P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceedings of the 5th International Conference on Computer Vision, Boston. IEEE Computer Society Press, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....estimation. So the two are usually viewed as separate problems. In spite of the fact that the robustness of existing algorithms has been studied quite extensively, it has been suggested that the fact that the structure and motion estimation are decoupled typically hinders their performance [11]. Some algorithms address the problem of motion and structure (shape) recovery simultaneously either in batch [16] or recursive fashion [11] The approaches to the motion estimation only, can be partitioned into the discrete and differential methods depending on whether they use as an input set ....

.... been studied quite extensively, it has been suggested that the fact that the structure and motion estimation are decoupled typically hinders their performance [11] Some algorithms address the problem of motion and structure (shape) recovery simultaneously either in batch [16] or recursive fashion [11]. The approaches to the motion estimation only, can be partitioned into the discrete and differential methods depending on whether they use as an input set of point correspondences or image velocities. Among the efforts to solve this problem, one of the more appealing approaches is the essential ....

Philip F. McLauchlan and David W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceeding of Fifth International Conference on Computer Vision, pages 314--320, Cambridge, MA, USA, 1995. IEEE Comput. Soc. Press.

....outliers and work well for small to medium baselines and non planar as well as planar motions. 1 Introduction The structure from motion problem has been studied extensively over the past decades and many algorithms have been proposed for general camera motion (see [12] for batch methods, [5, 10] for recursive methods, 11, 13, 14] for factorization methods and [2] for projective methods) However, most of these algorithms are not designed to give accurate answers when the baselines are small, which is the most complex case because the signal to noise ratio is small. Since the small ....

P. McLauchlan and D. Murray. A unifying framework for structure and motion recovery from image sequences. In International Conference on Computer Vision and Pattern Recognition, pages 314--20, 1995.

....P (z k k 1 ) and P (x k k ) in order to correctly represent the quality of the reconstruction at time k. Traditionally, these probabilities can be represented as Gaussian distributions. This is the approach taken in the approaches based on the Extended Kalman Filter (EKF) 1] 3] 4] 14] [15] [20] However, given the fact that covariance representation is only a linear approximation to the uncertainty in the highly nonlinear SFM problem, the covariance representation is not a valid uncertainty representation for SFM in situations when (1) the correspondence noise is relatively large ....

P. McLauchlan and D. Murray. A unifying framework for structure and motion recovery from image sequences. In International Conference on Computer Vision, 1995.

....subspace constraints [8] are applied to image measurements from multiple frames. The problem of estimating the 3D motion of a moving camera observing a single static object is well studied in the computer vision community [4, 7] see, for example, reviews of batch methods [17] recursive methods [12, 16], orthographic case [18] and projective reconstruction [20] The problem of estimating the 3D motion of multiple moving objects observed by a moving camera is more recent and has received a lot of attention over the past few years [1, 3, 5, 6, 15, 19, 21] Costeira and Kanade [3] proposed an ....

....(T o (t 0 ) T c (t 0 ) R(t, t 0 )q oc (t 0 ) T (t, t 0 ) where (R(t, t 0 ) T (t, t 0 ) can be interpreted as the change in the relative pose of the object with respect to the camera between times t 0 and t. There are a number of methods to estimate (R, T ) from image measurements [17, 12, 16, 18, 20]. Here we choose a simple linear method based on rank constraints on the multiple view matrix [11] because it exploits the fact that the depth vector is known from the factorization method of the previous section. Assume that we take measurements at discrete time instants t = t 1 , t m ....

P. McLauchlan and D. Murray. A unifying framework for structure and motion recovery from image sequences. In International Conference on Computer Vision and Pattern Recognition, pages 314--20, 1995.

....1. Introduction In this paper, we deal with the problem of motion and structure estimation from long image sequences, assuming that feature correspondences (point matches in our case) across all images have been established. Sequential matchers have proven to be the most successful (see e.g. [17, 3, 10, 23]) but this is not the topic of this paper. It is sufficient to say here that we do not assume that a point feature appears in all images. The length of a point track can be any value equal or larger than 2. The optimal way to recover motion and structure from long sequences is to use bundle ....

....to say here that we do not assume that a point feature appears in all images. The length of a point track can be any value equal or larger than 2. The optimal way to recover motion and structure from long sequences is to use bundle adjustment which involves minimization of reprojection errors [6, 12, 10]. The reader is referred to [20] for an excellent survey of the theory of bundle adjustment as well as many implementation strategies. However, bundle adjustment does not give a direct solution; it is a refining process and requires a good starting point. The starting point can be obtained with ....

