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38
3D Model Acquisition from Extended Image Sequences
, 1995
"... This paper describes the extraction of 3D geometrical data from image sequences, for the purpose of creating 3D models of objects in the world. The approach is uncalibrated  camera internal parameters and camera motion are not known or required. Processing an image sequence is underpinned by token ..."
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Cited by 236 (29 self)
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This paper describes the extraction of 3D geometrical data from image sequences, for the purpose of creating 3D models of objects in the world. The approach is uncalibrated  camera internal parameters and camera motion are not known or required. Processing an image sequence is underpinned by token correspondences between images. We utilise matching techniques which are both robust (detecting and discarding mismatches) and fully automatic. The matched tokens are used to compute 3D structure, which is initialised as it appears and then recursively updated over time. We describe a novel robust estimator of the trifocal tensor, based on a minimum number of token correspondences across an image triplet; and a novel tracking algorithm in which corners and line segments are matched over image triplets in an integrated framework. Experimental results are provided for a variety of scenes, including outdoor scenes taken with a handheld camcorder. Quantitative statistics are included to asses...
Robust Parameterization and Computation of the Trifocal Tensor
 Image and Vision Computing
, 1997
"... The constraint that rigid motion places on the image positions of points and lines over three views is captured by the trifocal tensor. This paper demonstrates a novel robust estimator of the trifocal tensor, based on a minimum number of correspondences across an image triplet. In addition, it i ..."
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Cited by 124 (25 self)
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The constraint that rigid motion places on the image positions of points and lines over three views is captured by the trifocal tensor. This paper demonstrates a novel robust estimator of the trifocal tensor, based on a minimum number of correspondences across an image triplet. In addition, it is shown how the robust estimate can be used to find a minimal parameterization that enforces the constraints between the elements of the tensor. The matching techniques used to estimate the tensor are both robust (detecting and discarding mismatches) and fully automatic. Results are given for real image sequences. 1 Introduction The trifocal tensor plays a similar role for three views to that played by the fundamental matrix for two. It encapsulates all the (projective) geometric constraints between three views that are independent of scene structure. The tensor only depends on the motion between views and the internal parameters of the cameras, but it can be computed from image corre...
Projective Reconstruction and Invariants from Multiple Images
, 1994
"... This paper in vestigates projective reco n#k ruction of geometric con figuration s seen in two or more perspective views,an d the computation of projective in varian ts of these con figuration s from their images. A basic tool in this in vestigation is the fun#6 men tal matrix which describes the ..."
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Cited by 95 (9 self)
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This paper in vestigates projective reco n#k ruction of geometric con figuration s seen in two or more perspective views,an d the computation of projective in varian ts of these con figuration s from their images. A basic tool in this in vestigation is the fun#6 men tal matrix which describes the epipolar correspon#1640 between image pairs. It is proven that on ce the epipolar geometry iskn# wn , the co n#k uratio n# of man y geometric structures (for in#2 an#2 sets of poin ts orlin es) are determin ed up to a collin eation of projective 3space # 3 by their projection in two in#25 en# den t images. This theorem is the ey to a method for the computation of i n# aria n# s of the geometry. I n# aria n# s of 6 d of fourlin esin # 3 are defin#2 a n# discussed. An example with real images shows that they are e#ective in distin guishi n# di#eren t geometrical con#2 uration#2 Si n#k the fun#2 men tal matrix is a basic tool in the computation of these in varian ts,n ew methods of computin g the fun#0 men tal matrix from 7 poin t correspon#22459 in two images or 6 poin t correspon den cesin 3 images are given
Linear Multi View Reconstruction and Camera Recovery
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2001
"... This paper presents a linear algorithm for the simultaneous computation of 3D points and camera positions from multiple perspective views, based on having four points on a reference plane visible in all views. The reconstruction and camera recovery is achieved, in a single step, by finding the null ..."
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Cited by 66 (5 self)
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This paper presents a linear algorithm for the simultaneous computation of 3D points and camera positions from multiple perspective views, based on having four points on a reference plane visible in all views. The reconstruction and camera recovery is achieved, in a single step, by finding the nullspace of a matrix using singular value decomposition. Unlike factorization algorithms, the presented algorithm does not require all points to be visible in all views. By simultaneously reconstructing points and views the numerically stabilizing effect of having wide spread cameras with large mutual baselines is exploited. Experimental results are presented for both finite and infinite reference planes. An especially interesting application of this method is the reconstruction of architectural scenes with the reference plane taken as the plane at infinity which is visible via three orthogonal vanishing points. This is demonstrated by reconstructing the outside and inside (courtyard) of a building on the basis of 35 views in one single SVD.
Invariants of Six Points and Projective Reconstruction from Three Uncalibrated Images
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... There are three projective invariants of a set of six points in general position in space. It is well known that these invariants cannot be recovered from one image, however an invariant relationship does exist between space invariants and image invariants. This invariant relationship is first deriv ..."
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Cited by 59 (16 self)
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There are three projective invariants of a set of six points in general position in space. It is well known that these invariants cannot be recovered from one image, however an invariant relationship does exist between space invariants and image invariants. This invariant relationship is first derived for a single image. Then this invariant relationship is used to derive the space invariants, when multiple images are available. This paper establishes that the minimum number of images for computing these invariants is three, and the computation of invariants of six points from three images can have as many as three solutions. Algorithms are presented for computing these invariants in closed form. The accuracy and stability with respect to image noise, selection of the triplets of images and distance between viewing positions are studied both through real and simulated images. Applications of these invariants are also presented. Both the results of Faugeras [1] and Hartley et al. [2] for...
