## Weak Calibration and Image-Based Rendering Algorithms (1999)

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Genc99weakcalibration,

author = {Yakup Genc},

title = {Weak Calibration and Image-Based Rendering Algorithms},

institution = {},

year = {1999}

}

### OpenURL

### Abstract

This thesis introduces twonovel techniques for the analysis and synthesis of image sequences: a linear algorithm for weak calibration of a stereo rig from point correspondences, and an algorithm for image-based rendering without explicit three-dimensional reconstruction based on point and line correspondences. By recasting the epipolar constraint in a projective setting with an appropriate basis choice, we first show that Jepson's and Heeger's linear subspace algorithm for infinitesimal motion estimation can be generalized to the finite motion case. This yields a linear method for weak calibration. The algorithm has been implemented and tested on both real and synthetic images, and it is compared to other linear and non-linear approaches to weak calibration. We then show that the set of all images of a rigid scene taken by a Euclidean camera is a six-dimensional variety, and we introduce a parameterization (called parameterized image variety, or PIV in short) of this variety for weak perspective and paraperspective cameras in terms of the image positions of three reference points. This parameterization can be estimated via linear least-squares and non-linear least-squares with low-degree equations. We use parameterized image varieties of both point and line features to synthesize new images from a set of pre-recorded pictures without actual three-dimensional reconstruction (image-based rendering) in an integrated framework. The method has been implemented and extensively tested on real data sets. Finally, we show how to adapt recent advances in statistically-unbiased least-squares methods to our image-based rendering approach. The point-based PIV involves equations with bilinear or higher-order data dependencies and we showhow to efficiently estimate its parameters by adapting L...

### Citations

2740 |
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography
- Fischler, Bolles
- 1981
(Show Context)
Citation Context ...rovided by their authors. For our own data sets, we have implemented a version of the Harris corner detector [32] and matched the points using a simple RANSAC (random sample consensus) type algorithm =-=[23]-=-. We then eliminated visible bad matches by hand. The line segments were extracted in images using the publicly available software environment VISTA [89] and the line correspondences are established b... |

2120 |
Matrix computations
- Golub, Loan
- 1996
(Show Context)
Citation Context ... #k# = # #k### it can be shown that = 1, and the convergence can be measured from # ### # 1#. In the actual implementation, we also follow [59] and use generalized singular value decomposition [29] to improve the numerical behavior of the method. If # #k### c and # #k### c are the Cholesky decompositions of the matrices # #k### and # #k### respectively, the solution # #k# is obtained by compu... |

1498 |
Robot Vision
- Horn
- 1986
(Show Context)
Citation Context ...pective camera with unit focal length observes some scene. Let p =(u; v; 1) T denote the position of an image point, and _ p =(_u; _ v; 0) T denote the corresponding motionseld; it is well known (see =-=[46]-=- for example) that if the instantaneous motion of the camera is described in a coordinate system attached to the scene by the translational velocity t and the rotational velocity !, then # # _ u _ v #... |

1173 | Light field rendering
- Levoy, Hanrahan
- 1996
(Show Context)
Citation Context ...ative to the classical model-based rendering methods. In recentyears, there has been a proliferation of research on image-based rendering in both computer vision [57, 95, 56, 3] and computer graphics =-=[9, 30, 61]-=-. The computer graphics techniques are based on the idea that the set of all visual rays (lightseld) is four-dimensional, and can thus be characterized from a two-dimensional sample of images of a rig... |

964 | Modeling and rendering architecture from photographs: A hybrid geometry- and image-based approach
- Debevec, Taylor, et al.
- 1996
(Show Context)
Citation Context ...ith dierent paradigms such as structure from motion (e.g., [55, 108, 19, 105]), shape from stereo (e.g., [70, 79]), shape from shading (e.g., [49, 84]), and other model reconstruction methods (e.g., [=-=13, 104]-=-). The extracted model may be a complete CAD model or just the positions of some geometric features like points and lines. Once the 3D model representing the scene has been reconstructed, a new view o... |

945 | Shape and motion from image streams under orthography: a factorization method
- Tomasi, Kanade
- 1992
(Show Context)
Citation Context ...iterature on image matching, including various methods 6 for detecting feature points [76, 18, 32, 81, 92, 15], hypothesizing initial correspondences (e.g., correlation [28, 79, 24], feature tracking =-=[75, 108, 118]-=- and structural matching [4, 98, 45, 115]), establishing new correspondences once an initial estimate of the epipolar geometry has been obtained [117, 80], andsnding and rejecting false matches using ... |