P. McLauchlan and D. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. Fifth International Conference on Computer Vision, pages 314--320, Cambridge, Massachusetts, June 1995.

....undergoing a rigid body motion and observing a cloud of points, recover camera motion and (Euclidean) scene structure from their correspondences among multiple images. The problem has been extensively studied in the literature (see, for example, reviews of batch methods [13] recursive methods [8, 12], orthographic case [14] and projective reconstruction [16] Nevertheless, there are some important issues that have not yet been answered. First of all, we do not yet have a clear understanding of the relationship between multilinear constraints and the (statistical) optimality of motion and ....

.... for motion and structure recovery from multiple views [13, 14, 16] and is a necessary extension of the unconstrained nonlinear least squares method [13] We believe that our results, especially the normalized epipolar constraint, may help to improve existing recursive methods such as those in [8, 12] if the filter objective function is modified to the one given by us. Moreover, studying the Hessian of such an objective will allow to extend existing sensitivity studies [1, 6] to the multiview case. 2. Notation and Problem Statement We first introduce some notation which will be frequently ....

P. McLauchlan and D. Murry. A unifying framework for structure and motion recovery from image sequences. In Proceedings of 5th ICCV, pages 314--20. IEEE Comp. Soc. Press, 1995.

.... structure (3D position of the points) from their correspondences in multiple images (position of each point projected in each one of the images) With such a vast body of literature studying almost every aspect of this problem (see, for example, reviews of batch methods [15] recursive methods [8, 14], orthographic case [16] and projective reconstruction [19] it is quite reasonable to ask what, if anything, can still be new in this topic. First of all, we do not yet have a clear picture about the relationship between multilinear constraints and the (statistical) optimality of motion and ....

.... the clari cation of the relationship between geometric and algebraic dependency among multilinear constraints is an important complement to the results in [5, 7, 12, 18] Our results, especially the normalized epipolar constraint, may also help improve existing recursive methods such as those in [8, 14] if the lter objective function is modi ed to the one given by us. Moreover, studying the Hessian of such an objective will allow to extend existing sensitivity studies [1, 6] to the multiview case. 2. Notation and Problem Statement. We rst introduce some notation which will be frequently used ....

P. F. McLauchlan and D. W. Murry, A unifying framework for structure and motion recovery from image sequences. In Proceedings of 5th ICCV, pp. 314-20, Cambridge, MA, USA, 1995. IEEE Com. Soc. Press.

....in submap B. This is likely to be the case if the robot spends long periods of time con ned to each submap region, rather than frequently moving between regions. There are still many issues to settle with this kind of approach, such as how submap areas should be delineated. McLauchlan s VSDF [17] is a powerful framework which marries sequential and batch methods, and has been used in several di erent vision applications. It is based on the propagation of inverse covariance matrices (called information matrices) a strategy which provides some computational advantages, and o ers an ecient ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceedings of the 5th International Conference on Computer Vision, Boston. IEEE Computer Society Press, 1995.

....in Section 5.4.4 later in this chapter which demonstrates how the full covariance approach greatly improves on this. Some previous authors have tackled the problem of producing real time implementations of map building using the full covariance matrix. McLauchlan s Variable State Dimension Filter [63, 64] ingeniously reduces the complexity of updates by operating on the inverse of the covariance matrix (often called the information matrix) which in certain problems has a simple block diagonal form. This is indeed the case with map building in cases where there is no prior information about the ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston. IEEE Computer Society Press, 1995. 143

....in computer vision. As is commonly the case in SFM, the model that is being learned is the location of all features in 3D, along with the cameras positions in 6D. In this paper, we make the commonly made assumption that all 3D features are seen in all images (Tomasi Kanade, 1992; Hartley, 1994; McLauchlan Murray, 1995). However, the method we propose does not depend crucially on this assumption, and we will discuss at the end of this paper how to extend it to more general imaging situations with occlusions and spurious measurements. More importantly, we do not assume any prior knowledge on the camera positions ....

....association problem. The vast majority of literature on SFM considers special situations where the data association problem can be solved trivially. Some approaches simply assume that data correspondence is known a priori (Ullman, 1979; LonguetHiggins, 1981; Tsai Huang, 1984; Hartley, 1994; McLauchlan Murray, 1995; Morris Kanade, 1998) Other approaches only consider situations where images are recorded in a sequence, so that features can be tracked from frame to frame (Broida Chellappa, 1991; Tomasi Kanade, 1992; Szeliski Kang, 1993; Azarbayejani Pentland, 1995; Poelman Kanade, 1997) Several ....

