S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... multibody a#ne constraint was recently proposed in [24] 3 D motion segmentation and estimation based on 2 D imagery is a more recent problem and various special cases have been analyzed using a geometric approach: multiple points moving linearly with constant speed [9, 16] or in a conic section [1], multiple moving objects seen by an orthographic camera [5, 13] self calibration from multiple motions [8, 10] or two object segmentation from two perspective views [30] Alternative probabilistic approaches are based on model selection techniques [22, 13] combine normalized cuts with EM [7] ....

....nothing but the epipolar lines associated with the multibody epipolar line F# n (x 1 ) which can be computed using the polynomial factorization technique of Section 5.1 as described in Section 5.2. Notice that, in particular, we can obtain the three columns of F i up to scale by choosing x 1 = [1, 0, 0] , x 1 = 0, 1, 0] x 1 = 0, 0, 1] respectively. However: 1. We do not know the fundamental matrix to which the recovered epipolar lines belong; 2. The recovered epipolar lines, hence the columns of each F i , are obtained up to a scale factor only. Hence, we do not know the relative ....

[Article contains additional citation context not shown here]

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

.... cuts [13] or the eigenvectors of a similarity matrix [17] 3D motion segmentation and estimation based on 2D imagery is a more recent problem and various special cases have been analyzed using a geometric approach: multiple points moving linearly with constant speed [8, 12] or in a conic section [1], multiple moving objects seen by an orthographic camera [3, 10] self calibration from multiple motions [7] or two object segmentation from two perspective views [18] Alternative probabilistic approaches to 3D motion segmentation are based on model selection techniques [15, 10] or combine ....

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

.... 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 algorithm to estimate the motion of multiple moving objects relative to a static orthographic camera, based on discrete image measurements for each object. They use a factorization method based on the fact that, under orthographic projection, discrete image ....

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

....to the case of multiple motions # Research supported by ONR N00014 00 1 0621, ARO DAAD19 99 1 0139, NSF ECS 0200511. yet. Instead, various special cases have been analyzed using geometric techniques, e.g. multiple points moving linearly with constant speed [5, 13] or in a conic section [1], and two body [18] and multi body [17] motion segmentation from two perspective views. Alternative probabilistic approaches to 3 D motion segmentation are based on model selection techniques [16, 7] combine normalized cuts with a mixture of probabilistic models [4] or compute statistics of the ....

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

....for rigid scenes can also be employed for scenes composed of multiple, independently moving objects [3, 5, 15] which requires however that enough features be extracted for each object, making segmentation, at least implicitly, possible. On the other hand, there is a growing body of literature [1, 6, 7, 10, 11, 14, 16] dealing with the case of independently moving features, often termed as dynamic features. The goal of these works is to provide algorithms for dynamic structure and motion recovery as well as matching tensors for images of dynamic features. General, as well as highly constrained, dynamic ....

....General, as well as highly constrained, dynamic scenarios, involving monocular or stereo views, have been investigated. In this paper, we consider that the observed scene has both a static and a dynamic part. The static part is unconstrained (but has to be 3D) whereas on the other hand, as in [1, 6, 7, 11, 14, 16], we consider that dynamic features move along straight lines, termed motion lines. To further constrain the scenario, we consider that all motion lines lie on a motion plane and converge to an incidence point. Figure 2 illustrates this setting. Note that no assumption is made about the camera ....

[Article contains additional citation context not shown here]

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4):348--357, April 2000.

No context found.

S. Avidan and A. Shashua. Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence. IEEE Transaction on Pattern Analysis and Machine Intelligence(PAMI), Vol. 22(4),pp.348--357,2000.

No context found.

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

....dimension up to k m. The task is to recover the global transformations A i from the observations. The definition above is a generalization of particular cases which were introduced in the past under the name of dynamic SFM, or SFM of multiply moving points, and the relevant literature includes [1, 15, 19, 13, 17, 8, 14, 9, 18]. For instance, 15] consider the case where n =3(points Q i belong to the 2D projective plane) m =3and k =2. In other words, a configuration of coplanar points are viewed by a moving camera and the points move along arbitrary straight lines (k =2) or stay fixed ( static , k =1) while the camera ....