922 | The Lumigraph
- Gortler, Grzeszczuk, et al.
- 1996
(Show Context)
Citation Context ...ative to the classical model-based rendering methods. In recentyears, there has been a proliferation of research on image-based rendering in both computer vision [57, 95, 56, 3] and computer graphics =-=[9, 30, 61]-=-. The computer graphics techniques are based on the idea that the set of all visual rays (lightseld) is four-dimensional, and can thus be characterized from a two-dimensional sample of images of a rig... |

708 | Plenoptic modeling: An image-based rendering system
- McMillan, Bishop
- 1995
(Show Context)
Citation Context ...two reference images. 42 4.3 Light-Field Methods The computer graphics techniques developed by Chen [9], Gortler, Grzeszczuk, Szeliski and Cohen [30], Levoy and Hanrahan [61], and McMillan and Bishop =-=[74]-=- are based on the idea that the set of all visual rays (lightseld) is four-dimensional, and can thus be characterized from a two-dimensional sample of two-dimensional images of a rigid scene. The ligh... |

680 |
A computer algorithm for reconstructing a scene from two projections. Nature
- Longuet-Higgins
- 1981
(Show Context)
Citation Context ... the fundamental matrix whichisa3# 3 singular matrix) [21]. When the cameras are calibrated, i.e., the intrinsic parameters of the cameras are known, this relation is captured by the essential matrix =-=[63]-=-. The image of a scene point in one image lies on the corresponding epipolar line. The epipolar lines in one image go through the epipole, i.e., the intersection of the image plane with the baseline c... |

560 | View interpolation for image synthesis
- Chen, Williams
- 1993
(Show Context)
Citation Context ...ypes of models) whereas the light-eld methods do not assume anything about the re ectance properties of the scene. Thesrst method we will review is the view interpolation method of Chen and Williams [=-=10]-=- which generates intermediate images by morphing images stored at nearby viewpoints. The morphing process requires a pixel correspondence map that is computed using a priori known range data and the c... |

521 |
What can be seen in three dimensions with an uncalibrated stereo rig
- Faugeras
- 1992
(Show Context)
Citation Context .... Developing accurate and reliable methods for weak calibration is very important in practice because of the central role of epipolar geometry in stereo and motion algorithms: in particular, Faugeras =-=[19]-=- and Hartley, Gupta and Chang [39] have shown that it is possible to reconstruct the three-dimensional projective structure of a scene observed by a weakly calibrated stereo rig without any knowledge ... |

498 |
Three-Dimensional Computer Vision
- Faugeras
- 2001
(Show Context)
Citation Context ...e versa. In particular, # = # # # # # b a #as# b #d #c cs+ d ds# # b # cs# # a # #cs# # ds# + a # + b # # # # # # : (2.4) 2.2 Current Approaches to Weak Calibration As mentioned by Faugeras [20], the problem of estimating the epipoles and the epipolar transformations compatible with seven point correspondences wassrst posed by Chasles [8] and solved byHesse[44] (see the article by Sturm [103... |

496 | A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry
- Zhang, Deriche, et al.
- 1994
(Show Context)
Citation Context ... a weakly calibrated stereo rig without any knowledge of the intrinsic parameters of the cameras (see [55, 75, 99, 88] for related work). As demonstrated byXuet al. [117] [80] and Deriche et al. [16] =-=[120]-=-, estimating the epipolar geometry from initial point correspondences is also the key to establishing further correspondences in image matching. Luong and Faugeras [68] discuss many other applications... |

490 | The plenoptic function and the elements of early vision
- Adelson, Bergen
- 1991
(Show Context)
Citation Context ...ys (lightseld) is four-dimensional, and can thus be characterized from a two-dimensional sample of two-dimensional images of a rigid scene. The lightseld is a simplied form of the plenoptic function [=-=1]-=-. The plenoptic function at a point (x; y; z) determines the radiant energy emitted from the scene along a ray passing through this point. More precisely, the plenoptic function is normally written as... |

484 | QuickTime VR — an image-based approach to virtual environment navigation
- Chen
- 1995
(Show Context)
Citation Context ...ative to the classical model-based rendering methods. In recentyears, there has been a proliferation of research on image-based rendering in both computer vision [57, 95, 56, 3] and computer graphics =-=[9, 30, 61]-=-. The computer graphics techniques are based on the idea that the set of all visual rays (lightseld) is four-dimensional, and can thus be characterized from a two-dimensional sample of images of a rig... |