[Article contains additional citation context not shown here]

McLauchlan, P., & Murray, D. (1995). A unifying framework for structure and motion recovery from image sequences. In Int. Conf. on Computer Vision (ICCV), pp. 314--320.

.... structure (3D position of the points) from their correspondences in multiple images (position of each point projected in each one of the images) With such a vast body of literature studying almost every aspect of this problem (see, for example, reviews of batch methods [15] recursive methods [8, 14], orthographic case [16] and projective reconstruction [19] it is quite reasonable to ask what, if anything, can still be new in this topic. First of all, we do not yet have a clear picture about the relationship between multilinear constraints and the (statistical) optimality of motion and ....

.... of the statistical relationship between bilinear and trilinear constraints is an important complement to the well known algebraic or geometric results [5, 7, 12, 18] Our results, especially the normalized epipolar constraint, may also help improve existing recursive methods such as those in [8, 14] if the lter objective function is modi ed to the one given by us. Moreover, studying the Hessian of such an objective will allow to extend existing sensitivity studies [1, 6] to the multiview case. 2. Notation and Problem Statement. We rst introduce some notation which will be frequently used ....

P. F. McLauchlan and D. W. Murry, A unifying framework for structure and motion recovery from image sequences. In Proceedings of 5th ICCV, pp. 314-20, Cambridge, MA, USA, 1995. IEEE Com. Soc. Press.

....estimation. Thus the two are usually viewed as separate problems. In spite of the fact that the robustness of existing algorithms has been studied quite extensively, it has been suggested that the fact that the structure and motion estimation are decoupled typically hinders their performance [15]. Some algorithms Research supported in part by ARO under the MURI grant DAAH04 96 1 0341. 1 address the problem of motion and structure (shape) recovery simultaneously either in batch [21] or recursive fashion [15] Approaches to motion estimation alone, can be partitioned into the discrete ....

....and motion estimation are decoupled typically hinders their performance [15] Some algorithms Research supported in part by ARO under the MURI grant DAAH04 96 1 0341. 1 address the problem of motion and structure (shape) recovery simultaneously either in batch [21] or recursive fashion [15]. Approaches to motion estimation alone, can be partitioned into the discrete and differential methods depending on whether they use as input a set of point correspondences or image velocities. Among the efforts to solve the motion estimation problem, one of the more appealing approaches is the ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceeding of Fifth International Conference on Computer Vision, pages 314--320, Cambridge, MA, USA, 1995. IEEE Comput. Soc. Press.

.... problem and apart Supported by the ESPRIT Reactive LTR project 21914, CUMULI Supported by the Swedish Research Council for Engineering Sciences (TFR) project 95 64 222 from the reconstructed object also the camera motion is obtained, cf. Tomasi and Kanade 1992, Koenderink and van Doorn 1991, McLauchlan and Murray 1995, Sturm and Triggs 1996, Sparr 1996, Shashua and Navab 1996, Weng, Huang and Ahuja 1992, Ma 1993) There are two major diOEculties that have to be dealt with. The rst one is to obtain corresponding points (or lines, conics, etc. throughout the sequence. The second one is to choose an appropriate ....

McLauchlan, P. F. and Murray, D. W.: 1995, A unifying framework for structure and motion recovery from image sequences, Proc. 5th Int. Conf. on Computer ?? 19 Vision, MIT, Boston, MA, IEEE Computer Society Press, Los Alamitos, California, pp. 314320.

....still images, conversely, the major problem is feature matching, so we have designed an interface based on Java and OpenGL that allows the user to place each image in turn by hand, providing an approximate registration that is then optimsed. We employ the Variable State Dimension Filter (VSDF) [6, 5] to implement sequential bundle adjustment. The VSDF supports standard sparse matrix techniques that are used to accelerate bundle adjustment iterations. The sequential feature of the VSDF is important for two reasons: firstly it allows long sequences to be registered in a reasonaable length of ....

P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, pages 314--320, June 1995.

....calibration is difficult owing to uncertain camera motions, changes in internal parameters (focus, zooming) or the use of several cameras. In response to these needs, there has recently been a significant amount of theoretical work on the structure of multi image projection and reconstruction [8, 7, 14, 13, 17, 1, 16, 6, 11, 12, 23, 20, 21, 2]. The problem turns out to have a surprisingly rich mathematical structure, and several complimentary approaches exist. The field is developing rapidly and there is no space for a complete survey here, so I will only mention a few isolated results. The epipolar constraint (the geometry of stereo ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In E. Grimson, editor, IEEE Int. Conf. Computer Vision, pages 314--20, Cambridge, MA, June 1995.

