## Dynamic Estimation in Computational Vision (1992)

Citations: | 19 - 4 self |

### BibTeX

@TECHREPORT{Chin92dynamicestimation,

author = {Toshio Michael Chin},

title = {Dynamic Estimation in Computational Vision},

institution = {},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

Spatial coherence constraints are commonly used to regularize the problems of reconstructing dense visual fields like depth, shape, and motion. Recent developments in theory and practice show that the local nature of spatial coherence constraints allows us to solve single-frame reconstruction problems efficiently with, for example, multiresolution approaches. While it is reasonable to impose temporal as well as spatial coherence on the unknown for a more robust estimation through data fusion over both space and time, such temporal, multi-frame extensions of the problems have not been as widely considered, perhaps due to the different and severe computational demands imposed by the sequential arrival of the image data. We present here an efficient filtering algorithm for sequential estimation of dense visual fields, using stochastic descriptor dynamic system models to capture temporal smoothness and dynamics of the fields. Theoretically, standard Kalman filtering techniques (generalized...

### Citations

5315 |
Matrix Analysis
- Horn, Johnson
- 1985
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Citation Context ...ecreasing sequence \Delta (n+1)s\Delta (n) ; 8n: (B.4) The sequence n \Delta (n) o is also upper-bounded. To see this, note that unitary transforms preserve the Frobenius norm 1 of the operand matrix =-=[35]-=-. In particular, we have fl fl fl fl fl fl fl 2 6 4 P (n) Q (n) 3 7 5 fl fl fl fl fl fl fl 2 F = fl fl flP (n) fl fl fl 2 F + fl fl flQ (n) fl fl fl 2 F = K; 8n; where K is a constant. Thus, \Delta (n... |

4177 |
Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
- Geman, Geman
- 1984
(Show Context)
Citation Context ...ry. An estimation theoretic interpretation of a single-frame visual reconstruction problem is possible by treating the spatial coherence constraint as the prior model in a Bayesian estimation problem =-=[17, 65, 71]-=-. Similarly, a multi-frame problem can be considered as an estimation problem by modeling the time-varying visual field as a stochastic process, for which a Kalman filter can be used to compute the es... |

3372 | Active contour models
- Kass, Witkin, et al.
- 1988
(Show Context)
Citation Context ...e useful. A constraint of the form �� 1 fl fl fl fl fl @ @s f fl fl fl fl fl 2 + �� 2 fl fl fl fl fl @ 2 @s 2 f fl fl fl fl fl 2 (3.4) has been used to model the structure of object boundary c=-=ontours [41]-=-, where f(s) represents the coordinate vector (i.e., the location in the space) of a point on the contour and s is the index along the contour. The first order derivative term keeps the structural int... |

1949 | Determining optical flow
- Horn, Schunck
- 1981
(Show Context)
Citation Context ...optical flow estimate b f is obtained as the solution of the inverse problem (H T NH+ LM ) b f = H T Ng: This equation is a discrete version of the Euler-Lagrange equation derived by Horn and Schunck =-=[34]-=- who used Gauss-Seidel iterations to solve the equation numerically. Each iteration essentially involves computation of only the previously mentioned, locally weighted sum for each component of the fi... |

1523 |
Robot Vision
- Horn
- 1986
(Show Context)
Citation Context ...problem is often decomposed into subproblems. By far, the most popular approach is to characterize the computational task by a "bottom-up" hierarchical system of mostly independent processin=-=g modules [33, 52]-=-. In the early 1 i.e., light intensity or low-level stages, structural and functional properties such as the depth, motion, and shape 2 of the imaged surfaces are inferred from the measurements while ... |

1205 |
Vision: A Computational Investigation Into the Human Representation and Processing of Visual Information
- Marr, Ullman, et al.
- 2010
(Show Context)
Citation Context ...problem is often decomposed into subproblems. By far, the most popular approach is to characterize the computational task by a "bottom-up" hierarchical system of mostly independent processin=-=g modules [33, 52]-=-. In the early 1 i.e., light intensity or low-level stages, structural and functional properties such as the depth, motion, and shape 2 of the imaged surfaces are inferred from the measurements while ... |