451 | Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
- Shewchuk
- 1996
(Show Context)
Citation Context ...her points and lines. To create a shaded picture, we can construct a constrained Delaunay triangulation of these line segments and points (using, for example Shewuck's Triangle public-domain software =-=[101]-=-) whose vertices and edges form a superset of the input points and line segments. Texture mapping is then easily achieved by using the same triangulation in one of the input images. This section detai... |

440 |
Measurement Error Models
- Fuller
- 1987
(Show Context)
Citation Context ...meter estimation problem encountered in Chapter 5 and state the reasons whywechoose this model. We also provide some background necessary to follow the discussion in later sections (we largely follow =-=[25-=-]). A statistical model is a specication of [25, p. 9]: # the variables and the parameters of interest, # the relationships among the variables, # the assumptions about the statistical properties of t... |

434 |
Recognition by linear combination of models
- Ullman, Basri
- 1989
(Show Context)
Citation Context ...ticular, if the center of mass of the observed feature points is chosen as the origin of the image coordinate system, it can be shown that an ane image is the linear combination of three model images =-=[112]-=-, that the measurement matrix # # = # # # # # # # # # # # # # # u ### # ::: u ### m ::: ::: ::: u #f# # ::: u #f# m v ### # ::: v ### m ::: ::: ::: v #f# # ::: v #f# m # # # # # # # # # # # # # # has ... |

374 | Camera self-calibration: theory and experiments
- Faugeras, Luong, et al.
- 1992
(Show Context)
Citation Context ...s weak calibration. More precisely, two uncalibrated perspective images of a rigid object are related by the epipolar geometry (or equivalently by the fundamental matrix whichisa3# 3 singular matrix) =-=[21]-=-. When the cameras are calibrated, i.e., the intrinsic parameters of the cameras are known, this relation is captured by the essential matrix [63]. The image of a scene point in one image lies on the ... |

340 | Determining the epipolar geometry and its uncertainty: a review
- Zhang
- 1998
(Show Context)
Citation Context ... methods are needed suchas[109]. We will propose in Chapter 3 a new method for weak calibration and compare it to other approaches [65, 68, 37, 6]. We brie y describe these here for completeness (see =-=[119]-=- for a review of other techniques that are not covered here). 2.2.1 Linear Methods Note that the epipolar constraint (2.2) is a linear equation in the nine coecients of the fundamental matrix # . Sinc... |

306 |
Afne structure from motion
- Koenderink, Doorn
- 1991
(Show Context)
Citation Context ...at it is possible to reconstruct the three-dimensional projective structure of a scene observed by a weakly calibrated stereo rig without any knowledge of the intrinsic parameters of the cameras (see =-=[55, 75, 99, 88]-=- for related work). As demonstrated byXuet al. [117] [80] and Deriche et al. [16] [120], estimating the epipolar geometry from initial point correspondences is also the key to establishing further cor... |

305 |
Faugeras. A theory of selfcalibration of a moving camera
- Maybank
- 1992
(Show Context)
Citation Context ...compatible with seven point correspondences wassrst posed by Chasles [8] and solved byHesse[44] (see the article by Sturm [103] for an analysis of Hesse's method and the paper by Faugeras and Maybank =-=[72]-=- for a modern account). Hesse's approach is mostly of theoretical interest since it only exploits the minimum number of point correspondences necessary to estimate the epipolar geometry and is thus un... |

301 | Estimation of relative camera positions for uncalibrated cameras
- Hartley
- 1992
(Show Context)
Citation Context ...eknowledge of the epipoles and of the homography, called epipolar transformation, relating the pencils of epipolar lines in the two images, or equivalently, by the knowledge of the fundamental matrix =-=[21, 39, 33, 64, 68]-=-. This chapter reviews current approaches to the problem of estimating the epipolar geometry from point correspondences, a process known as weak calibration. Developing accurate and reliable methods f... |

284 |
Cooperative computation of stereo disparity
- Marr, Poggio
- 1976
(Show Context)
Citation Context ...ount of work in the computer vision literature on model reconstruction from intensity images with dierent paradigms such as structure from motion (e.g., [55, 108, 19, 105]), shape from stereo (e.g., [=-=70, 79]-=-), shape from shading (e.g., [49, 84]), and other model reconstruction methods (e.g., [13, 104]). The extracted model may be a complete CAD model or just the positions of some geometric features like ... |

