Abstract
The detection of discontinuities in motion, intensity, color, and depth is a well-studied but difficult problem in computer vision [6]. We discuss the first hardware circuit that explicitly implements either analog or binary line processes in a deterministic fashion. Specifically, we show that the processes of smoothing (using a first-order or membrane type of stabilizer) and of segmentation can be implemented by a single, two-terminal nonlinear voltage-controlled resistor, the “resistive fuse”; and we derive its current-voltage relationship from a number of deterministic approximations to the underlying stochastic Markov random fields algorthms. The concept that the quadratic variation functionals of early vision can be solved via linear resistive networks minimizing power dissipation [37] can be extended to non-convex variational functionals with analog or binary line processes being solved by nonlinear resistive networks minimizing the electrical co-content.
We have successfully designed, tested, and demonstrated an analog CMOS VLSI circuit that contains a 1D resistive network of fuses implementing piecewise smooth surface interpolation. We furthermore demonstrate the segmenting abilities of these analog and deterministic “line processes” by numerically simulating the nonlinear resistive network computing optical flow in the presence of motion discontinuities. Finally, we discuss various circuit implementations of the optical flow computation using these circuits.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A.Blake and A.Zisserman. Visual Reconstruction. MIT Press: Cambridge, MA, 1987.
A.Blake. “Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction,” IEEE Trans. PAMI 11:2–12, 1989.
P.B. Chou and C. Brown. “Multimodal reconstruction and segmentation with Markov random fields and HCF optimization,” Proc. Image Understanding Workshop, pp. 214–221. Cambridge, MA, February, 1988.
E.Gamble and T.Poggio. “Integration of intensity edges with stereo and motion,“ Artif. Intell. Lab Memo No. 970, MIT, Cambridge, 1987.
D.Geiger and F.Girosi. “Parallel and deterministic algorithms for MRFs: surface reconstruction and integration,” AI Memo No. 1114, MIT, Cambridge, 1989.
S.Geman and D.Geman. “Stochastic relaxation, Gibbs distribution and Bayesian restoration of images,“ IEEE Trans. PAMI 6:721–741, 1984.
W.E.L.Grimson, From Images to Surfaces. MIT Press: Cambridge, MA, 1981.
J.G. Harris. “Solving early vision problems with VLSI constraint networks,” AAAI Neural Architectures for Computer Vision Workshop, Minneapolis, August 20, 1988.
J.G.Harris. “An analog VLSI chip for thin plate surface interpolation.“ In Neural Information Processing Systems, D.Touretzky (ed.). Morgan Kaufmann: Palo Alto, 1989.
J.G. Harris and C. Koch. “Resistive fuses: circuit implementations of line discontinuities in vision,” Snowbird Neural Network Workshop, April 4–7, 1989.
J.G.Harris, C.Koch, J.Luo, and J.Wyatt. “Resistive fuses: Analog hardware for detecting discontinuities in early vision,” In Analog VLSI Implementations of Neural Systems, pp. 27–56. C.Mead and M.Ismail (eds.). Kluwer: Norwell, MA, 1989.
E.C.Hildreth. The Measurement of Visual Motion. MIT Press: Cambridge, MA, 1984.
J.J.Hopfield and D.W.Tank. “Neural computation in optimization problems,” Biological Cybernetics 52:141–152, 1985.
B.K.P.Horn. “Determining lightness from an image,” Comput. Graphics Image Process. 3(1): 277–299, 1974.
B.K.P.Horn. Robot Vision. MIT Press: Cambridge, 1986.
B.K.P.Horn. “Parallel networks for machine vision,” Artif. Intell. Lab. Memo, 1071, MIT, Cambridge, 1988.
B.K.P.Horn and B.G.Schunk. “Determining optical flow,” Artificial Intelligence 17:185–203, 1981.
K.Huang. Statistical Mechanics. Wiley: New York, 1963.
J.Hutchinson, C.Koch, J.Luo, and C.Mead. “Computing motion using analog and binary resistive networks,” IEEE Computer 21:52–63, 1988.
K.Ikeuchi and B.K.P.Horn. “Numerical shape from shading and occluding boundaries,” Artificial Intelligence 17:141–184, 1981.
C.Koch. “Seeing chips: analog VLSI circuits for computer vision,” Neural Computation 1:184–200, 1989.
C. Koch, J. Luo, J. Hutchinson, and C. Mead. “Optical flow and surface interpolation in resistive networks: Algorithms and analog VLSI chips,” In Neural Networks, B. Shriver (ed.). IEEE Computer Science Press Book, in press, 1990.