.... motion: How to recover camera motion and (Euclidean) scene structure from correspondences of a cloud of points seen in multiple (perspective) images With such a vast body of literature studying almost every aspect of this problem (see, for example, reviews of batch methods [13] recursive methods [7, 12], orthographic case [14] and projective reconstruction [16] it is quite reasonable to ask what, if anything, can still be new in this topic. First of all, we do not yet have a clear picture about the relationship between multilinear constraints and the (statistic) optimality of motion and ....

.... revelation of the statistic relationship between bilinear and trilinear constraints is an important complement to the well known algebraic or geometric results [4, 6, 10, 15] Our results, especially the normalized epipolar constraint, may also help improve existing recursive methods such as in [7, 12] if the filter objective function is modified to the one given by us. Moreover, studying the Hessian of such an objective will allow an extension of existing sensitivity study [1, 5] to the multiview case. 2 Camera Model We first introduce some notation which will be frequently used in this paper ....

P. F. McLauchlan and D. W. Murry. A unifying framework for structure and motion recovery from image sequences. In Proceedings of IEEE fifth International Conference on Computer Vision, pages 314--20, Cambridge, MA USA, 1995. IEEE Com. Soc. Press.

....and n features and it has linear convergence. The algorithm was developed for the orthogonal camera model, and the sequential metric transformation was developed as well, see [4] for details. The algorithm, however, does not address the problem of missing and reappearing features. McLauchlan et al. [2,3] used the variable state dimension filter (VSDF) to handle missing and new features. They posed the structure from motion problem as a parameter estimation problem and solved it by applying the Extended Kalman Filter (EKF) to the measurement equation (2) They updated the complete structure and ....

McLauchlan P. and Murray D.. "A unifying framework for structure and motion recovery from image sequences" Proc. 5 th ICCV, MIT, pp. 314-320, 1995.

....3D coordinate system is not immediately available. As a means for integrating different types of features in the context of scene reconstruction, the implicit approach is related to previous reconstruction approaches that incorporate both points and lines. In particular, McLauchlan and Murray [5] developed an approach for reconstructing points and lines using a recursive filtering technique. While points and lines were represented and reconstructed differently, the same filter mechanism was used to integrate measurements over time. Morris and Kanade [6] demonstrated a factorization method ....

P. F. McLauchlan and D. W. Murray, "A unifying framework for structure and motion recovery from image sequences," in Proc. 5th International Conference on Computer Vision, pp. 314--320, 1995.

....It is a framework for optimal recursive estimation of structure and motion based solely on the assumption that image measurement errors are independent and Gaussian distributed. The VSDF can be used with different measurement equations corresponding to distinct camera models (such as perspective [12], affine [11] or projective [12] In the present work we focus on its affine variant (the reasons for this choice are presented in [4] Since the type of structure recovered by the affine mode of the VSDF is non metric, the motion recovered with it is not necessarily rigid, contrary to our own ....

....recursive estimation of structure and motion based solely on the assumption that image measurement errors are independent and Gaussian distributed. The VSDF can be used with different measurement equations corresponding to distinct camera models (such as perspective [12] affine [11] or projective [12]) In the present work we focus on its affine variant (the reasons for this choice are presented in [4] Since the type of structure recovered by the affine mode of the VSDF is non metric, the motion recovered with it is not necessarily rigid, contrary to our own approach. So, to be fair, we ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. IEEE Int. Conf. on Comp. Vis., pages 314--320, 1995.

....independent of the chosen coordinate systems in the images and that the relative depths of the points are needed in order to carry out the factorisation. There are also several attempts towards recursive algorithms, i.e. algorithms where more and more images are used as they become available, 9] [7]. The drawback of these algorithms, when used in the projective case, is that the result is dependent on the chosen coordinate systems in the images and in [7] also on the used initial values obtained from three different images. Another attempt towards more generic algorithms has been made in ....

.... are also several attempts towards recursive algorithms, i.e. algorithms where more and more images are used as they become available, 9] 7] The drawback of these algorithms, when used in the projective case, is that the result is dependent on the chosen coordinate systems in the images and in [7], also on the used initial values obtained from three different images. Another attempt towards more generic algorithms has been made in [12] and [4] There the reconstruction problem is solved by minimising a variational formula that is independent of the chosen coordinate system in the images ....

