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 hand-held camcorder. Quantitative statistics are included to asses...

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...

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 3-space # 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

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-space 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.

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.

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 low-end 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

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...

. Given multiple image data from a set of points in 3-D, there are two fundamental questions that can be addressed: ffl What is the structure of the set of points in 3-D? 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...

oints. This new al gorithm integrates bothl ines and points into onel inear framework. This contrasts with previousl y known al gorithms that have been specific to either point sets (for exampl# the 8-pointal#886P3S of [5, 6]) orl#85 sets ([3, 4]). Previousl# to deal with both points andl#360 at the same time, an iterativel east-squares approach has been necessary. The newal#8z8PN3 has not to date been tried on mixed sets of points andl#d3P5 However, the resul#= obtained in ([3, 4]) forl#5=fi and in [7] using points, both special cases of this al gorithm show quite good resul#5z Thanks are du# to Long Qu an and Andrew Zisserman for discu# sions before and du## ng the preparation of this note. 2Not at ion Al# vectors are written asl ower case bo l#l#5W58P3 such asu or #. Such a notation denotes a col umn vector. A row vector is written as a transposedcol umn vector such # .The inner product of two vectors is written as a # b, that is by viewing a vectors as a matrix with onl# one col

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...