851 |
Stochastic Processes and Filtering Theory
- Jazwinski
- 1970
(Show Context)
Citation Context ... gramian. by contradiction, 1 ! 3 . 2 If the information matrix is not invertible, then certain linear combinations of the elements of the mean of the corresponding random vector cannot be determined =-=[39]. Th-=-e information pair representation is more advantageous than the mean-covariance pair representation x �� ( b x; P x ) because the former always exists while the latter exists only if L x is invert... |

812 |
Optimal Filtering
- Anderson, Moore
- 1979
(Show Context)
Citation Context ... of a Kalman filter such uncertainty, which is expressed via the incorporation of "process noise", can serve the purpose of making the filter stable against modeling errors and responsive to=-= new data [4, 16, 45]-=-. Certainly, a filtering algorithm based on a more systematic approximation of Kalman filter is desirable. This thesis offers such algorithms. Specifically, we first formulate a general Kalman filteri... |

772 | Visual Reconstruction
- Blake, Zisserman
- 1987
(Show Context)
Citation Context ... of the field over time and update the model using the measurements from the most recent image at each time step. MRF models are used extensively in single-frame visual reconstruction problems, e.g., =-=[17, 11, 71, 29]-=-; they are quite versatile modeling tools especially suitable for the important problem of estimating the locations of discontinuity in visual fields [17, 11]. Used in reconstruction of entirely smoot... |

732 |
R.Bulirsch, Introduction to Numerical Analysis
- Stoer
- 1980
(Show Context)
Citation Context ... Givens Rotation The Given rotation is a rudimentary unitary operation that nulls a specific matrix element, and QR factorization can be considered as a precisely ordered sequence of Givens rotations =-=[18, 70]-=-. A single Givens rotation operates on only a pair of rows in a matrix at a time; thus, Givens rotations operating on disjoint pairs of rows can be performed simultaneously. A clever scheduling of rot... |

716 |
Matrix Iterative Analysis
- Varga
- 1962
(Show Context)
Citation Context ...lementation of the information filter. Diagonal dominance We introduce here a matrix property important for convergence of the series representation of the inverse matrix in (5.16). Definition 4 (cf. =-=[35, 75]-=-) A matrix A is said to be diagonally dominant if its elements a ij , where i and j are the row and column indices, satisfy ja ii jsX j 6=i ja ij j ; 8i: If the inequality is a strict inequality, then... |

325 |
The Interpretation of a Moving Retinal Image
- Lnguet-Higgins, Prazdny
- 1980
(Show Context)
Citation Context ...e computed apparent motion in an image sequence can provide us with information necessary to detect object boundaries [56, 29] and to derive 3-D motion and structure of the objects in the image frame =-=[48, 59]-=-. Computing motion from image sequences is also important in applications in fields outside of robotics and brain sciences, such as in assessing motility of the heart [13, 64] and in interpretation an... |

288 |
Modulation Theory: Part I
- Trees, Detection
- 2001
(Show Context)
Citation Context ...t to our visual reconstruction problems as well as establish some notation that will be used frequently in the sequel. For derivations and other details, introductory texts on estimation theory (e.g. =-=[16, 45, 74]-=-) should be consulted. The maximum likelihood (ML) estimation problem deals with estimation of an unknown vector x based on an observed sample of a random vector y whose distribution is parameterized ... |

253 |
Regularisation of inverse visual problems involving discontinuities
- Terzopoulos
- 1986
(Show Context)
Citation Context ...ces. Reconstruction of dense visual fields can be regarded as a problem in inverse optics, since physical properties of 3-D surfaces are to be recovered from the 2-D images that the surfaces generate =-=[31, 73]-=-. The inverse problems arising in visual field reconstruction are generally ill-posed [7], as the measurements from images do not constrain the desired solution sufficiently. An established approach t... |

242 |
W.: An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences
- Nagel, Enkelmann
- 1986
(Show Context)
Citation Context ...ess of the imaged surfaces [30]. This is obviously violated along most object boundaries. More sophisticated versions of the constraint have been proposed to address the problems at object boundaries =-=[58, 67]-=- with limited success. Spatial coherence is essentially a local constraint and cannot capture global characteristics of boundaries in images. Nevertheless, spatial coherence constraints are considered... |

