### Citations

5041 |
Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images
- Geman, Geman
- 1984
(Show Context)
Citation Context ...drawn into the ground state, the positions of discontinuities will be stable in the required manner. And this is precisely what is achieved by certain statistical algorithms (Kirkpatrick et al. 1982, =-=Geman and Geman 1984-=-), and the deterministic “Graduated Non-convexity” (GNC) algorithm, proposed in this book. Some examples of the operation of the GNC algorithm, reconstructing various kinds of visual data, are shown i... |

4106 | Communicating Sequential Processes
- Hoare
- 1978
(Show Context)
Citation Context ...theories of Psychophysics (e.g. Julesz 1971, Marr 1976b) Cognitive Science (e.g. Hinton and Sejnowski 1983, Hopfield 1984), Pattern Recognition (e.g. Rosenfeld et al. 1976) and Computer Science (e.g. =-=Brookes et al. 1984-=-, Milner 1980). In vision, there have been cooperative algorithms for optical flow computation (Horn and Schunk 1981), analysis of shading (Woodham 1977, Ikeuchi and Horn 1981), analysis of motion (Ul... |

3829 |
Dynamic Programming
- Bellman
- 1957
(Show Context)
Citation Context ...obtaining the convex F ∗ is generally applicable to integer programming problems, but at the price of being a rather poor approximation compared with the F ∗ used in GNC. Finally dynamic programming (=-=Bellman and Dreyfus 1962-=-), previously used for curve detection by Montanari (1971), has been successfully applied to the weak string by Papoulias (1985). 6.3.2 Simulated annealing Simulated annealing is a powerful, general m... |

2327 |
Neural networks and physical systems with emergent collective computational abilities
- Hopfield
- 1982
(Show Context)
Citation Context ...ally feasible can be designed for them. Furthermore, how far can energy functions be built or refined by inductive learning, as exhibited to some degree in neural networks (Hinton and Sejnowski 1983, =-=Hopfield 1982-=-, Wallace 1985). 8.2 Hardware Implementation It is clear from the parallel nature of the GNC algorithm (when simultaneous updating is used) that it maps efficiently onto massively parallel machines, w... |

1796 | A Practical Guide to Splines - Boor - 2001 |

1707 |
Robot Vision
- Horn
- 1986
(Show Context)
Citation Context ...end itself more naturally to VLSI implementation. Another intriguing possibility is that of parallel analogue hardware. Classical quadratic schemes can of course be realised with analogue components (=-=Horn 1986-=-, Poggio et al. 1985). Is this still true when weak continuity constraints are in force? We have done some simulations that strongly suggest feasibility. The benefits in terms of simplicity and speed ... |

1605 | Spatial interaction and the statistical analysis of lattice systems (with discussion - Besag - 1974 |

1227 |
A Treatise on the Theory of Bessel Functions
- Watson
- 1944
(Show Context)
Citation Context ... configuration u is given by ∫ u(x) = where the Green’s function is G(x, x ′ ) = 1 K0 2πλ2 G(x, x ′ )d(x ′ ) dA (4.31) ( ) ′ |x − x | λ (4.32) and K0 is a modified Bessel function of the second kind (=-=Watson 1952-=-). The energy is ∫ E = d(x)(d(x) − u(x)) dA (4.33) This is a straightforward analogue of the 1D method. Further details are given in appendix A. The Green’s function has the important asymptotic prope... |

916 |
Receptive fields and functional architecture of monkey striate cortex
- Hubel, Wiesel
- 1968
(Show Context)
Citation Context ...alian vision is understood in some detail (Marks et al. 1964); and the elegant, orderly, spatial correspondence of feature detectors in the brain with the array of cells in the retina, is well known (=-=Hubel and Wiesel 1968-=-). There has also been much dialogue between psychophysics and neurophysiology/neuroanatomy. Examples are the discovery of spatial bandpass channels (Campbell and Robson 1968, Braddick et al. 1978), a... |

807 |
Neurons with graded response have collective computational properties like those of two-state neurons
- Hopfield
- 1984
(Show Context)
Citation Context ... achieve a useful effect.6 Chapter 1 Networks of this kind have received much attention in theories of Psychophysics (e.g. Julesz 1971, Marr 1976b) Cognitive Science (e.g. Hinton and Sejnowski 1983, =-=Hopfield 1984-=-), Pattern Recognition (e.g. Rosenfeld et al. 1976) and Computer Science (e.g. Brookes et al. 1984, Milner 1980). In vision, there have been cooperative algorithms for optical flow computation (Horn a... |

743 | Differential geometry of curves and surfaces - Carmo, P - 1976 |

666 |
Scale-space filtering
- Witkin
- 1983
(Show Context)
Citation Context ...t coarse and fine scales. But under linear filters such as the gaussian and its derivatives, complex structure arises, which is difficult to track and harder still to interpret (Asada and Brady 1986, =-=Witkin 1983-=-). A weak string scale-space for a silhouette taken from a real image, is shown Figure 2.14: Scale-space filtering. The hand drawn curve (a) segmented at coarse scale (b) and reconstructed by fitting ... |

642 |
Neural computations of decisions in optimization problems
- Hopfield, Tank
- 1985
(Show Context)
Citation Context ...course with totally different extrema. Hopfield’s procedure uses F (p) with an intermediate value of p. Recent work suggests that, as in GNC, sweeping p from 1 to 0 may be useful in the neural model (=-=Hopfield and Tank 1985-=-). Whereas such a strategy will be proven, in the next chapter, to be effective in GNC, there are as yet no corresponding proofs for neural networks. The main difference from GNC is that the convex ap... |