C. Koch, J. Harris, T. Horiuchi, A. Hsu, and J. Luo. “Realtime computer vision and robotics using analog VLSI circuits,” Neural Inform. Process. Systems Conf., Denver, November, 1989.
C.Koch, J.Marroquin, and A.Yuille. “Analog neuronal networks in early vision,” Proc. Natl. Acad. Sci. USA 83:4263–4267, 1986.
S.C. Liu and J.G. Harris. “Generalized smoothing networks in solving early vision problems,” Comput. Vision Pattern Recog. Conf., 1989
J. Luo, C. Koch, and C. Mead. “An experimental subthreshold, analog CMOS two-dimensional surface interpolation circuit,” Neural Inform. Process. Systems Conf., Denver, November, 1988.
D.Marr and T.Poggio. “Cooperative computation of stereo disparity,” Science 194:283–287, 1976.
J.L.Marroquin. “Probabilistic solution of inverse problems,” AI Lab Memo No. 860, MIT, Cambridge, 1985.
J.Marroquin, S.Mitter, and T.Poggio. “Probabilistic solution of ill-posed problems in computational vision,” J. Amer. Statistic. Assoc. 82:76–89, 1987.
J.C.Maxwell. A Treatise on Electricity and Magnetism, 3rd ed., vol. I, pp. 407–408, 1891 Republished by Dover Publications: New York 1954.
C.A. Mead. “A sensitive electronic photoreceptor.” In 1985 Chapel Hill Conference on Very Large Scale Integration, pp. 463–471, 1985.
C.A.Mead. Analog VLSI and Neural Systems. Addison-Wesley: Reading, MA, 1989.
W.Millar. “Some general theorems for non-linear systems possessing resistance,” Philosophical Magazine 42:1150–1160, 1951.
H.H.Nagel. “On the estimation of optical flow: Relations between different approaches and some new results,” Artificial Intelligence 33:299–324, 1987.
J.M.Ortega and W.C.Rheinboldt. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press: New York, 1970.
P. Perona and J. Malik. “A network for multiscale image segmentation,” Proc. 1988 IEEE Intern. Symp. on Circuits and Systems, pp. 2565–2568, Espoo, Finland, June, 1988.
T.Poggio and C.Koch. “Ill-posed problems in early vision: From computational theory to analogue networks,” Proc. Roy. Soc. Lond. B 226:303–323, 1985.
T.Poggio, E.B.Gamble, and J.J.Little. “Parallel integration of vision modules,” Science 242:436–440, 1988.
T.Poggio, V.Torre, and C.Koch. “Computational vision and regularization theory,” Nature 317:314–319, 1985.
T.Poggio, H.Voorhees, and A.Yuille. “A regularized solution to edge detection,” Artif. Intell. Lab Memo No. 833, MIT, Cambridge, 1986.
M.A.Sivilotti, M.A.Mahowald, and C.A.Mead. “Real-time visual computation using analog CMOS processing arrays.” In 1987 Stanford Conf. VLSI, pp. 295–312. MIT Press: Cambridge, 1987.
J.E. Tanner. “Integrated optical motion detection.” Ph.D. Thesis, Dept. of Computer Science, Caltech, 1986.
D.Terzopoulos. “Multilevel computational processes for visual surface reconstruction,” Comput. Vision Graph. Image Process. 24:52–96, 1983.
D.Terzopoulos. “Regularization of inverse problems involving discontinuities,” IEEE Trans. PAMI 8:413–424, 1986.
A.Verri and T.Poggio. “Motion field and optical flow: Qualitative properties,” IEEE Trans. PAMI 11:490–498, 1989.
A.Verri, F.Girosi, and V.Torre. “Mathematical properties of the two dimensional motion field: From singular points to motion parameters,” J. Opt. Soc. Amer. A 6:469–712, 1989.
J.L.WyattJr. and D.L.Standley. “Criteria for robust stability in a class of lateral inhibition networks coupled through resistive grids,” Neural Computation 1:58–67, 1989.
A.Yuille and N.M.Grzywacz. “A computational theory for the perception of coherent visual motion,” Nature 333:71–73, 1988.
Y.T.Zhou and R.Chellappa. “Computation of optical flow using a neural network.” Proc IEEE Intern. Conf. Neural Networks 2:71–78, San Diego, CA, July, 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Harris, J.G., Koch, C., Staats, E. et al. Analog hardware for detecting discontinuities in early vision. Int J Comput Vision 4, 211–223 (1990). https://doi.org/10.1007/BF00054996
Issue Date:
DOI: https://doi.org/10.1007/BF00054996