233 | Kalman filter-based algorithms for estimating depth from image sequences
- Matthies, Kanade, et al.
- 1989
(Show Context)
Citation Context ... the image frame) makes the filter computationally unfeasible in its optimal form. Kalman filtering solutions for multi-frame visual reconstruction problem have been proposed in a variety of contexts =-=[55, 71, 27, 10, 69]-=-; however, in each of these cases some ad hoc simplifying assumptions are made in order to avoid the computational complexity issues. For example, in none of these previously proposed methods, is the ... |

210 | Numerical shape from shading and occluding boundaries
- Ikeuchi, Horn
- 1981
(Show Context)
Citation Context ... structural integrity ("rigidity") on the whole. This approach has been successful in a wide variety of visual field reconstruction problems including depth interpolation [21, 22], shape fro=-=m shading [32, 36, 37]-=-, and optical flow computation [34, 30]. Mathmatically, these reconstruction problems are formulated as least-squares problems in which the spatial coherence constraints are implemented as cost terms ... |

201 | Ill-posed problems in early vision
- Bertero, Poggio, et al.
- 1988
(Show Context)
Citation Context ...ce physical properties of 3-D surfaces are to be recovered from the 2-D images that the surfaces generate [31, 73]. The inverse problems arising in visual field reconstruction are generally ill-posed =-=[7]-=-, as the measurements from images do not constrain the desired solution sufficiently. An established approach to making such problems solvable is to impose an additional constraint on the solution by ... |

195 |
Bayesian Modeling of Uncertainty in Low-Level Vision
- Szeliski
- 1989
(Show Context)
Citation Context ...ufficiently. An established approach to making such problems solvable is to impose an additional constraint on the solution by assuming that the field to be reconstructed varies "smoothly" o=-=ver space [7, 33, 71]-=-. A physical basis for such an assumption, commonly known as the smoothness or spatial coherencesconstraint [71], is that most surfaces in natural scenes exhibit some geometrical smoothness and struct... |

182 | Direct passive navigation
- Negahdaripour, Horn
- 1987
(Show Context)
Citation Context ...e computed apparent motion in an image sequence can provide us with information necessary to detect object boundaries [56, 29] and to derive 3-D motion and structure of the objects in the image frame =-=[48, 59]-=-. Computing motion from image sequences is also important in applications in fields outside of robotics and brain sciences, such as in assessing motility of the heart [13, 64] and in interpretation an... |

169 |
Factorization Methods for Discrete Sequential Estimation
- Bierman
- 1977
(Show Context)
Citation Context ... an information Kalman filter, or a square root information filter (SRIF), improves numerical stability in such near-singular estimation problems by reducing numerical dynamic ranges of the variables =-=[9, 47]-=-. Besides providing an increased margin for numerical roundoff errors, such reduction in the dy85 namic ranges can also relieve memory requirements (i.e., the number of bits required to represent each... |

157 |
On the computation of motion from sequences of images - a review
- Aggarwal, Nandhakumar
- 1988
(Show Context)
Citation Context ... sparse but relatively reliable 2-D motion vectors. Computational complexity involved with this method, especially for the inter-frame matching or the correspondence problem, is in general quite high =-=[1, 2]-=-. The other method is based directly on the measured pixel values in the images, and it generally yields a dense vector field of apparent motion, or optical flow 1 . Efficient computation of optical f... |

148 |
Model for the Extraction of Image Flow
- Heeger
- 1987
(Show Context)
Citation Context ...this minimum often involves a non-linear search. In another method based on the same intuition, a flow field is computed from the difference in the phases of Fourier transforms of I 0 (s) and I 1 (s) =-=[24]-=-. The assumption that the optical flow is 1 also called image flow uniform over an image region is an obvious weakness of these approaches, as the flow vectors in general vary from one pixel location ... |