596 |
The Interpretation of Visual Motion
- Ullman
- 1979
(Show Context)
Citation Context ... practice by executing an algorithm that implements them, on a computer. All this has led to considerable enrichment of studies of human vision (e.g. Marr and Poggio 1979, Mayhew 1982, Hildreth 1984, =-=Ullman 1979-=-b, Koenderinck and van Doorn 1976). 3. Complete, though simple, vision systems can be built and tested. The restriction to study the visual systems that nature has kindlyModelling Piecewise Continuit... |

517 |
Theory of Elasticity
- Landau, Lifschitz
- 1959
(Show Context)
Citation Context ...y can be creased without any associated energy increase. In order to detect creases, a 2nd order surface must be used - one which has a high energy density where it is tightly curved. The thin plate (=-=Landau and Lifschitz 1959-=-, Grimson 1981, Terzopoulos 1983) has this property: intuitively it is easy to crease a sheet of elastic (a membrane) but hard to crease a sheet of steel. In this chapter, it is shown that the plate (... |

408 |
Scene labeling by relaxation operations
- Rosenfeld, Hummel, et al.
- 1976
(Show Context)
Citation Context ...orks of this kind have received much attention in theories of Psychophysics (e.g. Julesz 1971, Marr 1976b) Cognitive Science (e.g. Hinton and Sejnowski 1983, Hopfield 1984), Pattern Recognition (e.g. =-=Rosenfeld et al. 1976-=-) and Computer Science (e.g. Brookes et al. 1984, Milner 1980). In vision, there have been cooperative algorithms for optical flow computation (Horn and Schunk 1981), analysis of shading (Woodham 1977... |

382 |
Numerical solution of partial differential equations: finite difference methods
- Smith
- 1990
(Show Context)
Citation Context ...-relaxation (SOR): SOR can be made to converge much faster than Jacobi. If the decay time for Jacobi is γ then that for SOR is reduced to √ γ/8 - provided the following optimal SOR parameter is used (=-=Smith 1978-=-): ( w = 2 1 + √ 1 + 2γ 1 + γ )−1 . (7.40) Assuming λ (µ 2 ) to be somewhat greater than 1, this is approximated by ( w = 2 1 + √ ) −1 2/γ . (7.41) Experiments confirm that this value of w does indeed... |

376 |
Application of Fourier analysis to the visibility of gratings
- Campbell, Robson
- 1968
(Show Context)
Citation Context ...n the retina, is well known (Hubel and Wiesel 1968). There has also been much dialogue between psychophysics and neurophysiology/neuroanatomy. Examples are the discovery of spatial bandpass channels (=-=Campbell and Robson 1968-=-, Braddick et al. 1978), and understanding the perception of coloured light (Livingstone and Hubel 1984, Jameson and Hurvich 1961) and surface colour (Land 1983, Zeki 1983). These instances are but pa... |

373 |
The interpretation of a moving retinal image
- Longuet-Higgins, Prazdny
- 1980
(Show Context)
Citation Context ...however, the28 Chapter 2 sudden change in depth at the occluding edge, falling off one step onto the next, is quite unambiguous. (Motion parallax similarly facilitates perception of occluding edges (=-=Longuet-Higgins and Prazdny 1980-=-)). 2.2.4 Surface descriptions There are two distinct types of usage of information about visible surfaces: reasoning about visible objects, and path planning or collision avoidance. In the first, the... |

356 |
Principles of Neurodynamics
- Rosenblatt
- 1962
(Show Context)
Citation Context ...ear system 4 . So purely linear systems are inadequate for visual reconstruction. There must be some non-linearity, even if it is just a thresholding operation. This is what occurs in the Perceptron (=-=Rosenblatt 1962-=-, Minsky and Papert 1969), a simple, neuron-like switching element that computes a weighted 4 A linear system is one that simply outputs a weighted sum of its inputs.Modelling Piecewise Continuity 11... |

326 |
Machine perception of three-dimensional solids
- Roberts
- 1965
(Show Context)
Citation Context ...). These instances are but parts of a very large body of knowledge of biological vision. Over the last two decades, computers have introduced a new strand into the study of vision. The earliest work (=-=Roberts, 1965-=-) produced systems able to recognise simple objects and manipulate them in a controlled way (Ambler et al. 1975). These systems were, of course, vastly inferior to the biological systems studied by th... |

279 |
Computational vision and regularization theory
- Poggio, Torre, et al.
- 1985
(Show Context)
Citation Context ...more naturally to VLSI implementation. Another intriguing possibility is that of parallel analogue hardware. Classical quadratic schemes can of course be realised with analogue components (Horn 1986, =-=Poggio et al. 1985-=-). Is this still true when weak continuity constraints are in force? We have done some simulations that strongly suggest feasibility. The benefits in terms of simplicity and speed are tempting, and th... |

254 |
Symbolic reasoning among 3-D models and 2-D images
- Brooks
- 1981
(Show Context)
Citation Context ...shape of the patch. This is nothing to be ashamed of - descriptions of this sort are already a powerful handle for matching visible surfaces to one another (Pollard et al. 1987) and to stored models (=-=Brooks 1981-=-). New sources of information, such as analysis of surface shading, might add usefully to such descriptions - but that possibility must be left for discussion elsewhere (Ikeuchi and Horn 1981, Ikeuchi... |

248 | Numerical shape from shading and occluding boundaries
- Ikeucbi, Horn
- 1981
(Show Context)
Citation Context ...and Computer Science (e.g. Brookes et al. 1984, Milner 1980). In vision, there have been cooperative algorithms for optical flow computation (Horn and Schunk 1981), analysis of shading (Woodham 1977, =-=Ikeuchi and Horn 1981-=-), analysis of motion (Ullman 1979a), computation of lightness (Horn 1974, Blake 1985c) and reconstruction of stereoscopically viewed surfaces (Grimson 1981, Terzopoulos 1983). The implementation of w... |

243 |
Multi-level adaptive solutions to boundary value problems
- BRANDT
- 1977
(Show Context)
Citation Context ...ons do, however, exist: “simultaneous over-relaxation” and “chequerboard SOR”. 6.2.2 Multi-grid algorithms Terzopoulos greatly enhanced the basic SOR algorithm by making use of multi-grid techniques (=-=Brandt 1977-=-), in which relaxation takes place simultaneously, on coarse and fine arrays. Use of four arrays, with density inThe Discrete Problem 123 Nodes: i ∈ {0, ..., N}, j ∈ {0, ..., N}. Iterate n = 1, 2, ..... |

234 | The curvature primal sketch
- Asada, Brady
- 1986
(Show Context)
Citation Context ...ary role. Commonly, a curve is converted to tangent angle/arc-length (θ, s) form, and filtered to detect corners (step discontinuities in θ) and possibly also curvature discontinuities (Perkins 1978, =-=Asada and Brady 1986-=-, Ramer 1975, Zucker et al. 1977, Zucker 1982, Blake et al. 1986a). This may be done at a variety of spatial scales in order to obtain both coarse and fine views of the curve’s shape. Corners, for ins... |

206 |
Convex Functions
- Roberts, Varberg
- 1973
(Show Context)
Citation Context ... ∑ by “balancing” the positive second derivatives in the first term D = (ui − di) 2 against the negative second derivatives in the g∗ terms. The i balancing procedure is to test the Hessian matrix H (=-=Roberts and Varberg 1976-=-) of F ∗ : if H is positive definite then F ∗ (u) is a convex function1 of u. The Hessian H of F ∗ is ∂2 F ∗ Hij = ∂ui∂uj = 2Ii,j + ∑ g ∗′′ (uk − uk−1)Qk,iQk,j, (7.1) where I is the identity matrix an... |

179 |
PMF: A stereo correspondence algorithm using a disparity gradient limit
- Pollard, Mayhew, et al.
- 1985
(Show Context)
Citation Context ... stereo data. A stereo pair (a) of a foam block, with a step discontinuity across the middle, that is all but invisible monocularly. Stereo correspondence using a state-of-the-art matching algorithm (=-=Pollard et al. 1985-=-) produces depths along sparse contours (b). The reconstructed surface is shown with its contour of discontinuity (c).Applications of Piecewise Continuous Reconstruction 31 Figure 2.11: Isometric plo... |

157 | Anatomy and physiology of a color system in the primate visual cortex
- Livingstone, Hubel
- 1984
(Show Context)
Citation Context ...physics and neurophysiology/neuroanatomy. Examples are the discovery of spatial bandpass channels (Campbell and Robson 1968, Braddick et al. 1978), and understanding the perception of coloured light (=-=Livingstone and Hubel 1984-=-, Jameson and Hurvich 1961) and surface colour (Land 1983, Zeki 1983). These instances are but parts of a very large body of knowledge of biological vision. Over the last two decades, computers have i... |

140 |
Determining Lightness from an Image
- Horn
- 1974
(Show Context)
Citation Context ...een cooperative algorithms for optical flow computation (Horn and Schunk 1981), analysis of shading (Woodham 1977, Ikeuchi and Horn 1981), analysis of motion (Ullman 1979a), computation of lightness (=-=Horn 1974-=-, Blake 1985c) and reconstruction of stereoscopically viewed surfaces (Grimson 1981, Terzopoulos 1983). The implementation of weak continuity constraints can be achieved very naturally too, we shall s... |

113 | The singularities of the visual mapping - Koenderink, Doorn - 1976 |

89 |
Multilevel computational processes for visual surface reconstruction
- Terzopoulos
- 1983
(Show Context)
Citation Context ...ading (Woodham 1977, Ikeuchi and Horn 1981), analysis of motion (Ullman 1979a), computation of lightness (Horn 1974, Blake 1985c) and reconstruction of stereoscopically viewed surfaces (Grimson 1981, =-=Terzopoulos 1983-=-). The implementation of weak continuity constraints can be achieved very naturally too, we shall see, by cooperative networks. 1.2 Continuity and cooperativity 1.2.1 Cooperativity in physical models ... |

88 |
Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image
- Land
- 1983
(Show Context)
Citation Context ...atial bandpass channels (Campbell and Robson 1968, Braddick et al. 1978), and understanding the perception of coloured light (Livingstone and Hubel 1984, Jameson and Hurvich 1961) and surface colour (=-=Land 1983-=-, Zeki 1983). These instances are but parts of a very large body of knowledge of biological vision. Over the last two decades, computers have introduced a new strand into the study of vision. The earl... |

