voorhees, H. and Poggio, T. 1987. Detecting textons and texture boundaries in natural images. In Proc. 1st Int. Conf. on Computer Vision, London, England.

  • Wildes R.P. 1981. Direct recovery of three-dimensional scene geometry from binocular stereo disparity. IEEE Trans. Pattern Anal. and Machine Intell., 13(8):761–774.

    Google Scholar 

  • Witkin A.P. 1981. Recovering surface shape and orientation from texture. J. of Artificial Intelligence, 17:17–45.

    Google Scholar 

  • Witkin, A.P. 1983. Scale-space filtering. In Proc. 8th Int. Joint Conf. Art. Intell., Karlsruhe, West Germany, pp. 1019–1022.

  • Young R.A. 1985. The Gaussian derivative theory of spatial vision: Analysis of cortical cell receptive field line-weighting profiles. Technical Report GMR-4920, Computer Science Department, General Motors Research Lab., Warren, Michigan.

    Google Scholar 

  • Young R.A. 1987. The Gaussian derivative model for spatial vision: I. Retinal mechanisms. Spatial Vision, 2:273–293.

    Google Scholar 

  • Yuille A.L. and Poggio T.A. 1986. Scaling theorems for zerocrossings. IEEE Trans. Pattern Anal. and Machine Intell., 8:15–25.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computational Vision and Active Perception Laboratory (CVAP), Department of Numerical Analysis and Computing Science, KTH (Royal Institute of Technology), S-100 44, Stockholm, Sweden

    Jonas Gårding & Tony Lindeberg

Authors
  1. Jonas Gårding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tony Lindeberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

We would like to thank Jan-Olof Eklundh for continuous support and encouragement. We are grateful to Narendra Ahuja at University of Illinois and John P. Frisby at University of Sheffield for kindly providing several of the images used in the paper. This work was partially performed under the Esprit-BRA project InSight and the Esprit-NSF collaboration Diffusion. The support from the Swedish National Board for Industrial and Technical Development, NUTEK, and the Swedish Research Council for Engineering Sciences, TFR, is gratefully acknowledged. The first author has carried out part of this work while visiting the AIVRU group at University of Sheffield, and he is grateful for their hospitality as well as for the financial support of the Foundation Blanceflor Boncompagni-Ludovisi, née Bildt, and the Swedish Institute.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gårding, J., Lindeberg, T. Direct computation of shape cues using scale-adapted spatial derivative operators. Int J Comput Vision 17, 163–191 (1996). https://doi.org/10.1007/BF00058750

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00058750

Keywords

Search

Navigation