130 | Calculating the reflectance map
- Horn, Sjoberg
- 1979
(Show Context)
Citation Context ... structural integrity ("rigidity") on the whole. This approach has been successful in a wide variety of visual field reconstruction problems including depth interpolation [21, 22], shape fro=-=m shading [32, 36, 37]-=-, and optical flow computation [34, 30]. Mathmatically, these reconstruction problems are formulated as least-squares problems in which the spatial coherence constraints are implemented as cost terms ... |

119 |
Uncertain Dynamic Systems
- Schweppe
- 1973
(Show Context)
Citation Context ... other optimization criteria for choosing L a . For example, we can choose L a to be the matrix with the particular neighborhood structure that minimizes the Bhattacharyya and other distance measures =-=[68] for proba-=-bility density functions. Recall that an information pair implicitly defines Gaussian density function, so that we can choose L a to be one that minimizes the "distance" between the Gaussian... |

110 |
Adaptive smoothing: a general tool for early vision
- Saint-Marc, Chen, et al.
- 1991
(Show Context)
Citation Context ...ions in the images such as at object boundaries, and detection of such locations of spatial discontinuities have been actively pursued by modifying and supplementing the spatial coherence constraints =-=[11, 17, 58, 66, 67]-=-. The issue of dealing with discontinuities in the visual fields is beyond the scope of this thesis. This chapter is concerned with describing an estimation theoretic formulation of a general low-leve... |

108 |
Determining surface orientations of specular surfaces by using the photometric stereo method
- Ikeuchi
- 1981
(Show Context)
Citation Context ... structural integrity ("rigidity") on the whole. This approach has been successful in a wide variety of visual field reconstruction problems including depth interpolation [21, 22], shape fro=-=m shading [32, 36, 37]-=-, and optical flow computation [34, 30]. Mathmatically, these reconstruction problems are formulated as least-squares problems in which the spatial coherence constraints are implemented as cost terms ... |

98 |
Computations underlying the measurement of visual motion
- Hildreth
- 1984
(Show Context)
Citation Context ...hole. This approach has been successful in a wide variety of visual field reconstruction problems including depth interpolation [21, 22], shape from shading [32, 36, 37], and optical flow computation =-=[34, 30]-=-. Mathmatically, these reconstruction problems are formulated as least-squares problems in which the spatial coherence constraints are implemented as cost terms penalizing large spatial derivatives in... |

93 | Block Preconditioning for the Conjugate Gradient method
- Concus, Golub, et al.
- 1985
(Show Context)
Citation Context ...ic, banded structure described above, these elements can be deduced from O(N) intermediate values such as fu i g and fv j g. Recursive inversion of symmetric block tri-diagonal matrices Concus et al. =-=[14]-=- have presented a recursive algorithm to obtain the sequences fu i g and fv j g introduced above for a symmetric tri-diagonal matrix T. Their result can be generalized to a block tri-diagonal, symmetr... |

80 | Optical Flow Estimation: An Error Analysis of Gradient-Based Methods with Local Opt imisat ion
- Kearney, Thompson, et al.
- 1987
(Show Context)
Citation Context ...reduce the discretization effects Presmoothing the brightness A way to reduce the effects of signal sampling 4 on BCCE is to intentionally blur the images before gradient computations. Kearney et al. =-=[42]-=- advocates such presmoothing because ffl The second and highter order brightness gradients are diminished (so that (2.17) is approximated more closely over the sampled signal). ffl The effects of nois... |

72 |
Measuring Visual Motion from Image Sequences
- Anandan
- 1987
(Show Context)
Citation Context ...) is constant over a certain subregion in the image frame and that object brightness does not change over the \Deltat time interval, the following criterion allows us to compute an optical flow field =-=[60, 3]-=-: min f jI 1 ( s + (\Deltat)f ) \Gamma I 0 (s)j : Obtaining this minimum often involves a non-linear search. In another method based on the same intuition, a flow field is computed from the difference... |

69 |
An Implementation of a Computational Theory of Visual Surface Interpolation
- Grimson, E
- 1983
(Show Context)
Citation Context ...me geometrical smoothness and structural integrity ("rigidity") on the whole. This approach has been successful in a wide variety of visual field reconstruction problems including depth inte=-=rpolation [21, 22]-=-, shape from shading [32, 36, 37], and optical flow computation [34, 30]. Mathmatically, these reconstruction problems are formulated as least-squares problems in which the spatial coherence constrain... |