81 |
From Images to Surfaces
- Grimson
- 1981
(Show Context)
Citation Context ...maps may be produced by stereopsis, in which images obtained from two slightly different viewpoints (e.g. two eyes) are compared and matched (Marr and Poggio 1979, Mayhew and Frisby 1981, Baker 1981, =-=Grimson 1981-=-); triangulation is then used to compute the depths. Alternatively depths may be obtained by appropriate processing of optic flow (Bruss 1983) or, artificially, from an optical rangefinder. • Sets of ... |

81 |
A four mechanism model for threshold spatial vision. Vision Research
- Wilson, Bergen
- 1979
(Show Context)
Citation Context ...ly effective scales would be determined by the data. 8.4.1 Psychophysical models The literature on Gaussian multi-channel models of contrast sensitivity is well-established (Campbell and Robson 1968, =-=Wilson and Bergen 1979-=-, Watt and Morgan 1985). It would be interesting to know however, whether such models successfully predict systematic localisation error for asymmetric stimuli (figure 4.10). A pair of such stimuli, p... |

70 |
An operator which locates edges in digitized pictures
- Hueckel
- 1971
(Show Context)
Citation Context ...to 2D the use of blurring that we have already seen in 1D (Haralick 1980, Canny 1983, Marr and Hildreth 1980). The second kind use regression to fit step-shaped templates, locally, to intensity data (=-=Hueckel 1971-=-, O’Gorman 1978, Leclerc 1985, Gennert 1986). Where the template fits well, there must be a step discontinuity in the data. The third kind, also uses regression, but acts globally across the data, wit... |

67 |
The visual ambiguity of a moving plane
- Longuet-Higgins
- 1984
(Show Context)
Citation Context ...ontinuity - continuity along curves and surface features (Mayhew and Frisby 1981). Analysis of optical flow also appears to require assumptions of continuity, either in regions (Horn and Schunk 1981, =-=Longuet-Higgins 1984-=-) or along curves (Hildreth 1984). Computation of lightness, the perceptual correlate of surface reflectivity (i.e. surface colour), needs constraints on continuity both of the reflectivity itself, an... |

61 |
Determining optical
- Horn, Schunck
- 1981
(Show Context)
Citation Context ...rticular, by figural continuity - continuity along curves and surface features (Mayhew and Frisby 1981). Analysis of optical flow also appears to require assumptions of continuity, either in regions (=-=Horn and Schunk 1981-=-, Longuet-Higgins 1984) or along curves (Hildreth 1984). Computation of lightness, the perceptual correlate of surface reflectivity (i.e. surface colour), needs constraints on continuity both of the r... |

54 |
Boundary conditions for lightness computation in Mondrian World
- Blake
- 1985
(Show Context)
Citation Context ...tive algorithms for optical flow computation (Horn and Schunk 1981), analysis of shading (Woodham 1977, Ikeuchi and Horn 1981), analysis of motion (Ullman 1979a), computation of lightness (Horn 1974, =-=Blake 1985-=-c) and reconstruction of stereoscopically viewed surfaces (Grimson 1981, Terzopoulos 1983). The implementation of weak continuity constraints can be achieved very naturally too, we shall see, by coope... |

54 |
Visual hyperacuity: spatiotemporal interpolation in human vision
- Fahle, Poggio
- 1981
(Show Context)
Citation Context ...dense, using a continuous membrane (i.e. minimising (4.36) with very large α) at small scale λ. 4.5.1 Hyperacuity The problem of handling sparse data is closely related to the problem of hyperacuity (=-=Fahle and Poggio 1984-=-, Krotkov 1986) - that is, obtaining 3 Actually this problem is ill-posed as it stands - it has no continuous solution. To be technically correct, u(x) should be constrained to be constant along some ... |

52 |
A theory of the primitive spatial code in human vision
- Watt, Morgan
- 1985
(Show Context)
Citation Context ...d be determined by the data. 8.4.1 Psychophysical models The literature on Gaussian multi-channel models of contrast sensitivity is well-established (Campbell and Robson 1968, Wilson and Bergen 1979, =-=Watt and Morgan 1985-=-). It would be interesting to know however, whether such models successfully predict systematic localisation error for asymmetric stimuli (figure 4.10). A pair of such stimuli, positioned appropriatel... |

49 | An extremum principle for shape from contour - Brady, Yuille - 1984 |

48 | Bessel functions for engineers - Mclachlan - 1955 |

47 | Visual control of orientation behaviour in the fly. Part I. A quantitative analysis. Quarterly Reviews of Biophysics 9: 311–75– 428–38. T he J ou rn al o f E xp er im en ta l B io lo gy - Reichardt, Poggio - 1976 |

45 | Integrals of Bessel Function - Luke - 1962 |

45 |
A regularized solution to edge detection
- Poggio, Voorhees, et al.
- 1985
(Show Context)
Citation Context ...satile still are splines (de Boor 1978) - sequences of polynomials joined smoothly together. There is an interesting connection between cubic splines and elastic systems like the sheet in figure 1.1 (=-=Poggio et al. 1984-=-, Terzopoulos 1986). A flexible rod, such as draughtsmen commonly use to draw smooth curves is an elastic system. If it is loaded or clamped at several points, it takes up a shape - its minimum energy... |

43 |
Curve-fitting with piecewise parametric cubics
- Plass, Stone
- 1983
(Show Context)
Citation Context ...ts must be done automatically. An algorithm to do that might consist of constructing an initial spline fit, and then adding knots until the regression error measure reached an acceptably small value (=-=Plass and Stone 1983-=-). This would ensure a spline that closely fitted the data points. For visual reconstruction that is not enough. The requirement for stability has already been discussed, which means that the multiple... |