F. McLauchlan, P. and W. Murray, D. A unifying framework for structure and motion recovery from image sequences. In ICCV'95, IEEE Computer Society Press, pages 314--320, 1995.

.... assumption puts strong constraints on both the types of motion that can be recovered (e.g. rigid [2 6] articulated [7] parametric [8] isometric [9] and the scenes that can be analyzed (e.g. known 3D shape [10] known shape dynamics [11, 12] availability of distinguished feature points [2 5, 7]) As a result, little is currently known about how to recover the 3D motion and shape of unknown scenes that are simultaneously viewed from two or more distinct viewpoints, about the constraints and ambiguities that this problem embodies, and about the algorithms required to solve it. In this ....

P. F. McLauchlan and D. W. Murray, "A unifying framework for structure and motion recovery from image sequences," in Proc. 5th IEEE Int. Conf. Comp. Vis., pp. 314--320, 1995.

....but seems to be tacitly discouraged in computer vision, where the traditional emphasis is on A.I. image understanding rather than precision (however cf. 17, 10, 19, 14, 9] Efficient numerical methods exist for handling large problems, both off line and in a linearized recursive framework [1, 18]. Rigorous, statistically weighted least squares should not be confused with unweighted or linear least squares minimization of ad hoc algebraic distances sums of squared algebraic constraint violations with no direct relation to measured image residuals. For example the linear method ....

....take into account as many as possible of the above properties, and can be used as input to nonlinear methods if more precision is required. Partly in response to this, there has recently been a significant amount of work on the theoretical foundations of multi image projection and reconstruction [11, 10, 19, 18, 23, 2, 22, 8, 15, 16, 31, 27, 28, 3]. The problem turns out to have a surprisingly rich mathematical structure and several complementary approaches exist. The field is developing rapidly and there is no space for a survey here, so I will only mention a few isolated results. The epipolar constraint (the geometry of stereo pairs) is ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In E. Grimson, editor, IEEE Int. Conf. Computer Vision, pages 314--20, Cambridge, MA, June 1995.

....or the type of algorithms they use for estimating motion and or structure. Most techniques try to decouple the two problems by estimating the motion first, followed by the estimation of structure. Thus the two are usually viewed as separate problems, leading to either recursive algorithms [11] in case not all the frames are available or iterative two stage techniques, where motion and structure estimation comprise the two steps [12, 3] Making approximations about the camera model allows to render the problem as a linear one and estimate the shape and motion simultaneously using ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceeding of Fifth International Conference on Computer Vision, pages 314--320, Cambridge, MA, USA, 1995. IEEE Comput. Soc. Press.

....for two reasons: i) the number of parameters to estimate does not grow all the time, ii) the amount of processed data does not grow all the time. One idea would be to recursively update the motion (the camera matrix) and the structure (the reconstruction) at each time instant as is done in [9]. This is still a very large amount of data to update. Another idea is to recursively update the motion (the camera matrix) only. This is where the study of multilinear constraints are needed. The discussion above shows that the trilinear forms of images k Gamma 2;k Gamma 1 and k are needed to ....

McLauchlan, P. F., Murray, D. W., A unifying framework for structure and motion recovery from image sequences, Proc. 5'th ICCV, 1995.

.... or three views of line scenes [2, 3, 8, 6] However most current reconstruction methods either work only for the minimal number of views (typically two) or at very least single out a few such privileged views for initialization before bootstrapping themselves to the multi image case [5, 10, 9]. For robustness and accuracy, there is a need for methods that uniformly take into account all of the data in all of the images, without making restrictive special assumptions or relying on privileged images or features for bootstrapping. The orthographic and paraperspective structure motion ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In E. Grimson, editor, IEEE Int. Conf. Computer Vision, pages 314--20, Cambridge, MA, June 1995.

.... from at least two views of point scenes or three views of line scenes [2, 3, 8, 6] Most current reconstruction methods either work only for the minimal number of views (typically two) or single out a few privileged views for initialization before bootstrapping themselves to the multi view case [5, 10, 9]. For robustness and accuracy, there is a need for methods that uniformly take To appear in CVPR 96. This work was supported by an EC HCM grant and INRIA Rhone Alpes. I would like to thank Peter Sturm and Richard Hartley for enlightening discussions. account of all the data in all the images, ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In E. Grimson, editor, IEEE Int. Conf. Computer Vision, pages 314--20, Cambridge, MA, June 1995.