63 |
Two-dimensional discrete Markovian fileds
- Woods
- 1972
(Show Context)
Citation Context ...ving noise e i is given by e i �� ( 0; L ) : This dynamic model is shown to be a Markov Random Field (MRF) [44], which has a multi-dimensional extension of the Markovian property for causal proces=-=ses [77]-=-. Interpreting the information matrix L as an MRF model for the estimation error e f can be quite useful, as it connects our ML estimation formulations directly with other important formulations in vi... |

57 |
Optimal Estimation
- Lewis
- 1986
(Show Context)
Citation Context ... of a Kalman filter such uncertainty, which is expressed via the incorporation of "process noise", can serve the purpose of making the filter stable against modeling errors and responsive to=-= new data [4, 16, 45]-=-. Certainly, a filtering algorithm based on a more systematic approximation of Kalman filter is desirable. This thesis offers such algorithms. Specifically, we first formulate a general Kalman filteri... |

56 |
A element method applied to new active contour models and 3D reconstruction from cross sections
- Cohen, Cohen
- 1990
(Show Context)
Citation Context ...jects in the image frame [48, 59]. Computing motion from image sequences is also important in applications in fields outside of robotics and brain sciences, such as in assessing motility of the heart =-=[13, 64]-=- and in interpretation and prediction of marine and atomospheric processes [51, 12]. Motion information is also useful for managing the image sequences themselves as it offers a basis for image sequen... |

51 |
A survey of linear singular systems
- Lewis
- 1986
(Show Context)
Citation Context ...coherence principle. Specifically, we examine several potentially useful temporal coherence constraints and show that the most natural format to express the dynamics is the descriptor system 1 format =-=[49, 50, 46]-=-. We use the information form of Kalman filter, or information filter, in which the information pair is propagated over time instead of the mean-covariance pair. The information filter equations [4, 4... |

50 |
Advances in mathematical models for image processing
- JAIN
- 1981
(Show Context)
Citation Context ...the field f in which the spatial random process i specifies the probabilistic behavior of the field f by controlling certain interactions, defined by the matrix operator L, among components of f (cf. =-=[38]-=-). In single-frame visual reconstruction problems, the matrix L has a certain sparsely banded structure, reflecting the local properties of the spatial coherence and measurement terms. Besides the pre... |

44 |
The cyclic Jacobi method for computing the principal values of a complex matrix
- Forsythe, Henrici
- 1960
(Show Context)
Citation Context ...his nulling operation. Motivated by computational efficiency, our algorithm makes use of selective nulling by Givens rotations, similar to that used in the Jacobi method for eigenvalue computations 2 =-=[15, 18, 70]-=-, which can lead to parallel implementation. Let us call the N \Theta N lower block the eliminatee block and the N \Theta N upper block the elminator block. A diagonal band of the eliminatee block Q i... |

39 |
Dynamic equations in descriptor form
- Luenberger
- 1977
(Show Context)
Citation Context ...coherence principle. Specifically, we examine several potentially useful temporal coherence constraints and show that the most natural format to express the dynamics is the descriptor system 1 format =-=[49, 50, 46]-=-. We use the information form of Kalman filter, or information filter, in which the information pair is propagated over time instead of the mean-covariance pair. The information filter equations [4, 4... |

35 |
Direct Estimation of Structure and Motion From Multiple Frames,” AI Memo 1190
- Heel
- 1990
(Show Context)
Citation Context ... as well as the measurement processes must be expressed in a state-space dynamic system format. Gauss-Markov system models for f(t) and the corresponding Kalman filtering solutions have been proposed =-=[55, 71, 26, 27, 69]-=-. These methods, however, deal with computational complexity associated with Kalman filters by rather ad hoc approximate methods. We approach such a computational issue more systematically, leading to... |

33 | Kalman filtering and riccati equations for descriptor systems
- Nikoukhah, Willsky, et al.
- 1992
(Show Context)
Citation Context ...ing locally-specified MRF's. To filtering theory Some aspects of the proposed filtering algorithms for visual reconstruction are related to several recent developments in signal processing. First, in =-=[62]-=-, the use of the max17 imum likelihood estimation formalism is shown to be equally applicable to descriptor dynamic systems, yielding a generalization of standard Kalman filter algorithms. Using this ... |