263 | A paraperspective factorization method for shape and motion recovery
- Poelman, Kanade
- 1997
(Show Context)
Citation Context ...tation matrices are orthonormal yielding 3f nonlinear constraints on the vectors a and b for each image. The factorization method has been extended to weak perspective and paraperspective projections =-=[85]-=- as well as to line features [90]. 4.2 Transfer-Based Methods The computer vision techniques for image-based rendering without actual three-dimensional reconstruction proposed by Laveau and Faugeras [... |

259 |
Statistical Optimization for Geometric Computation: Theory and Practice
- Kanatani
- 1996
(Show Context)
Citation Context ... s #j associated with w jo , and # # ! denotes the pseudo-inverse of # ! . Several solutions to (6.8) have been proposed, including total least squares [48] and the renormalization method of Kanatani =-=[53]-=-. These methods all involve approximations of the objective function in (6.8). The total-least-squares solution [48] is obtained by assuming that the error in linearized observation vectors are from a... |

254 | View morphing
- SEITZ, DYER
- 1996
(Show Context)
Citation Context ...plicitly reconstructs the scene up to an ane transformation. Once again a new view is dened by the image positions of the reference points. For more restricted virtual camera motions, Seitz and Dyer [=-=96]-=- use a technique called view morphing to render novel images of a rigid scene from two images. Their method assumes that the virtual camera center lies on the baseline (i.e., the line connecting the c... |

251 |
Stereo from uncalibrated cameras
- Hartley, Gupta, et al.
- 1992
(Show Context)
Citation Context ... methods for weak calibration is very important in practice because of the central role of epipolar geometry in stereo and motion algorithms: in particular, Faugeras [19] and Hartley, Gupta and Chang =-=[39]-=- have shown that it is possible to reconstruct the three-dimensional projective structure of a scene observed by a weakly calibrated stereo rig without any knowledge of the intrinsic parameters of the... |

244 | The Fundamental Matrix: Theory, Algorithms, and Stability Analysis
- Luong, Faugeras
- 1996
(Show Context)
Citation Context ...] [80] and Deriche et al. [16] [120], estimating the epipolar geometry from initial point correspondences is also the key to establishing further correspondences in image matching. Luong and Faugeras =-=[68]-=- discuss many other applications, including the construction of stereo projective invariants [31, 34, 35, 99], the synthesis of new images from old ones [57, 95], convex hull computation [91], image r... |

208 | Numerical Shape from Shading and Occluding Boundaries
- Ikeuchi, Horn
- 1981
(Show Context)
Citation Context ...iterature on model reconstruction from intensity images with dierent paradigms such as structure from motion (e.g., [55, 108, 19, 105]), shape from stereo (e.g., [70, 79]), shape from shading (e.g., [=-=49, 84]-=-), and other model reconstruction methods (e.g., [13, 104]). The extracted model may be a complete CAD model or just the positions of some geometric features like points and lines. Once the 3D model r... |

200 |
Towards automatic visual obstacle avoidance
- Moravec
- 1977
(Show Context)
Citation Context ...process have been correctly established by a separate matching process. Let us just mention that there is a vast literature on image matching, including various methods 6 for detecting feature points =-=[76, 18, 32, 81, 92, 15]-=-, hypothesizing initial correspondences (e.g., correlation [28, 79, 24], feature tracking [75, 108, 118] and structural matching [4, 98, 45, 115]), establishing new correspondences once an initial est... |

198 | Survey of texture mapping
- Heckbert
- 1986
(Show Context)
Citation Context ...ion, a picture of the scene can be synthesized for example by ray tracing (for more information on ray tracing see [41, Chapter 14]). To achieve more realistic images one can use texture mapping (see =-=[42]-=- for a review) using the texture extracted from the input images. Depending on the details in the model, model-based methods can yield very realistic images. A complete image-based rendering system th... |

185 | An image-based approach to three-dimensional computer graphics
- McMillan
- 1997
(Show Context)
Citation Context ... by arbitrary planar projective transformations) unless additional scene constraints are taken into account. Related methods have been proposed by several authors in both the ane and projective cases =-=[3, 56, 95, 73]-=-. For three images taken by a calibrated pinhole camera, Avidan and Shashua [3] have used trifocal tensors [100] to constrain the reprojection of the points in these images. In other words, the three ... |

185 |
Structural description and inexact matching
- Shapiro, Haralick
- 1981
(Show Context)
Citation Context ...various methods 6 for detecting feature points [76, 18, 32, 81, 92, 15], hypothesizing initial correspondences (e.g., correlation [28, 79, 24], feature tracking [75, 108, 118] and structural matching =-=[4, 98, 45, 115]-=-), establishing new correspondences once an initial estimate of the epipolar geometry has been obtained [117, 80], andsnding and rejecting false matches using techniques from robust statistics [83, 97... |

166 |
defence of the 8-point algorithm
- In
- 1995
(Show Context)
Citation Context ...ar geometry. Section 2.2 presents previous approaches to weak calibration, including the non-linear distance minimization technique of Luong et al. [65, 68], Hartley's normalized eightpoint algorithm =-=[3-=-7], and the virtual parallax approachofBoufama and Mohr [6]. Section 2.3 claries the relationship between Jepson's and Heeger's linear subspace approach to innitesimal motion analysis [50, 43, 51] and... |

165 |
The Algebraic Theory of Modular Systems
- Macaulay
- 1916
(Show Context)
Citation Context ... eliminating three variables (the last row of the camera rotation) amongsve quadratic equations (the Euclidean constraints associated with perspective images), a formidable task in elimination theory =-=[69]-=-. 80 0 20 40 25% training Image Point Reconstruction Using PIV 0 5 10 50% training Error in Reconstruction [Pixels] 0 2 4 6 8 75% training KITCHEN HOUSE LQBOX TOWER XL1BOX FLOWER 0 2 4 100% training D... |

165 |
Theory of Reconstruction from Image Motion
- Maybank
- 1992
(Show Context)
Citation Context ...by Luong and Faugeras [67, 68] for the non-linear method of Luong et al. [65, 68] using both statistical techniques 34 and the notion of critical surfaces from photogrammetry (see the books byMaybank =-=[71]-=- and Faugeras [20] for discussions of these surfaces in the computer vision context). Akey part of our approachisthechoice of an appropriate basis for projective space, which assumes that four referen... |

160 |
Motion and structure from motion in a piecewise planar environment
- OD, Lustman
- 1988
(Show Context)
Citation Context ...mation of the homographies associated with several groups of four or more coplanar points; these groups can be found, when they exist, by using generate-and-test methods such as the ones described in =-=[22, 31, 102, 91-=-].) In general, four coplanar scene points are not guaranteed to exist, and the virtual parallax associated with one of these points is the dierence between the position of its actual image projection... |

149 |
Subspace methods for recovering rigid motion I: Algorithm and implementation
- Heeger, Jepson
- 1992
(Show Context)
Citation Context ... from a set of pre-recorded pictures is called image-based rendering. In this thesis, we investigate these two problems and develop algorithms to solve them. It has been shown by Jepson and Heeger in =-=[43, 50-=-] that motion estimation for calibrated cameras undergoing innitesimal displacements can be reduced to a linear problem. A primary objective of this thesis was to answer the following question: is it ... |

141 | Disparity Analysis of Images
- Barnard, Thomson
- 1980
(Show Context)
Citation Context ...various methods 6 for detecting feature points [76, 18, 32, 81, 92, 15], hypothesizing initial correspondences (e.g., correlation [28, 79, 24], feature tracking [75, 108, 118] and structural matching =-=[4, 98, 45, 115]-=-), establishing new correspondences once an initial estimate of the epipolar geometry has been obtained [117, 80], andsnding and rejecting false matches using techniques from robust statistics [83, 97... |

131 |
Constructing virtual worlds using dense stereo
- Narayanan, Rander, et al.
- 1998
(Show Context)
Citation Context ...he details in the model, model-based methods can yield very realistic images. A complete image-based rendering system that represents the scene using depth maps has been described by Kanade et al. in =-=[52, 78]-=-. They have described a visual medium, called virtualized reality, where a representation of a real scene is captured as a collection of stereo intensity images along with reconstructed depth maps. A ... |

123 |
Aparallel stereo algorithm that produce dense depth maps and preserves image features
- Fua
- 1993
(Show Context)
Citation Context ... mention that there is a vast literature on image matching, including various methods 6 for detecting feature points [76, 18, 32, 81, 92, 15], hypothesizing initial correspondences (e.g., correlation =-=[28, 79, 24]-=-, feature tracking [75, 108, 118] and structural matching [4, 98, 45, 115]), establishing new correspondences once an initial estimate of the epipolar geometry has been obtained [117, 80], andsnding a... |

115 | A computational approach for corner and vertex detection, Int Conf of Computer Vision 10
- Deruche, Giraudon
- 1993
(Show Context)
Citation Context ...process have been correctly established by a separate matching process. Let us just mention that there is a vast literature on image matching, including various methods 6 for detecting feature points =-=[76, 18, 32, 81, 92, 15]-=-, hypothesizing initial correspondences (e.g., correlation [28, 79, 24], feature tracking [75, 108, 118] and structural matching [4, 98, 45, 115]), establishing new correspondences once an initial est... |

107 |
Trilinearity in visual recognition by alignment
- Shashua
- 1994
(Show Context)
Citation Context ...ds have been proposed by several authors in both the ane and projective cases [3, 56, 95, 73]. For three images taken by a calibrated pinhole camera, Avidan and Shashua [3] have used trifocal tensors =-=[100]-=- to constrain the reprojection of the points in these images. In other words, the three images of a scene pointobeycertainmultilinear matching constraints captured by the trifocal tensor that can be c... |

107 | Structure and motion from line segments in multiple images
- Taylor, Kriegman
- 1995
(Show Context)
Citation Context ...he rendering process. There is a tremendous amount of work in the computer vision literature on model reconstruction from intensity images with dierent paradigms such as structure from motion (e.g., [=-=55, 108, 19, 105]-=-), shape from stereo (e.g., [70, 79]), shape from shading (e.g., [49, 84]), and other model reconstruction methods (e.g., [13, 104]). The extracted model may be a complete CAD model or just the positi... |

106 | Outlier Detection and Motion Segmentation
- Torr
- 1995
(Show Context)
Citation Context ...g the construction of stereo projective invariants [31, 34, 35, 99], the synthesis of new images from old ones [57, 95], convex hull computation [91], image rectication [38, 94], motion segmentation [=-=80, 110]-=-, and self calibration [21, 36]. We propose in Chapter 3 a linear algorithm for weak calibration that generalizes Jepson's and Heeger's method to thesnite motion case. This algorithm has been implemen... |

101 | Novel View Synthesis in Tensor Space
- Avidan, Shashua
- 1997
(Show Context)
Citation Context ...e-dimensional model, oering an alternative to the classical model-based rendering methods. In recentyears, there has been a proliferation of research on image-based rendering in both computer vision [=-=57, 95, 56, 3]-=- and computer graphics [9, 30, 61]. The computer graphics techniques are based on the idea that the set of all visual rays (lightseld) is four-dimensional, and can thus be characterized from a two-dim... |

100 | Stereo correspondence through feature grouping and maximal cliques
- Horaud, Skordas
- 1989
(Show Context)
Citation Context ...various methods 6 for detecting feature points [76, 18, 32, 81, 92, 15], hypothesizing initial correspondences (e.g., correlation [28, 79, 24], feature tracking [75, 108, 118] and structural matching =-=[4, 98, 45, 115]-=-), establishing new correspondences once an initial estimate of the epipolar geometry has been obtained [117, 80], andsnding and rejecting false matches using techniques from robust statistics [83, 97... |

93 | Relative 3d reconstruction using multiple uncalibrated images
- Mohr, Veillon, et al.
- 1993
(Show Context)
Citation Context ...at it is possible to reconstruct the three-dimensional projective structure of a scene observed by a weakly calibrated stereo rig without any knowledge of the intrinsic parameters of the cameras (see =-=[55, 75, 99, 88]-=- for related work). As demonstrated byXuet al. [117] [80] and Deriche et al. [16] [120], estimating the epipolar geometry from initial point correspondences is also the key to establishing further cor... |

92 | On determining the fundamental matrix: analysis of different methods and experimental results,” INRIA, Tech. Rep. Raport de Recherche 1894
- Luong, Deriche, et al.
- 1993
(Show Context)
Citation Context .... Section 2.1 summarizes the main elements of epipolar geometry. Section 2.2 presents previous approaches to weak calibration, including the non-linear distance minimization technique of Luong et al. =-=[65, 68-=-], Hartley's normalized eightpoint algorithm [37], and the virtual parallax approachofBoufama and Mohr [6]. Section 2.3 claries the relationship between Jepson's and Heeger's linear subspace approach ... |