.... together recent developments in algorithms for visual tracking, specifically: ffl The fixation point transfer algorithm of Reid Murray [21] ffl A simplified version of the robust feature matching method of Torr et al. 27] ffl The recursive VSDF 3D reconstruction algorithm described in [15, 16]. Our approach is to combine shape reconstruction (2D planar reconstruction rather than the usual 3D) from stereo motion with motion estimation, using recently developed robust and efficient feature matching methods. While this may seem overblown when the goal is simply to measure range, we argue ....

....and allowing image deformations, but then the algorithm takes on the character of a feature tracker [23] 4. Feature tracking, which track point and line features (typically) over an image sequence [29, 22, 24] sometimes in conjunction with rigidity constraints to impose global consistency [18, 16]. While the context of highways and vehicles is clearly very structured, we avoid using direct scene models in the low level tracking algorithms, and this distinguishes our work from that of Dickmanns s group [5] for instance. Thus we have rejected model based trackers (class 1) We draw on the ....

[Article contains additional citation context not shown here]

P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, June 1995.

....tracking moving objects at considerably faster than frame rate. 1 Introduction Relative motion of objects in the environment with respect to a vision system causes visual motion. Analysis of such visual motion in sequences of images has been addressed by many researchers over a number of years [20, 18, 12, 19]. The techniques that have been used include optical flow [9, 13, 1, 2] feature point correspondence [8, 5] edge or contour correspondence [16, 7, 21, 23, 6] active contour models [15, 3, 4] and model based tracking [10, 17] Recently there has been an increase in robotic applications that ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int. Conf. on Computer Vision, Cambridge, Massachusetts, June 1995.

....calibration is difficult owing to uncertain camera motions, changes in internal parameters (focus, zooming) or the use of several cameras. In response to these needs, there has recently been a significant amount of theoretical work on the structure of multi image projection and reconstruction [8, 7, 14, 13, 17, 1, 16, 6, 11, 12, 23, 20, 21, 2]. The problem turns out to have a surprisingly rich mathematical structure, and several complimentary approaches exist. The field is developing rapidly and there is no space for a complete survey here, so I will only mention a few isolated results. The epipolar constraint (the geometry of stereo ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In E. Grimson, editor, IEEE Int. Conf. Computer Vision, pages 314--20, Cambridge, MA, June 1995.

.... used for providing initial estimates for the nonlinear optimization [2] The interest in the active vision systems with changing intrinsic and extrinsic parameters initiated an ascent of the uncalibrated methods and gave rise to many new algorithms for recovering both structure and motion [10, 3, 33, 13, 18]. Within the uncalibrated setting the notions of projective and affine structure recovery have been used with the justification that these representations are suitable for certain types of tasks [21] Another line of work explored the problem of camera self calibration in the projective case ....

Philip F. McLauchlan and David W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceedings of IEEE fifth Internation Conference on Computer Vision, pages 314--20, Cambridge, MA USA, 1995. IEEE Com. Soc. Press.

....reconstruction, one of the major current trends of computer vision is the use of techniques that incorporate the computation of the three dimensional scene structure into the process of real time pose and motion estimation, instead of working from a predefined scene model. We refer the reader to [45] for a review of some of the fundamental advances in this area. However, it is also known that these techniques have certain limitations when applied to the control of robotic systems (for instance) 46] So, an interesting future direction would be to explore these uncalibrated techniques and ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th IEEE Int. Conf. on Computer Vision, pages 314--320, 1995.

....[10, 1] and Luong et al. [3] respectively provide linearized least squares models for 3D point and line reconstruction and fundamental matrix estimation. Mohr et al. [5] formulate multi image reconstruction as a batch mode nonlinear least squares problem, and more recently McLauchlan Murray [4] describe a suboptimal but practically efficient linearized incremental framework for several types of reconstruction. 2 Homogenized Affine Least Squares To motivate the projective model we will re express classical least squares for affine points in homogeneous coordin1 ates. Consider a random ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In E. Grimson, editor, IEEE Int. Conf. Computer Vision, Cambridge, MA, June 1995.

....The VSDF achieves this goal by linearizing the (typically non linear) imaging equations relating the measurements to the unknown parameters around the current estimates for the values of these parameters. Different measurement equations corresponding to distinct camera models (such as perspective [24], affine [23] or projective [24] can be used within this general framework. The VSDF only requires some of the unknown parameters (typically the structure parameters) to be local, in the sense that they can only be related to a unique feature and must remain constant across different scenes. The ....