42 |
Segmentation of textured images using Gibbs random fields
- Derin, Cole
- 1984
(Show Context)
Citation Context ...he most disturbing thing is that one is forced to accept that the surface model is a probabilistic one, and therefore includes an element of randomness. This may be appropriate for modelling texture (=-=Derin and Cole 1986-=-), but in a model of smooth surfaces it has rather counter-intuitive consequences, illustrated in figure 1.5. A “1st order” MRF6 , for instance, ranks a noisy but horizontal plane more probable than a... |

31 |
Variational Calculus with Elementary Convexity
- Troutman
- 1983
(Show Context)
Citation Context ...it can be shown (Blake 1984) that the integrand E is a non-convex function of ux, ... . So even with a fixed set of discontinuities, it is not known whether there is a uniquely optimal u to be found (=-=Troutman 1983-=-). This problem is dealt with, in an approximate way 1 , by using a 1st order plate, as already proposed for the non-invariant case. First, estimates for ux(x, y), uy(x, y) are obtained by fitting an ... |

30 |
Finding edges and lines
- Canny
- 1983
(Show Context)
Citation Context ...e kinds of filter for labelling discontinuities. Those of the first kind use blurring (linear filtering), naturally extending to 2D the use of blurring that we have already seen in 1D (Haralick 1980, =-=Canny 1983-=-, Marr and Hildreth 1980). The second kind use regression to fit step-shaped templates, locally, to intensity data (Hueckel 1971, O’Gorman 1978, Leclerc 1985, Gennert 1986). Where the template fits we... |

29 |
Local Control of Bias and Tension in Betasplines
- Barsky, Beatty
- 1983
(Show Context)
Citation Context ...ly, a mixture of first and second order energies may be used, to give: ∫ { E = (u − d) 2 + λ 2 u ′2 4 ′′2 + µ u } dx + P. (5.2) When u is continuous, this is somewhat akin to “splines under tension” (=-=Barsky and Beatty 1983-=-), and is used for reconstruction by Terzopoulos (1983, 1985).Properties of the Weak Rod and Plate 99 Now that the energy is second order it is possible to include penalties both for steps and crease... |

27 |
Channels in vision: Basic aspects
- Braddick
- 1978
(Show Context)
Citation Context ...n (Hubel and Wiesel 1968). There has also been much dialogue between psychophysics and neurophysiology/neuroanatomy. Examples are the discovery of spatial bandpass channels (Campbell and Robson 1968, =-=Braddick et al. 1978-=-), and understanding the perception of coloured light (Livingstone and Hubel 1984, Jameson and Hurvich 1961) and surface colour (Land 1983, Zeki 1983). These instances are but parts of a very large bo... |

27 |
Relaxation and its role in vision
- Hinton
- 1977
(Show Context)
Citation Context ... is to reach a satisfactory formalisation of “continuity almost everywhere”. We do that here by borrowing the idea of a “weak constraint” - a constraint that can be broken occasionally - from Hinton (=-=Hinton 1978-=-). With an appropriate class of continuous surface patches, this leads to “weak continuity constraints” (Blake 1983b) - preferring continuity, but grudgingly allowing occasional discontinuities if tha... |

25 |
Analyzing cooperative computation
- Hinton, Sejnowski
- 1983
(Show Context)
Citation Context ...isions between messages, to achieve a useful effect.6 Chapter 1 Networks of this kind have received much attention in theories of Psychophysics (e.g. Julesz 1971, Marr 1976b) Cognitive Science (e.g. =-=Hinton and Sejnowski 1983-=-, Hopfield 1984), Pattern Recognition (e.g. Rosenfeld et al. 1976) and Computer Science (e.g. Brookes et al. 1984, Milner 1980). In vision, there have been cooperative algorithms for optical flow comp... |

21 |
Invariant Surface Reconstruction Using Weak Continuity Constraints
- Blake, Zisserman
- 1986
(Show Context)
Citation Context ...on-invariant weak membrane, multiple step discontinuities tend to appear near extremal boundaries, where surface energy is (in theory) unbounded (figure 4.26). The cure is to use an invariant energy (=-=Blake and Zisserman 1986-=-c) based on surface area (membrane) or surface area and curvatures (plate). The simple, non-invariant membrane and plate are in fact approximations to these invariant energies. The approximations are ... |

20 | The least disturbance principle and weak constraints
- Blake
- 1983
(Show Context)
Citation Context ...f a “weak constraint” - a constraint that can be broken occasionally - from Hinton (Hinton 1978). With an appropriate class of continuous surface patches, this leads to “weak continuity constraints” (=-=Blake 1983-=-b) - preferring continuity, but grudgingly allowing occasional discontinuities if that makes for a simpler overall description. Another important theme emerges later in the book - cooperativity. Where... |

20 |
Modifications of the classical notion of Panum’s fusional area
- Burt, Julesz
- 1980
(Show Context)
Citation Context ...into the stereo algorithm itself, so that a subset of the “ghost field” of potential stereo matches is grouped directly into surfaces. Indeed this is somewhat related to the disparity gradient limit (=-=Burt and Julesz 1980-=-) already used by Pollard et al. (1985) for elimination of ghost matches. There is little doubt that energy functions with appropriate weak constraints could be set up for these problems. The real que... |

20 | Discontinuity Detection For Visual Surface Reconstruction - Grimson, Pavlidis - 1985 |

19 |
Opponent chromatic induction: experimental evaluation and theoretical account
- Jameson, Hurvich
- 1961
(Show Context)
Citation Context ...neuroanatomy. Examples are the discovery of spatial bandpass channels (Campbell and Robson 1968, Braddick et al. 1978), and understanding the perception of coloured light (Livingstone and Hubel 1984, =-=Jameson and Hurvich 1961-=-) and surface colour (Land 1983, Zeki 1983). These instances are but parts of a very large body of knowledge of biological vision. Over the last two decades, computers have introduced a new strand int... |

18 |
Monocular depth perception from optical flow by space time signal processing
- Buxton, Buxton
- 1983
(Show Context)
Citation Context ...ensity data direct from photoreceptors, in the form of an array of numbers • “Optic flow” - measures of velocities of points in an image, obtained perhaps from a suitable spatio-temporal filter (e.g. =-=Buxton and Buxton 1983-=-). • A depth map, consisting of points embedded, usually sparsely, in the viewer’s coordinate-frame. At each point, depth (distance from the viewer) is known. Depth maps may be produced by stereopsis,... |

18 |
Review of CLIP image processing system
- Duff
- 1978
(Show Context)
Citation Context ...ardware Implementation It is clear from the parallel nature of the GNC algorithm (when simultaneous updating is used) that it maps efficiently onto massively parallel machines, whether with cellular (=-=Duff 1978-=-, Marks 1980) or a less regularly structured “MIMD” architecture. The latter, it can be argued (Blake 1983a) is a more efficient use of computing power. The former might lend itself more naturally to ... |

17 | Rotationally symmetric operators for surface Interpolation
- Michael, Horn
- 1981
(Show Context)
Citation Context ...ut simple first and second order energies are not entirely suitable for this purpose. This is because they are not fully invariant in 3D. They are, of course, invariant to rotation in the x, y plane (=-=Brady and Horn 1983-=-) but not to changes of viewpoint. This means that the optimal surface (the one that minimises such a non-invariant energy, subject to appropriate constraints) may wobble as the viewpoint varies (figu... |

17 |
Visual pigments of single primate cones
- Marks, Dobelle, et al.
- 1964
(Show Context)
Citation Context ...hat provides some answers in the case of biological systems (see Uttal (1981) for a taxonomy). For instance, the functioning of light-sensitive cells in mammalian vision is understood in some detail (=-=Marks et al. 1964-=-); and the elegant, orderly, spatial correspondence of feature detectors in the brain with the array of cells in the retina, is well known (Hubel and Wiesel 1968). There has also been much dialogue be... |

17 |
Geometrical modeling from multiple stereo views
- Pollard, Pridmore, et al.
- 1989
(Show Context)
Citation Context ... is little further to be deduced about the shape of the patch. This is nothing to be ashamed of - descriptions of this sort are already a powerful handle for matching visible surfaces to one another (=-=Pollard et al. 1987-=-) and to stored models (Brooks 1981). New sources of information, such as analysis of surface shading, might add usefully to such descriptions - but that possibility must be left for discussion elsewh... |

16 |
Regularization of inverse problems involving discontinuities
- Terzopoulos
- 1986
(Show Context)
Citation Context ...ines (de Boor 1978) - sequences of polynomials joined smoothly together. There is an interesting connection between cubic splines and elastic systems like the sheet in figure 1.1 (Poggio et al. 1984, =-=Terzopoulos 1986-=-). A flexible rod, such as draughtsmen commonly use to draw smooth curves is an elastic system. If it is loaded or clamped at several points, it takes up a shape - its minimum energy configuration - w... |

15 |
Image Restoration by a Powerful Maximum Entropy Method
- Burch, Gull, et al.
(Show Context)
Citation Context ...es of this sort have recently attracted much interest both in Vision and in Image Processing (Blake 1983a,b, Geman and Geman 1984, Mumford and Shah 1985, Blake and Zisserman 1985a, Smith et al. 1983, =-=Burch et al. 1983-=-). The results of edge detection by fitting a weak membrane (that is, an elastic membrane under weak continuity constraints) are shown in figures 2.4 and 2.5. As in 1D (the weak string), discontinuiti... |

12 | A Coopera.tive Algorithm (or Determining Surface Orientations from a. Single View
- Woodham
- 1977
(Show Context)
Citation Context ... et al. 1976) and Computer Science (e.g. Brookes et al. 1984, Milner 1980). In vision, there have been cooperative algorithms for optical flow computation (Horn and Schunk 1981), analysis of shading (=-=Woodham 1977-=-, Ikeuchi and Horn 1981), analysis of motion (Ullman 1979a), computation of lightness (Horn 1974, Blake 1985c) and reconstruction of stereoscopically viewed surfaces (Grimson 1981, Terzopoulos 1983). ... |

10 |
Some properties o.f weak continuity constraints and the GNC algorithm
- Blake, Zisserman
- 1986
(Show Context)
Citation Context ...on-invariant weak membrane, multiple step discontinuities tend to appear near extremal boundaries, where surface energy is (in theory) unbounded (figure 4.26). The cure is to use an invariant energy (=-=Blake and Zisserman 1986-=-c) based on surface area (membrane) or surface area and curvatures (plate). The simple, non-invariant membrane and plate are in fact approximations to these invariant energies. The approximations are ... |