29 |
Dynamic motion vision
- Heel
- 1992
(Show Context)
Citation Context ...tion on how the estimated field from time t \Gamma 1 should be warped in order to fit into the image frame at time t. For example, in multi-frame estimation of dynamically evolving depth fields, Heel =-=[25, 26, 27, 28]-=- has proposed a method to adaptively construct A(t) based on the knowledge of relative motion between the imaged objects and the image frame. Also, in Chapter 6 we will show that for multi-frame optic... |

27 |
Correspondence processes in dynamic scene analysis
- Aggarwal, Davis, et al.
- 1981
(Show Context)
Citation Context ... sparse but relatively reliable 2-D motion vectors. Computational complexity involved with this method, especially for the inter-frame matching or the correspondence problem, is in general quite high =-=[1, 2]-=-. The other method is based directly on the measured pixel values in the images, and it generally yields a dense vector field of apparent motion, or optical flow 1 . Efficient computation of optical f... |

27 | Image intensity understanding - Horn - 1977 |

26 | Kalman filtering in two dimensions
- Woods, Radewan
- 1977
(Show Context)
Citation Context ...e approximation techniques can be considered to be extensions of the techniques based on reducedorder modeling such as the "reduced update" and "strip filter" approximations for th=-=e 2-D Kalman filter [78, 57, 79, 76]-=-. Also, a novel, iterative implementation of square root information Kalman filter is presented. To optical flow computation Optical flow is a dense field of perceptual motion vectors. Estimation of t... |

25 |
Motion-compensated television coding
- Netravali, Robbins
- 1979
(Show Context)
Citation Context ...omospheric processes [51, 12]. Motion information is also useful for managing the image sequences themselves as it offers a basis for image sequence compression for efficient transmission and storage =-=[60, 61]-=-. There are two major approaches in computing apparent motion in image sequences. One of these is based on extracting a set of relatively sparse, yet highly discriminatory features from each image fra... |

23 |
A model for the detection of motion over time
- Black, Anandan
- 1990
(Show Context)
Citation Context ...uires maintaining a correspondence between the image frame coor160 dinates and moving surface elements, e.g., using the estimated flow vectors to track the images of the surface elements in the frame =-=[10]. Tha-=-t is, using (6.4) as an intermediate step, (6.3) can be discretized as f(s; t) \Gamma f(s; t \Gamma 1) + " @ @s f # f(s; t \Gamma 1) = q(s; t) leading to a temporal dynamic model for f(t): f(t) =... |

19 |
Discrete Square Root Filtering: A Survey of Current Techniques
- Kaminski, Bryson, et al.
- 1971
(Show Context)
Citation Context ...s [4, 45] are algebraically equivalent to the standard, mean-covariance Kalman filter equations. The structure of the particular filtering problem governs the choice between the two sets of equations =-=[40, 8]-=-. For visual reconstruction, the information filter is a natural choice because of the possibilities that the information matrices can become singular at various stages of the estimation process. By v... |

17 |
Model-based motion estimation and its application to restoration and interpolation of motion pictures
- Martinez
- 1986
(Show Context)
Citation Context ...sequence of spatially discrete images. Let us first consider the effects of such signal sampling on motion perception. By assuming that the optical flow is constant, f , over space and time, Martinez =-=[54]-=- has derived the following relationship between the spatial and temporal bandwidths 3 although in practice brightness gradients are often used because f ? can be difficult to measure of the brightness... |

16 |
Temporal Surface Reconstruction
- Heel
- 1991
(Show Context)
Citation Context ... the image frame) makes the filter computationally unfeasible in its optimal form. Kalman filtering solutions for multi-frame visual reconstruction problem have been proposed in a variety of contexts =-=[55, 71, 27, 10, 69]-=-; however, in each of these cases some ad hoc simplifying assumptions are made in order to avoid the computational complexity issues. For example, in none of these previously proposed methods, is the ... |