....the (typically non linear) imaging equations relating the measurements to the unknown parameters around the current estimates for the values of these parameters. Different measurement equations corresponding to distinct camera models (such as perspective [24] affine [23] or projective [24]) can be used within this general framework. The VSDF only requires some of the unknown parameters (typically the structure parameters) to be local, in the sense that they can only be related to a unique feature and must remain constant across different scenes. The remaining parameters (typically ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. IEEE Int. Conf. on Comp. Vis., pages 314-- 320, 1995.

....estimation. So the two are usually viewed as separate problems. In spite of the fact that the robustness of existing algorithms has been studied quite extensively, it has been suggested that the fact that the structure and motion estimation are decoupled typically hinders their performance [11]. Some algorithms address the problem of motion and structure (shape) recovery simultaneously either in batch [16] or recursive fashion [11] The approaches to the motion estimation only, can be partitioned into the discrete and differential methods depending on whether they use as an input set of ....

.... been studied quite extensively, it has been suggested that the fact that the structure and motion estimation are decoupled typically hinders their performance [11] Some algorithms address the problem of motion and structure (shape) recovery simultaneously either in batch [16] or recursive fashion [11]. The approaches to the motion estimation only, can be partitioned into the discrete and differential methods depending on whether they use as an input set of point correspondences or image velocities. Among the efforts to solve this problem, one of the more appealing approaches is the essential ....

Philip F. McLauchlan and David W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceeding of Fifth International Conference on Computer Vision, pages 314--320, Cambridge, MA, USA, 1995. IEEE Comput. Soc. Press.

....using 5 reference points. Hartley [HGC92] derives from the fundamental matrix 2 projection matrices, equal to the true ones up to an unknown projective transformation. These are then used to perform reconstruction by triangulation[HS94] As for multiple images, most of the current methods [MVQ93, Har93, MM95] initially privilege a few views or points and thus do not treat all data uniformly. Recently, multi linear matching constraints have been discovered that extend the epipolar geometry of 2 views to 3 and 4 views. Shashua [Sha95] described the trilinear relationships between 3 views. Faugeras and ....

P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceedings of the 5th International Conference on Computer Vision, Cambridge, Massachusetts, USA, pages 314--320, 1995.

....time derivatives) does not preclude this, but perhaps makes it seem a little less likely. On the other hand,the simplicity of the joint image picture makes incremental recursive reconstruction techniques that correctly handle the measurement errors and constraint geometry seem more likely (c.f. [16]) 11.2. Tensors vs. the Rest This paper is as much about the use of tensors as a vehicle for mathematical vision as it is about image projection geometry. Tensors have seldom been used in vision and many people appear to be rather tensorphobic, so it seems appropriate to say a few words in their ....

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In E. Grimson, editor, IEEE Int. Conf. Computer Vision, Cambridge, MA, June 1995.

....spatial position but also a list of additional characteristics e.g. the surrounding pixels intensities. 4.2 Review of related work 51 short baselines, but all of the foregoing work was conducted using a stop look move paradigm leading to rather larger interframe motions. McLauchlan and Murray [68] have also demonstrated a method for tracking features which was specifically designed for real time operation. They use a formalism, known as the variable state dimension filter , which makes explicit provision for the creation and deletion of feature tracks. However there is no provision for ....

P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, pages 314--320, June 1995.

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P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, pages 314--320, June 1995.

....motion reconstruction. Our goal is to develop algorithmic and statistical tools that combine data from multiple images and other sensors. We have previously presented specific applications of our Variable State Dimension Filter (VSDF) method in the areas of 3D reconstruction from image sequences [34, 36], vehicle navigation [33] image mosaicing [32] camera calibration [37] We also envisage application to sensor fusion and active vision (e.g. tracking servoing) The thrust of this work is to develop general, scalable tools that allow data of multiple types to be incorporated (for instance point ....

....be borne in mind that the following discussion applies equally well to uncalibrated approaches. We shall at this point consider only the batch problem of recovering structure and motion from a number of images. In on line robotics and other real time applications, recursive methods are necessary [17, 38, 36], whereby new images are used to update an existing reconstruction, in the manner of the Kalman filter. We shall see how to generalize our techniques to recursive reconstruction in section 3.9. The basic algorithm we shall consider is the Levenberg Marquardt algorithm [41] which we shall describe ....

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P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, pages 314--320, June 1995. 51

....motion reconstruction. Our goal is to develop algorithmic and statistical tools that combine data from multiple images and other sensors. We have previously presented specific applications of our Variable State Dimension Filter (VSDF) method in the areas of 3D reconstruction from image sequences [15, 8], vehicle navigation [14] image mosaicing [13] and camera calibration [9] The thrust of this work is to develop general, scalable tools that allow data of multiple types to be incorporated (for instance point and line features) different projection models to be used (e.g. ....