8 | A Taxonomy of Visual Process - Uttal - 1981 |

7 |
Detecting half-edges and vertices in images
- Gennert
(Show Context)
Citation Context ...ady seen in 1D (Haralick 1980, Canny 1983, Marr and Hildreth 1980). The second kind use regression to fit step-shaped templates, locally, to intensity data (Hueckel 1971, O’Gorman 1978, Leclerc 1985, =-=Gennert 1986-=-). Where the template fits well, there must be a step discontinuity in the data. The third kind, also uses regression, but acts globally across the data, without the need for arbitrarily choice of nei... |

7 |
Foundations o f Cyclopean Perception. Uni versity of Chicago
- Julesz
- 1971
(Show Context)
Citation Context ...ropagation can be coordinated, unhindered by collisions between messages, to achieve a useful effect.6 Chapter 1 Networks of this kind have received much attention in theories of Psychophysics (e.g. =-=Julesz 1971-=-, Marr 1976b) Cognitive Science (e.g. Hinton and Sejnowski 1983, Hopfield 1984), Pattern Recognition (e.g. Rosenfeld et al. 1976) and Computer Science (e.g. Brookes et al. 1984, Milner 1980). In visio... |

7 |
Capturing the Local Structure of Image Discontinuities in Two Dimensions
- Leclerc
- 1985
(Show Context)
Citation Context ...t we have already seen in 1D (Haralick 1980, Canny 1983, Marr and Hildreth 1980). The second kind use regression to fit step-shaped templates, locally, to intensity data (Hueckel 1971, O’Gorman 1978, =-=Leclerc 1985-=-, Gennert 1986). Where the template fits well, there must be a step discontinuity in the data. The third kind, also uses regression, but acts globally across the data, without the need for arbitrarily... |

6 | Parallel computation in low level vision - Blake - 1983 |

6 | Reconstructing a visible surface
- Blake
- 1984
(Show Context)
Citation Context ...they correspond to occlusions and creases between surfaces in the scene. This is quite like the problem of detecting discontinuities of intensity. But, in addition, invariance to change of viewpoint (=-=Blake 1984-=-) must be ensured, in order to maintain stability under viewer motion. This would be of crucial importance in a real time system, but is important even for analysis of single frames, if surface descri... |

6 |
Using weak continuity constraints
- Blake, Zisserman
- 1985
(Show Context)
Citation Context ...y propagation, as we saw earlier. Global schemes of this sort have recently attracted much interest both in Vision and in Image Processing (Blake 1983a,b, Geman and Geman 1984, Mumford and Shah 1985, =-=Blake and Zisserman 1985-=-a, Smith et al. 1983, Burch et al. 1983). The results of edge detection by fitting a weak membrane (that is, an elastic membrane under weak continuity constraints) are shown in figures 2.4 and 2.5. As... |

6 |
Weak continuity constraints generate uniform scalespace descriptions of plane curves
- Blake, erman, et al.
- 1986
(Show Context)
Citation Context ...h (θ, s) form, and filtered to detect corners (step discontinuities in θ) and possibly also curvature discontinuities (Perkins 1978, Asada and Brady 1986, Ramer 1975, Zucker et al. 1977, Zucker 1982, =-=Blake et al. 1986-=-a). This may be done at a variety of spatial scales in order to obtain both coarse and fine views of the curve’s shape. Corners, for instance, appear as step discontinuities in tangent angle θ. Sharp ... |

6 |
dispersion matrices
- Davies
(Show Context)
Citation Context ...The calculation of vmax, for the weak string, rod, membrane and plate appears in appendix D.3. The task is made relatively easy by the fact that Q is (almost) a circulant, so that there is a formula (=-=Davies 1979-=-) which gives all its eigenvalues. The results are summarised in the following table. c ∗ string 1/2 membrane 1/4 rod 1/8 plate (Laplacian) 1/32 The value given for the plate is for the square Laplaci... |

5 | Constructing a depth map from images
- Ikeuchi
- 1983
(Show Context)
Citation Context ...ks 1981). New sources of information, such as analysis of surface shading, might add usefully to such descriptions - but that possibility must be left for discussion elsewhere (Ikeuchi and Horn 1981, =-=Ikeuchi 1983-=-, Blake et al. 1985d). And, of course, if the surface is visibly textured the shape ambiguity is resolved by stereoscopic vision, because the texture elements constitute features that can be stereosco... |

5 |
Reconstruction of objects from coded images by simulated annealing
- Smith, Paxman, et al.
- 1983
(Show Context)
Citation Context ...rlier. Global schemes of this sort have recently attracted much interest both in Vision and in Image Processing (Blake 1983a,b, Geman and Geman 1984, Mumford and Shah 1985, Blake and Zisserman 1985a, =-=Smith et al. 1983-=-, Burch et al. 1983). The results of edge detection by fitting a weak membrane (that is, an elastic membrane under weak continuity constraints) are shown in figures 2.4 and 2.5. As in 1D (the weak str... |

4 |
Is What You See What You Get
- Bruss
- 1983
(Show Context)
Citation Context ...arr and Poggio 1979, Mayhew and Frisby 1981, Baker 1981, Grimson 1981); triangulation is then used to compute the depths. Alternatively depths may be obtained by appropriate processing of optic flow (=-=Bruss 1983-=-) or, artificially, from an optical rangefinder. • Sets of discrete points making up curves in a 2D image, or in 3D (“space-curves”).4 Chapter 1 In each case, data must be reduced in quantity, with m... |

4 |
Relaxation and Constrained Optimisation by Local Processes." Comwputer Graphics and Issage Pwiceuing 10: 115-125 [Ulman 841 Ulmn5
- Ullman
- 1976
(Show Context)
Citation Context ... practice by executing an algorithm that implements them, on a computer. All this has led to considerable enrichment of studies of human vision (e.g. Marr and Poggio 1979, Mayhew 1982, Hildreth 1984, =-=Ullman 1979-=-b, Koenderinck and van Doorn 1976). 3. Complete, though simple, vision systems can be built and tested. The restriction to study the visual systems that nature has kindlyModelling Piecewise Continuit... |

3 | The structures of images - Koenderinck - 1984 |

3 |
Knowledge source for describing stereoscopically viewed textured surfaces
- McLauchlan, Zisserman, et al.
- 1987
(Show Context)
Citation Context ...t - just as with discontinuities of intensity. In fact computation can be saved by using a membrane (cheaper than a plate) to fill in the sparse depth data, followed by conventional linear filtering (=-=McLauchlan et al. 1987-=-). But as with any method based on linear filtering, accuracy is spoilt by blurring distortion. This drawback can be avoided by using weak continuity constraints. 2.2.3 Why reconstruct a surface anywa... |

2 |
Depth from edge and intensity based stereo. IJCAIconf
- Baker
- 1981
(Show Context)
Citation Context ...nown. Depth maps may be produced by stereopsis, in which images obtained from two slightly different viewpoints (e.g. two eyes) are compared and matched (Marr and Poggio 1979, Mayhew and Frisby 1981, =-=Baker 1981-=-, Grimson 1981); triangulation is then used to compute the depths. Alternatively depths may be obtained by appropriate processing of optic flow (Bruss 1983) or, artificially, from an optical rangefind... |

2 |
Representing solids with the Delaunay triangulation
- Boissonat
- 1984
(Show Context)
Citation Context ...sion of a given path in space, with the visible surface. Greater efficiency is achieved, though, if the visible surface can be “protected” by a bounding polygon, computed directly from sparse depths (=-=Boissonat 1984-=-), without the use of an intermediate depth map. The point is that direct applications for depth maps, as descriptions of visible surfaces, are at best limited and at worst, perhaps, non-existent. 2.2... |

2 |
Low level vision using an array processor
- Marks
- 1980
(Show Context)
Citation Context ...lementation It is clear from the parallel nature of the GNC algorithm (when simultaneous updating is used) that it maps efficiently onto massively parallel machines, whether with cellular (Duff 1978, =-=Marks 1980-=-) or a less regularly structured “MIMD” architecture. The latter, it can be argued (Blake 1983a) is a more efficient use of computing power. The former might lend itself more naturally to VLSI impleme... |

1 | Optic flow segmentation as an ill-posed and maximum likelihood problem - B - 1985 |

1 | A stochastic model for boundary detection. Image and vision computing - Geman - 1987 |

1 |
Edge and region analysis for digital image data. Computer graphics and image processing
- Haralick
- 1980
(Show Context)
Citation Context ... basically three kinds of filter for labelling discontinuities. Those of the first kind use blurring (linear filtering), naturally extending to 2D the use of blurring that we have already seen in 1D (=-=Haralick 1980-=-, Canny 1983, Marr and Hildreth 1980). The second kind use regression to fit step-shaped templates, locally, to intensity data (Hueckel 1971, O’Gorman 1978, Leclerc 1985, Gennert 1986). Where the temp... |

1 |
Visual hyperacuity: representation and computation of very high precision position information
- Krotkov
- 1986
(Show Context)
Citation Context ...us membrane (i.e. minimising (4.36) with very large α) at small scale λ. 4.5.1 Hyperacuity The problem of handling sparse data is closely related to the problem of hyperacuity (Fahle and Poggio 1984, =-=Krotkov 1986-=-) - that is, obtaining 3 Actually this problem is ill-posed as it stands - it has no continuous solution. To be technically correct, u(x) should be constrained to be constant along some short line seg... |

1 | Catastrophe theory and its Ramer,E.U - Pitman - 1975 |

1 | Chapter 8 Strang,G. and Fix,G.J - letters |

1 | Computing visible surface representations. AI memo 800 - Terzopoulos - 1985 |

1 |
Spin glass models of neural networks; size dependence of memory properties
- Wallace
- 1985
(Show Context)
Citation Context ...an be designed for them. Furthermore, how far can energy functions be built or refined by inductive learning, as exhibited to some degree in neural networks (Hinton and Sejnowski 1983, Hopfield 1982, =-=Wallace 1985-=-). 8.2 Hardware Implementation It is clear from the parallel nature of the GNC algorithm (when simultaneous updating is used) that it maps efficiently onto massively parallel machines, whether with ce... |

1 | Fingerprints theorems - Yuille, Poggio - 1984 |

1 |
Personal communication. 181 Zeki,S
- Yuille
- 1985
(Show Context)
Citation Context ...e methods is difficult because they solve different problems. The Hopfield scheme might be made to implement a weak string, for example, by extending it to deal with mixed real and boolean variables (=-=Yuille 1985-=-). The energy (6.20) would become a cubic polynomial in ui, li (taking the place of the Vi above), as in (3.3) on page 42. 6.3.4 Dynamic programming Dynamic programming is a technique for optimising f... |

1 | Finite elements and Zucker,S.W., Hummel,R.A. and Rosenfeld,A - Wiley - 1977 |