Reconstruction from uncalibrated sequences with a hierarchy of trifocal tensors
 In ECCV
, 2000
"... This paper considers projective reconstruction with a hierarchical computational structure of trifocal tensors that integrates feature tracking and geometrical validation of the feature tracks. The algorithm was embedded into a system aimed at completely automatic Euclidean reconstruction from uncal ..."
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Cited by 54 (5 self)
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This paper considers projective reconstruction with a hierarchical computational structure of trifocal tensors that integrates feature tracking and geometrical validation of the feature tracks. The algorithm was embedded into a system aimed at completely automatic Euclidean reconstruction from uncalibrated handheld amateur video sequences. The algorithm was tested as part of this system on a number of sequences grabbed directly from a lowend video camera without editing. The proposed approach can be considered a generalisation of a scheme of [Fitzgibbon and Zisserman, ECCV ‘98]. The proposed scheme tries to adapt itself to the motion and frame rate in the sequence by finding good triplets of views from which accurate and unique trifocal tensors can be calculated. This is in contrast to the assumption that three consecutive views in the video sequence are a good choice. Using trifocal tensors with a wider span suppresses error accumulation and makes the scheme less reliant on bundle adjustment. The proposed computational structure may also be used with fundamental matrices as the basic building block. 1
Recursive Structure and Motion from Image Sequences using Shape and Depth Spaces
 IN SCIA97
, 1997
"... In this paper a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace metho ..."
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Cited by 43 (6 self)
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In this paper a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace methods and is derived from both ordinary coordinate representations and camera matrices and from a so called depth and shape analysis. Furthermore, no initial phase is needed to start up the algorithm. It starts directly with the first two images and incorporates new images as soon as new corresponding points are obtained. The performance of the algorithm is shown on simulated data. Moreover, the two different approaches, one using camera matrices and the other using the concepts of affine shape and depth, are unified into a general theory of structure and motion from image sequences.
Dual Computation of Projective Shape and Camera Positions from Multiple Images
, 1998
"... Given multiple image data from a set of points in 3D, there are two fundamental questions that can be addressed: ffl What is the structure of the set of points in 3D? ffl What are the positions of the cameras relative to the points? In this paper we show that, for projective views and with stru ..."
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Cited by 35 (4 self)
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Given multiple image data from a set of points in 3D, there are two fundamental questions that can be addressed: ffl What is the structure of the set of points in 3D? ffl What are the positions of the cameras relative to the points? In this paper we show that, for projective views and with structure and position defined projectively, these problems are dual because they can be solved using constraint equations where space points and camera positions occur in a reciprocal way. More specifically, by using canonical projective reference frames for all points in space and images, the imaging of point sets in space by multiple cameras can be captured by constraint relations involving three different kinds of parameters only, which are the coordinates of :(1) space points, (2) camera positions (3) image points. The duality implies that the problem of computing camera positions from p points in q views can be solved with the same algorithm as the problem of directly reconstructing q + 4...
Algebraic Properties of Multilinear Constraints
, 1996
"... In this paper the dioeerent algebraic varieties that can be generated from multiple view geometry with uncalibrated cameras have been investigated. The natural descriptor, Vn , to work with is the image of IP 3 in IP 2 \Theta IP 2 \Theta \Delta \Delta \Delta \Theta IP 2 under a corresponding product ..."
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Cited by 35 (4 self)
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In this paper the dioeerent algebraic varieties that can be generated from multiple view geometry with uncalibrated cameras have been investigated. The natural descriptor, Vn , to work with is the image of IP 3 in IP 2 \Theta IP 2 \Theta \Delta \Delta \Delta \Theta IP 2 under a corresponding product of projections, (A1 \Theta A2 \Theta : : : \Theta Am). Another descriptor, the variety Vb , is the one generated by all bilinear forms between pairs of views, which consists of all points in IP 2 \Theta IP 2 \Theta \Delta \Delta \Delta \Theta IP 2 where all bilinear forms vanish. Yet another descriptor, the variety V t , is the variety generated by all trilinear forms between triplets of views. It has been shown that when m = 3, Vb is a reducible variety with one component corresponding to V t and another corresponding to the trifocal plane. Furthermore, when m = 3, V t is generated by the three bilinearities and one trilinearity, when m = 4, V t is generated by the six bil...
Geometry and Algebra of Multiple Projective Transformations
, 1995
"... In this thesis several dioeerent cases of reconstruction of 3D objects from a number of 2D images, obtained by projective transformations, are considered. Firstly, the case where the images are taken by uncalibrated cameras, making it possible to reconstruct the object up to projective transformatio ..."
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Cited by 34 (8 self)
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In this thesis several dioeerent cases of reconstruction of 3D objects from a number of 2D images, obtained by projective transformations, are considered. Firstly, the case where the images are taken by uncalibrated cameras, making it possible to reconstruct the object up to projective transformations, is described. The minimal cases of two images of seven points and three images of six points are solved, giving threefold solutions in both cases. Then linear methods for the cases where more points or more images are available are given, using multilinear constraints, based on a canonical representation of the multiple view geometry. The case of a continuous stream of images is also treated, giving multilinear constraints on the image coordinates and their derivatives. Secondly, the algebraic properties of the multilinear functions and the ideals generated by them are investigated. The main result is that the ideal generated by the bilinearities for three views have a primary decomposit...