....may be incorporated dynamically, and unwanted parameters discarded; hence the term Variable State Dimension Filter. Thus we can handle the introduction of newly visible parts of a scene as the camera scene moves, and the elimination of obscured or invisible features. Our work is based on [8], but developed in several ways: Parametrised constraints between blocks of the state vector can be incorporated. For instance, surface recovery can be integrated with the feature based reconstruction [16] Incorporation of the standard recursive partitioning 1 algorithm from ....

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P. McLauchlan and D. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, pages 314--320, June 1995.

.... together recent developments in algorithms for visual tracking, specifically: ffl The fixation point transfer algorithm of Reid Murray [15] ffl A simplified version of the robust feature matching method of Torr et al. 19] ffl The recursive VSDF 3D reconstruction algorithm described in [12]. Our approach is to combine shape reconstruction (2D planar reconstruction rather than the usual 3D) from stereo motion with motion estimation, using recently developed robust and efficient feature matching methods. While this may seem overblown when the goal is simply to measure range, we ....

....image velocity measurement trackers that compute velocity using image flow, correlation or similar methods [3, 14] 4. Feature tracking, which track point and line features (typically) over an image sequence [21, 16] sometimes in conjunction with rigidity constraints to impose global consistency [13, 12]. While the context of highways and vehicles is clearly very structured, we avoid using direct scene models in the low level tracking algorithms, and this distinguishes our work from that of Dickmanns s group [4] for instance. Thus we have rejected model based trackers (class 1) We draw on the ....

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P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, June 1995.

....below. ffl They only work for point features. The Tomasi Kanade algorithm has been extended to the case of lines and planes in [13] but at the expense of losing the optimality property. Bundle adjustment can be seamlessly generalized to other features such as lines, as we demonstrated in [11, 10]. ffl The projective algorithms do not minimize geometric error on the image plane, and so are not as accurate as bundle adjustment. Berthillson et al. report a 50 larger reprojection (geometric) error over the level of added noise. ffl They are batch methods. The Levenberg Marquardt algorithm ....

....Berthillson et al. report a 50 larger reprojection (geometric) error over the level of added noise. ffl They are batch methods. The Levenberg Marquardt algorithm used here can be extended easily to recursive operation, as has been achieved in the Variable State Dimension Filter (VSDF) [11, 12]. Nevertheless these algorithms are good ways to generate starting points for a projective bundle adjustment algorithm, and indeed Heyden makes the point in [7] that the combination of factorization methods and bundle adjustment would make an attractive combination of robustness and accuracy. For ....

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P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, pages 314--320, June 1995.

....to recursively update the structure of the tracked object, and employ the improved motion estimates to perform fixation point transfer. This is the method we have implemented. The reconstruction technique detailed below is a 2D affine version of the Variable State Dimension Filter (VSDF) algorithm [14]. The VSDF is a general algorithm for visual reconstruction that deals naturally with fragmentary data and combines data from multiple images in a near optimal manner. 3.3 2D Affine Reconstruction The 2D affine projection from scene to image can then be written in its most general form as 0 x ....

P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proc. 5th Int'l Conf. on Computer Vision, Boston, June 1995.

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P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceedings of the 5th International Conference on Computer Vision, Boston. IEEE Computer Society Press, 1995.

No context found.

P. F. McLauchlan and D. W. Murray. A unifying framework for structure and motion recovery from image sequences. In Proceedings of the 5th International Conference on Computer Vision, Boston. IEEE Computer Society Press, 1995.

No context found.

P.F. McLauchlan, D.W. Murray, A unifying framework for structure and motion recovery from image sequences, in: Proceedings of the Fifth International Conference on Computer Vision, Boston, MA, IEEE Computer Society Press, Silver Spring, MD, 1995.

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P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In 5th International Conference on Computer Vision, pages 314--320, Cambridge, Massachusetts, June 1995.

No context found.

P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In 5th International Conference on Computer Vision, pages 314--320, Cambridge, Massachusetts, June 1995.

No context found.

P. F. McLauchlan and D. W. Murray, "A unifying framework for structure and motion recovery from image sequences," in Proc. ICCV, pp. 314--320, 1995.

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McLauchlan, P., F., Murray, D., W., A unifying framework for structure and motion recovery from image sequences, Proc. ICCV'95, IEEE Computer Society Press, 1995, pp. 314-320.

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