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

....on # , thus two planar objects are sufficient to uniquely determine #. Once# is known the camera projection matrices and the projective reconstruction of scene points can be recovered (see [10] for a recent detailed overview of such material) Given the growing body of work on dynamic scenes [1, 14, 12, 16, 9, 8, 4], i.e. 3D scenes which contain multiply moving points or collections of points (bodies) seen under multiple views, we wish to extend the basic paradigm described above to the case where the scene contains multiple planar objects moving relative to each other by pure translational motion while the ....

....the 9 entries of # # ) denoted by # # . All the spaces # # intersect with # , thus the question is how many intersections are required in order to uniquely determine # . It is worthwhile noting that the issue of finding a common transversal in the context of dynamic scenes was first introduced in [1]. There the application of transversals was classic, i.e. finding the common intersecting 3D line (the trajectory of a moving point) of 4 other lines is a well known 1 exercise in invariant theory (see for example, 15] We will start with the necessary mathematical tools required for ....

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

....maps with their associated tensors (bifocal, trifocal and quadrifocal) can be found in [8] and earlier work in [4] The literature mentioned above is mostly relevant to a static scene, i.e. a rigid body viewed by an uncalibrated camera. Recently, however, a new body of work has appeared [1, 12, 10, 13, 7] which assumes a configuration of points in which every single point in the configuration can move independently along some arbitrary trajectory (straight line path and in some cases second order) while the camera is undergoing general motion (in 3D projective space) For brevity, we will refer to ....

....of rows of the original # # # camera projection matrix, i.e. each row of # # represents the line of intersection of the two planes represented by the corresponding rows of # . The resulting multi view tensors in the straight forward sense represent the trajectory triangulation introduced in [1] which models the application of a moving point # along a straight line # such that in the # th view we observe the projection of # # of # . Thus, # # # # ####for all views of # . In the situation of trajectory triangulation, in each view we have an image # # of a point which lies on the line ....

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

....for recovering homography matrices and for optic flows arising from infinitesimal motion assumption of 3D scenes [5, 9] Structure from Motion (SFM) of dynamic scenes, where each point moves independently along some trajectory, is a recent and growing topic. The topic was first introduced in [1] for 3D point configurations undergoing linear and curved motion with known projection matrices. For 2D point configurations across three views the motion constraints have a form of a # # # # # tensor from which the appropriate homography matrices can be recovered [7] The restriction to constant ....

S. Avidan and A. Shashua. Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence. IEEE Transaction on Pattern Analysis and Machine Intelligence(PAMI), Vol. 22(4),pp.348--357,2000.

....maps with their associated tensors (bifocal, trifocal and quadrifocal) can be found in [8] and earlier work in [4] The literature mentioned above is mostly relevant to a static scene, i.e. a rigid body viewed by an uncalibrated camera. Recently, however, a new body of work has appeared [1, 12, 10, 13, 7] which assumes a configuration of points in which every single point in the configuration # The length of this paper was considerably reduced to fit the length guidelines of this proceedings. The full length version of this work can be found in http: www.cs.huji.ac.il # ################### # ....

....of rows of the original # # # camera projection matrix, i.e. each row of # # represents the line of intersection of the two planes represented by the corresponding rows of # . The resulting multi view tensors in the straight forward sense represent the trajectory triangulation introduced in [1] which models the application of a moving point # along a straight line # such that in the # th view we observe the projection of # # of # . Thus, # # # # ####for all views of # . In the situation of trajectory triangulation, in each view we have an image # # of a point which lies on the line ....

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

No context found.

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

No context found.

S. Avidan and A. Shashua. Trajectory triangulation: 3D reconstruction of moving points from a monocular image sequence. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(4):348--357, 2000.

No context found.

S. Avidan and A. Shashua. Trajectory triangulation: 3d reconstruction of moving points from a monocular image sequence. PAMI, 22(4):348--357, April 2000.

No context found.

S. Avidan and A. Shashua. Trajectory triangulation: 3d reconstruction of moving points from a monocular image sequence. PAMI, 22(4):348--357, April 2000.

No context found.

S. Avidan and A. Shashua. Trajectory triangulation: 3d reconstruction of moving points from a monocular image sequence. PAMI, 22(4):348-357, April 2000.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC