R. Deriche and O. Faugeras. Tracking line segments. Proc. European Conference on Computer Vision, pages 259--268, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....establish line correspondences based on relaxation. McIntosh and Much [14] and Liu and Huang [15] propose algorithm for finding line correspondences. Sethi and Jain [16] present an algorithm for finding smooth point trajectories over image sequences. Crowley et al. 17] and Deriche and Faugeraus [18] present algorithm for tracking lines by using local affine models using four parameters for each line. Most discrete feature matching methods are based on maximizing the compatibility of 2D attributes and relative 2D locations. This paper is about finding corespondent pairs of feature points in ....

Deriche and O. Faugeras, "Tracking Line Segments," Proc. European Conf. Computer Vision, 1990, pp. 259-268.

....even assuming the corner is a surface marking on a plane. Line segments are regions of high image intensity gradient, and are usually assumed to correspond to line segments in space, though they may be occluding contours of curved surfaces. They are comparatively easy to detect and track [9] and, since they naturally connect, they can provide reinforcement for one another in each image, unlike corners. Line segments also delimit space and the image much better than corners, though planes are obviously still better. Unfor tunately the normal velocity (perpendicular to the line) and ....

....If line segments form a straight line in the images, then they form one in space. Without its endpoints this long line segment will only offer as much information as a single short one, but its image position and motion can be averaged along its length, making the measurements more accurate [9, 33]. Intersection: If three or more close line segments intersect in the images, then they do in space. Two line segments will always intersect in the image but are 1However, in a sufficiently structured scene, interpolation can provide epipolar tangencies [23] which are aligned with the direction ....

R. Deriche and O. Faugeras. Tracking line segments. In O. Faugeras, editor, Proc. 1st Euro. Conf. on Comp. Vis., pages 259-268. Springer-Verlag, 1990.

....demanding [6] A good initialization may be provided by a temporal tracking of the model which enables to resort to fast local (deterministic) optimization procedures. Kalman filtering techniques have been widely used in computer vision for tracking various image features (points [1] edges [5], regions [11] The case of deformable structures has been handled recently [2, 3, 13] by considering contours, characteristic points or regions as features for the Kalman filter governing equations. In this paper, we develop a Kalman filter which performs prediction and filtering of the global ....

R. DERICHE and O. FAUGERAS. -- Tracking Line Segments. -- In First European Conference on Computer Vision, pages 259--268, Antibes, France, April 1990. --

....time, which might for instance be used for interpretation purposes. A review of existing methods in curve tracking may be found in [7] Contrary to standard approaches, based on the tracking of discrete low level or intermediate level image primitives such as characteristic points [2] segments [19], or regions [42] the tracking procedure proposed here considers the structure of 182 KERVRANN AND HEITZ a b c d Figure 5: Segmentations with missing data and partial occlusions. interest and its possible deformations as a whole by tracking the hyperparameters Theta = M(k; T;b ) ....

....filter, the second order derivatives of the hyperparameters (i.e. their acceleration)are considered as (small) random accelerations, modeled as white noise. These assumptions correspond to a standard kinematic model that has, for instance, been used to track isolated points or line segments [19]. State variable model. If z t stands for T t ; b t , or M t , the state vector is defined as s t = z t z t ) T . The dynamic evolution of the system is described by: s t Deltat = A t s t t (28) where A t is the state transition matrix and t is a zero mean white Gaussian noise with ....

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R. Deriche and O. Faugeras, Tracking line segments, in Proc. European Conf. Computer Vision, Antibes, 1990, pp. 259-268

....27 12 2000; 9:23; p.5 6 Dellaert, Seitz, Thorpe Thrun 3. We also allow images to be taken from a set of arbitrary camera poses M = fm i ji 2 1: mg. This makes the data association harder: most existing approaches rely on the temporal continuity of an image stream to track features over time (Deriche Faugeras, 1990; Tomasi Kanade, 1992; Zhang Faugeras, 1992; Cox, 1993; Cox Hingorani, 1994) or otherwise constrain the data association problem (Beardsley et al. 1996) 4. In this paper, we adopt the commonly used assumption that all features x j are seen in all images (Tomasi Kanade, 1992; Hartley, ....

.... Durrant Whyte, 1992; Leonard et al. 1992) The classical target tracking literature provides a number of methods for data association (Bar Shalom Fortmann, 1988) that are used in computer vision (Cox, 1993) and CML (Cox Leonard, 1994; Feder et al. 1999) such as nearest neighbor tracking (Deriche Faugeras, 1990), the track splitting filter (Zhang Faugeras, 1992) and the multiple hypothesis filter (Reid, 1979; Cox Leonard, 1994; Cox Hingorani, 1994) Unfortunately the latter, more powerful methods have exponential complexity so suboptimal approximations are used in practice. Moreover, the ....

Deriche, R., & Faugeras, O. (1990). Tracking line segments. Image and Vision Computing, 8, 261--270.

....Assuming no occlusion and small deformations between frames, local forces derived from stereo images are sufficient to update the positions, orientations, and shapes of the models in 3D. Kalman filtering techniques have been applied in the vision literature for the estimation of dynamic features (Deriche Faugeras 1990) and rigid motion parameters (Dickmanns Graefe 1988; Broida, Chandrashekhar, Chellappa 1990) of objects from image sequences. We use a Kalman filter for the estimation of the object s shape and motion, which consequently allows the prediction of possible edge occlusion and disocclusion. The ....

Deriche, R., and Faugeras, O. 1990. Tracking Line Segments. Image and Vision Computing 8(4):261--270.

....additional data is unknown, i.e. it is hidden data. 3. We also allow images to be taken from a set of arbitrary camera poses , This makes the data association harder: most existing approaches rely on the temporal continuity of an image stream to track features over time (Deriche Faugeras, 1990; Tomasi Kanade, 1992; Zhang Faugeras, 1992; Cox, 1993; Cox Hingorani, 1994) or otherwise constrain the data association problem (Beardsley et al. 1996) 4. In this paper, we adopt the commonly used assumption that all features are seen in all images (Tomasi Kanade, 1992; Hartley, ....

.... et al. 1992) The classical target tracking literature provides a number of methods for data association (Bar Shalom Fortmann, 1988; Popoli Blackman, 1999) that are used in computer vision (Cox, 1993) and CML (Cox Leonard, 1994; Feder et al. 1999) such as nearest neighbor tracking (Deriche Faugeras, 1990), the track splitting filter (Zhang Faugeras, 1992) the Joint Probabilistic Data Association Filter (JPDAF) Rasmussen Hager, 1998) and the multiple hypothesis tracker (MHT) Reid, 1979; Cox Leonard, 1994; Cox Hingorani, 1994) Unfortunately the latter, more powerful methods have ....

Deriche, R., & Faugeras, O. (1990). Tracking line segments. Image and Vision Computing, 8, 261--270.

....a view sketch obtained by projecting a 3D polyhedral model of the vehicle into the image plane, using a hidden line algorithm to determine their visibility. The matching of image edge segments and model segments is based on the Mahalanobis distance of line segment attributes as described in [Deriche Faugeras 1990]. The midpoint representation of line segments is suitable for using different uncertainties parallel and perpendicular to the line segments. In order to avoid incorrect matches between model segments and image edge segments which arise from shadows of the vehicles, we enrich the applied a priori ....

....(see, e.g. the lower right image of Figure 4) Put Figure 4 about here. 4. 2 Finding Correspondences between Matching Primitives Correspondences between model and data segments are established using the Mahalanobis distance between attributes of the line segments as described in [Deriche Faugeras 1990]. We use the representation X # #c x # c y # ## l# of a line segment, defined as: c x # x1#x2 2 # c y # y1#y2 2 # # # arctan # y2#y1 x2#x1 # # l # p #x 2 # x 1 # 2 # #y 2 # y 1 # 2 # (3) where #x 1 # y 1 # T and #x 2 # y 2 # T are the endpoints of a line segment. The ....

[Article contains additional citation context not shown here]

Deriche, R. and Faugeras, O.D., 1990. Tracking line segments. Image and Vision Computing, 8:261--270.

....over the estimates for the single images evaluated in the initialization phase. After initialization we apply the recursive equations of the Kalman filter (e.g. Gelb [8] In the field of computer vision, Kalman filter approaches have been introduced by Broida Chellappa [3] and Deriche Faugeras [6] . Broida Chellappa incrementally estimate the model parameters of rigid objects from measured image points whereas Deriche Faugeras track grey value lines in the image plane. Our aim is to recognize non rigid movements. Since the body parts of pedestrians often are occluded by one another ....

R. Deriche, O. Faugeras, Tracking line segments, Image and Vision Comp. 8 (1990) 4, 261-270

....match individual line segments; and those that match groups of line segments. Individual line segments are generally matched on their geometric attributes orientation, length, extent of overlap (Medioni and Nevatia, 1985, Ayache, 1990, Zhang, 1994) Some such as (Crowley and Stelmazyk, 1990, Deriche and Faugeras, 1990, Huttenlocher et al. 1993) use a nearest line strategy which is better suited to image tracking where the images and extracted segments are similar. Matching groups of line segments has the advantage that more geometric information is available for disambiguation. A number of methods have been ....

Deriche, R. and Faugeras, O., 1990. Tracking line segments. In: Proc. ECCV, pp. 259--267.

....difference between our approach and existing approaches is the use of the topology constraint to drive global matches. Final matches are expected to be topologically correct and yield sub optimalities free correspondence. 2 Related work Many researchers attempted the matching of line segments [4], or piecewise linear representations of boundaries [14, 13, 7, 17] To limit the combinatorial search for pairings, additional constraints were needed, some of which restrict the domain of applicability to stereo correspondence. Maximum velocity, constant disparity gradient and epipolarity are ....

R. Deriche and O. Faugeras. Tracking line segments. INRIA, 8(4):261--270, November 1990.

....part of the corresponding line segment in space (and we say that the two 2D line segments overlap) Indeed, this assumption is minimal, and is what we use to match line segments between different views. We do not address the problem of matching line segments here. This can be done by tracking [4, 8] or other techniques [3] This paper is organized as follows. Section 2 describes the problem we want to solve and shows why we can determine 3D motion and structure from corresponding line segments between two images. Section 3 presents the algorithm for solving the motion problem. The epipolar ....

R. Deriche and O. Faugeras. Tracking line segments. In O. Faugeras, editor, Proc. First European Conf. Comput. Vision, pages 259--268, Antibes, France, April 1990. Springer, Berlin, Heidelberg.

....a rigid object. This 8 particle motion concept can be carried further, estimating the acceleration of a feature in the image plane a k as well as the velocity. Then a constant acceleration model for motion could be assumed, taking z k 1 = z k Deltav k Delta 2 a k : Deriche and Faugeras [32] use a constant acceleration dynamic model for tracking line segments in an image sequence. The dynamic model can be used to predict motion in 3D as well as motion in the image plane. Bradshaw et al. 33] use constant speed, constant velocity, and constant direction 3D dynamic models to estimate ....

....flow algorithm, then uses the results to update a rigid polyhedral object model in 3D. Edgelets are short line segments in input images. Unlike many tracking research, Bray presented an initialization method for the tracking, using a model based search based on edge matching. Deriche and Faugeras [32] compared two representations for line segments and performed an uncertainty analysis on the parameters of each. They used a Kalman filtering based scheme to track line segments with each representation. Gennery [10] uses edge detected images in a modified Kalman filter framework to track known 3D ....

R. Deriche and O. Faugeras, "Tracking line segments," Image and Vision Computing, vol. 8, pp. 261--270, Nov. 1991.

....features, missing features (in non overlapping regions) and by object occlusions in the scene. Fortunately it is usually unnecessary to perform an unconstrained two dimensional search of an image to find a feature match. Instead one can often make use of what is called the epipolar constraint [6, 7]. This constraint, discussed further in Section 3, is based on the fact that the true 3D location of the point in the scene must lie along the ray extending from the center of a camera, through the 2D image of the point, and into the scene. See Fig. 1. The crucial observation is that the image ....

R. Deriche and O.D. Faugeras. "Tracking Line Segments." In Proceedings of the 1st ECCV, pages 259-- 268. Springer Verlag, April 1990.

....we track these organized structures by exploiting principles of perceptual organization. So far, the typical approach to tracking has been to solve for correspondences between two frames and then to thread them together into feature tracks. Typical techniques involve predictive Kalman filtering [11], area correlation measures, optic flows [6] hierarchical matching [9] or deformable models [7] Our approach is to exploit the spatial and structural coherence of a feature over time to compute feature tracks simultaneously over a number of frames. A track thus extracted represents a globally ....

....[1, 2, 3, 4] straight lines [5, 6] contours[7] and 3D models [8, 9] The typical approach is to solve for the correspondence between frames using constraints such as motion smoothness, small motion, or shape coherence. The computational techniques include the use of predictive Kalman filtering [11], area correlation measures, optic flows [6] hierarchical matching [9] or deformable models [7] This paper describes a method to construct 2D feature tracks not by piecing together 2 frame correspondences but by exploiting perceptual organizational principles to extract the path simultaneously ....

R. Deriche and O. Faugeras, "Tracking line segments," in European Conference on Computer Vision, pp. 259--268, Apr. 1990.

.... In fact methods which extract explicit temporal structure (rather than independent motion estimates over time) are based on the matching and tracking of segmented features such as corners and employ motion models which, unlike affine motion models, contain temporal components in their motion models[5, 10, 11]. The method proposed in this paper addresses the problem of temporal independence. Motion results from one frame are used to guide the estimation of motion in the next. Specifically, previous optical flow fields are fed forward (actually warped forward) to act as initial estimates in an affine ....

R. Deriche and O. Faugeras. "Tracking Line Segments". Image and Vision Computing, 8(4):261--270, November 1990.

....part of the corresponding line segment in space (and we say that the two 2D line segments overlap) Indeed, this assumption is minimal, and is what we use to match line segments between dioeerent views. We do not address the problem of matching line segments here. This can be done by tracking [5, 9] or other techniques [4] This paper is organized as follows. Section 2 describes the problem we want to solve and shows why we can recover 3D motion and structure from corresponding line segments between two images. Section 3 presents the algorithm for solving the motion problem. The epipolar ....

R. Deriche and O. Faugeras. Tracking line segments. In O. Faugeras, editor, Proc. First European Conf. Comput. Vision, pages 259268, Antibes, France, April 1990. Springer, Berlin, Heidelberg.

....an error image. We define the error image E: E = jrI(x) Delta v I t (x)j (4) Finding the Object from the Error Image Since we assume that we are only looking for one small object we simply let the centroid (C) of the error image, represent the moving object. By using an ff fi tracker [3] we will get a more stable centroid over time. 4 Experiments and Results In this section we will show how the system performs in a few different situations. The target will move, while the observer undergoes ego motion. No knowledge about any of these motions is assumed. The experiments are ....

R. Deriche and O. Faugeras. Tracking line segments. In 1st ECCV, volume 427, pages 259--268, April 1990.

....or the next frame in a motion sequence. The position of a token in an image is given by the vector u. For orientated edge points this vector will store the pixel position and orientation, while for more complex features such as line segments a number of different representations are available [21]. The attributes (e.g. line length, greylevel, curvature, etc) of a token are stored in an attribute vector a = a 1 ; a 2 ; Normally a match fl is constructed from two features, one from each image i.e. fl = f; 0 g. However, the work of Sethi Jain [73] is best understood within ....

R. Deriche and O.D. Faugeras. "Tracking Line Segments". Image and Vision Computing, 8(4):261--270, November 1990.

....techniques [Ana89, Fua90] Another important case of systems using this assumption is that of tracking. The motion is supposed to be very small or very regular and the location of the features within an image of a sequence may be predicted from the knowledge of the previous images of the sequence [CS90, DF90]. 2. second assumption: some of the features or group of features remain qualitatively similar. In this case, matching is based on the search of particular features configurations: small graphs of segments [SH92] the whole graph of all the segments [HHVN90] symmetric features [HSV90] The first ....

R. Deriche and O. Faugeras. Tracking line segments. In Proceedings of the 1st European Conference on Computer Vision, Antibes, - France, pages 259--267. Springer-Verlag, April 1990.

....may not be correctly found using block matching for only point features. Hence, we proposed another algorithm (i.e. Algorithm 2) to overcome this problem. In Algorithm 2, line features in the wire frame model are used for the generation of more robust hypotheses. In the past, Deriche and Faugeras [6] and Zhang and Faugeras [22] have proposed line tracking methods which extracts line features by linking edge maps at first, and then tracking line features in the image sequence. Their methods can be referred to as a linking followed by matching approach. However, because extraction of line ....

R. Deriche and O. Faugeras, "Tracking Line Segments," Image and Vision Computing, Vol. 8, pp. 261-270, 1990.

....to the motion model or to the environment model. Such constraints include the introduction of a regularization term [HS81] assuming a limited model of the world [Adi85] restricting the range of possible motions [HW88] or assuming some type of temporal motion constancy over a longer sequence [DF90] 3D motion is often estimated from the optical or normal flow field derived between two frames [Adi85, LR83, HJ90, GU91, JH91, Sun91, NL91, HA91, TS91, AD92, DRD93] or from the correspondence of distinguished features (points, lines, contours) previously extracted from successive frames [FLT87, ....

....using a combined spatio temporal analysis [FJ90, Hee88, SM90] These methods assume motion constancy in the temporal regions, i.e. motion should remain uniform in the analyzed sequence. In feature based methods, features are tracked over a larger time interval using recursive temporal filtering [DF90] The issue of extracting good features and overcoming occlusions still remains. Methods for computing the ego motion directly from image intensities were also suggested [Han91, HW88, Taa92] Horn and Weldon [HW88] deal only with restricted cases (pure translation, pure rotation, or a general ....

R. Deriche and O.D. Faugeras. Tracking line segments. In European Conf. on Computer Vision, pages 259--268, April 1990.

....to find features that are robust to the changes expected between frames in the imagery. Edgel tracking is generally more robust to lighting changes than correlation and often excellent for tracking rigid objects with high contrast. An illustrative edge tracking scheme has been developed by Deriche[17]. A Kalman filter predicts the location of an edge and the Mahalanobis distance is used to compute a matching score. A more sophisticated tracker recently described by Sawhney uses a four parameter affine model that handles scale, rotation and translation to track collections of lines[42] ....

R. Deriche and O. Faugeras. Tracking line segments. In Proc. European Conf. Comp. Vis., pages 259--268, Antibes, France, April 1990.

....spaced, it is hard to track and distinguish one line segment from another because they have similar orientations. The procedure for line tracking typically consists of two steps: a prediction step and a matching step. There are two popular prediction techniques: Kalman filterbased prediction [4], and methods that apply epipolar constraints for prediction [1, 11] Kalman filter based techniques have two main problems: First, they take several frames to obtain reliable results. Second, they have difficulty in setting up the uncertainties for the segment tracking, which is usually tuned by ....

....areas. We solve the problem by using a simple filling operation. Even when line motion prediction is reliable, it is hard to distinguish closely spaced lines. We introduce a line direction attribute obtained at the edge extraction stage. While many matching functions have already been introduced [3, 4, 7, 11], very few of them deal with multiple line segments that are broken over an image sequence due to the problem of edge extraction. We propose a simple and expandable similarity function to track collinear multiple line segments. Our method is robust enough to handle real world image sequences taken ....

Deriche, R. and Faugeras, O., 1990. Tracking line segments. In: 1st European Conference on Computer Vision, Antibes, France, pp. 259-268.

....to the motion model or to the environment model. Such constraints include the introduction of a regularization term [HS81] assuming a limited model of the world [Adi85] restricting the range of possible motions [HW88] or assuming some type of temporal motion constancy over a longer sequence [DF90] 3D motion is often estimated from the optical or normal flow field derived between two frames [Adi85, LR83, HJ90, GU91, JH91, Sun91, NL91, HA91, TS91, AD92, DRD93] or from the correspondence of distinguished features (points, lines, contours) previously extracted from successive frames [OFT87, ....

....using a combined spatio temporal analysis [FJ90, Hee88, SM90] These methods assume motion constancy in the temporal regions, i.e. motion should remain uniform in the analyzed sequence. In feature based methods, features are tracked over a larger time interval using recursive temporal filtering [DF90] The issue of extracting good features and overcoming occlusions still remains. Methods for computing the ego motion directly from image intensities were also suggested [Han91, HW88, Taa92] Horn and Weldon [HW88] deal only with restricted cases (pure translation, pure rotation, or a general ....

R. Deriche and O. Faugeras. Tracking line segments. In Proc. 1st European Conference on Computer Vision, pages 259--268, Antibes, April 1990.

....Proper modelling of uncertainties in the detected object features is essential for fast and reliable object tracking and trajectory reconstruction. Since straight line segments are the smallest primitives that are directly used, the uncertainties must be modelled at this level. It has been shown [7] that the mid point representation for 2 D line segments, which consists of their midpoints, lengths and angles, is appropriate for this purpose. The mid point parameters can be Figure 2: Stereo view of the extracted straight line segments and the localized object projected on the original ....

....denotes an unknown scale parameter. The ratio oe k = oe must be determined experimentally. We assume that the uncertainties in both directions as well as the uncertainties in both end points are uncorrelated. The covariance matrix of the parameter vector [x m ; y m ; l] is given by [7] Sigma = oe 2 Sigma; Sigma = 2 6 6 6 6 6 4 oe 2 k cos 2 ( oe 2 sin 2 ( 2 (oe 2 k Gammaoe 2 ) sin( cos( 2 0 0 (oe 2 k Gammaoe 2 ) sin( cos( 2 oe 2 k sin 2 ( oe 2 cos 2 ( 2 0 0 0 0 2oe 2 l 2 0 0 0 0 2oe 2 k 3 7 7 7 7 7 5 ....

R. Deriche and O. Faugeras. Tracking line segments. In O. Faugeras, editor, Computer Vision --- ECCV '90; First European Conf. Computer Vision, Antibes, France, pages 259-- 268. Springer, Berlin, Heidelberg, 1990.

....and reactivity see [Ravela92] The kernel of the tracking system described in this paper is based on normalized correlation [Fennema91] in polar space. For studies of correlation and SSD see [Wood83]and [Anandan89] respectively. Tracking has been approached from a tokenbased view point and [Deriche91, Koller93] where the tokens are line segments or groups of segments. Direct methods for contour tracking were employed in [Kass88] for a comprehensive study see [Blake92] These track contours by associating a deformation model with a contour network. Model based approaches have also been studied ....

Deriche, R., and Faugeras, O., "Tracking line segments", Image and Vision Computing, pp 261-270, 1991.

....two costly operations: camera movement and multiple image processing. In [2] a method to obtain the 3D location of segments by the integration of several images taken from different points of view is described. The points of view are defined by a preprogrammed trajectory over the scene. 2] and [3] propose to do the matching between observation by tracking the projections in the image. The proposed matching function is based on thee Mahalanobis distance between the projections. In [4] a method to control the camera movement in order to improve the point of view with respect to the ....

.... of the projection with respect to the camera is LCP = xCP ; pP ; CP ) where: xCP = x cp ; y cp ; f; 0; 0; OE P ) T pP = 0; 0; 0; 0) T (4) CP = diag Gamma oe 2 yP ; 0; 0; oe 2 OEP Delta This representation of a segment is similar to the midpoint representation proposed in [3]. Because of that, the proposed covariance matrix CP is diagonal, and its uncertainty is independent of the location of the projection in the image plane. The values of oe 2 yP and oe 2 OEP depend on the size of the pixel and the length of the projection, as proposed in [6] I L E f P z x y ....

R. Deriche and O. Faugeras. Tracking line segments. In First European Conference on Computer Vision, pages 259--268, Antibes, France, 1990.

....techniques [Ana89, Fua90] Another important case of systems using this assumption is that of tracking. The motion is supposed to be very small or very regular and the location of the features within an image of a sequence may be predicted from the knowledge of the previous images of the sequence [CS90, DF90]. 2. second assumption: some of the features or group of features remain qualitatively similar. In this case, matching is based on the search of particular features configurations: small graphs of segments [SH92] the whole graph of all the segments [HHVN90] symmetric features [HSV90] The ....

R. Deriche and O. Faugeras. Tracking line segments. In Proceedings of the 1st European Conference on Computer Vision, Antibes, France, pages 259--267. Springer-Verlag, April 1990.

....approaches to line matching in the literature are of two types: those that match individual line segments; and those that match groups of line segments. Individual line segments are generally matched on their geometric attributes orientation, length, extent of overlap [1, 12, 20] Some such as [4, 5, 10] use a nearest line strategy which is better suited to image tracking where the images and extracted segments are similar. The advantage of matching groups of line segments is that more geometric information is available for disambiguation, the disadvantage is the increased complexity. A number of ....

R. Deriche and O. Faugeras. Tracking line segments. ECCV, 1990.

....derived from the correlation field as used in the directional averaging, ie it forms an estimate of R. In order to deal with discontinuities in the motion, we adopt a finite memory for the filter by linearly increasing the covariance of past measurements in a similar manner to that employed in [10]. This enables the filter to adapt quickly to changes in motion. An additional modification was also made to deal with cases in which blobs fail to find an adequate match in the new motion estimates, ie all the distance metrics d kl are too large. This can happen for instance when there is a ....

R. Deriche and O. Faugeras, "Tracking line segments ", Image and Vision Computing, 8(4), 1990.

....is hard to track and distinguish one line segment from another because they have similar orientations. The procedure for the line tracking method consists of two steps: a prediction step and a matching step. For the prediction step, there are two types of approaches: prediction by a Kalman filter [4] and prediction by the epipolar constraint between images [1, 10] The problem of the Kalman filter based techniques is that it has difficulty in setting up the uncertainties for the segment tracking which is usually tuned by hand. Although the epipolar constraint is geometrically powerful, it ....

R. Deriche and O. Faugeras, "Tracking line segments", ECCV, 1990.

.... constraints are usually added to the motion model or to the environment model, e.g. introducing a regularization term [HS81] assuming a limited model of the world [Adi85] restricting the range of possible motions [HW88] or assuming some type of temporal motion constancy over a longer sequence [DF90] 3D motion is often estimated from the optical or normal flow field derived between two frames [Adi85, LR83, GU91, JH91, Sun91, NL91, HA91, TS91, AD92] or from the correspondence of distinguished features (points, lines, contours) previously extracted from the two frames [OFT87, Hor90] Both ....

....using a combined spatio temporal analysis [FJ90, Hee88, SM90] These methods assume motion constancy in the temporal regions, i.e. motion should remain uniform in the analyzed sequence. In feature based methods, features are tracked over a larger time interval using recursive temporal filtering [DF90] The issue of extracting good features and overcoming occlusions still remains. Methods for computing the ego motion directly from image intensities were also suggested [Han91, HW88, Taa92] Horn and Weldon [HW88] deal only with restricted cases (pure translation,pure rotation, or general motion ....

R. Deriche and O. Faugeras. Tracking line segments. In Proc. 1st European Conference on Computer Vision, pages 259--268, Antibes, April 1990.

....depend on the feature extraction process, and on the intrinsic parameters of the camera calibration. ffl The camera uncertain location estimate, and its location covariance matrix. We propose an image segment model, which we will call 2D segment. Classical image segments representations [4, 5] consider image segments as 2D entities in the image plane. The 2D segment we propose is a 3D entity composed of the supporting line projection plane, plus the midpoint projection ray. Similarly the consistency between a projection and a 3D segment is not tested on the image, but considering a ....

R. Deriche and O. Faugeras. Tracking line segments. In First European Conference on Computer Vision, pages 259--268, Antibes, France, 1990.

....of an unknown stationary scene, when performing a rigid motion. The facility in a motion paradigm is that we can assume the disparity between two frames to be small, leading to easy solutions for the correspondence problem. These correspondences can efficiently been established (Token Tracking) [3, 32]. This problem is thus, given correspondences between points or lines, to recover, the motion, structure and calibration of the system. Let us first emphasis the generality of the approach we want to take here : in most of the artificial vision problems or paradigms , four quantities are to be ....

....accurate subpixel corner estimators for instance [4, 11] up to 1 or 2 pixels for standard feature detectors. We have verified the stability of the algorithm also considering large errors of 5 pixels because this corresponds to the error amplitudes when false matchings occur in an image sequence [3, 32]. 34 The precision of the estimate is measured considering the distance between the 11 components of the expected and estimated Qs representations in the parameter space. We have obtained the following experimental results : oe N = 0 1:3 10 6:23 10 5:08 10 9:80 10 2:12 ....

R. Deriche and O. D. Faugeras. Tracking Line Segments. In Proceedings of the 1st ECCV, Antibes, pages 259--269. SpringerVerlag, Berlin, 1990.

....[MB92] track contours in order to estimate time to collision; Curwen [CB92] track occluding contours in order to compute free space and to plan a possible path for a robot arm. Moreover feature tracking provides a good basis for the estimation of 3D motion and or structure [Sha86] BR86] Har92] DF90] SJ87] SA91] FP93] First investigations were concerned with the tracking of points [SJ87] and edge segments [CSD88] DF90] GCDVF93] However, this data is sparse and sensitive to occlusion. Consequently, interest was driven to the tracking of more complex and global primitives, such as ....

....space and to plan a possible path for a robot arm. Moreover feature tracking provides a good basis for the estimation of 3D motion and or structure [Sha86] BR86] Har92] DF90] SJ87] SA91] FP93] First investigations were concerned with the tracking of points [SJ87] and edge segments [CSD88] DF90] GCDVF93] However, this data is sparse and sensitive to occlusion. Consequently, interest was driven to the tracking of more complex and global primitives, such as contours and regions. Among theses tracking methods aimed at tracking global primitives, deformable models ( snakes ) have had a ....

R. Deriche and O.D. Faugeras. Tracking line segments. In First European Conference on Computer Vision, p. 259-268, Antibes, France, April 1990.

....of an unknown stationary scene, when performing a rigid motion. The facility in a motion paradigm is that we can assume the disparity between two frames to be small, leading to easy solutions for the correspondence problem. These correspondences can efficiently been established (Token Tracking) [3, 32]. This problem is thus, given correspondences between points or lines, to recover, the motion, structure and calibration of the system. Let us first emphasis the generality of the approach we want to take here : in most of the artificial vision problems or paradigms , four quantities are to be ....

....accurate subpixel corner estimators for instance [4, 11] up to 1 or 2 pixels for standard feature detectors. We have verified the stability of the algorithm also considering large errors of 5 pixels because this corresponds to the error amplitudes when false matchings occur in an image sequence [3, 32]. The precision of the estimate is measured considering the distance between the 11 components of the expected and estimated Qs representations in the parameter space. We have obtained the following experimental results : Noise Level Motion from Structure Structure from Motion oe N = 0 1:3 10 ....

R. Deriche and O. D. Faugeras. Tracking Line Segments. In Proceedings of the 1st ECCV, Antibes, pages 259--269. SpringerVerlag, Berlin, 1990.

....the epipolar geometry is also unknown. The methods reported in the literature all exploit some heuristics in one form or another, for example, intensity similarity, which are not applicable to most cases. The difficulty is partly bypassed by taking long sequences of images over short time interval [9, 58]. Indeed, as the time interval is small and object velocity is constrained by physical laws, the interframe displacements of objects are bounded, i.e. the correspondence of a token at the subsequent instant must be in the neighborhood of the first. However, in many cases, such as a pair of ....

R. Deriche and O. Faugeras. Tracking line segments. In O. Faugeras, editor, Proc. First European Conf. Comput. Vision, pages 259--268, Antibes, France, April 1990. Springer, Berlin, Heidelberg.

....tracking. Furthermore, the trajectories of the control points parameterizing the region contour and measured by the snake are smoothed using Kalman filtering, so as to diminish the influence of noise. Each coordinate x of the control points is filtered independently using an ff; fi tracker [8]. It is a steady state Kalman filter with a constant velocity model. For more details, see [8] The estimate of a control point coordinate x and its velocity x are given by: x t=t = Gamma(ff fi Gamma 2)x t Gamma1=t Gamma1 Gamma (1 Gamma ff)x t Gamma2=t Gamma2 ffv t ( Gammaff fi)v ....

....contour and measured by the snake are smoothed using Kalman filtering, so as to diminish the influence of noise. Each coordinate x of the control points is filtered independently using an ff; fi tracker [8] It is a steady state Kalman filter with a constant velocity model. For more details, see [8]. The estimate of a control point coordinate x and its velocity x are given by: x t=t = Gamma(ff fi Gamma 2)x t Gamma1=t Gamma1 Gamma (1 Gamma ff)x t Gamma2=t Gamma2 ffv t ( Gammaff fi)v t Gamma1 and x t=t = Gamma(ff fi Gamma 2) x t Gamma1=t Gamma1 Gamma (1 Gamma ff) x ....

R. Deriche and O.D. Faugeras. Tracking line segments. In First EuropeanConferenceon ComputerVision, p. 259-268, Antibes, France, April 1990.

No context found.

R. Deriche and O. Faugeras. Tracking line segments. Proc. European Conference on Computer Vision, pages 259--268, 1990.

No context found.

R. Deriche and O. Faugeras. Tracking line segments. Proc. European Conference on Computer Vision, pages 259--268, 1990.

No context found.

R. Deriche and O. Faugeras, "Tracking line segments ", Image and Vision Computing, 8(4), 1990.

No context found.

R. Deriche and O. Faugeras, "Tracking line segments, " Image and Vision Computing, vol. 8, pp. 261--270, 1990.

No context found.

R. Deriche and O. Faugeras. Tracking line segments. Proc. European Conference on Computer Vision, pages 259--268, 1990.

No context found.

R. Deriche and O. Faugeras. Tracking line segments. In European Conference on Computer Vision, pages 259--267, 1990.

No context found.

Deriche, D. and Faugeras, O.D., Tracking Line Segments, IVC-8, No. 4, p.261- 270, November 1990.

No context found.

R. Deriche and O. Faugeras, "Tracking line segments," in Proc. First European Conf. Comput. Vision, (O. Faugeras, ed.), (Antibes, France), pp. 259--268, Springer, Berlin, Heidelberg, April 1990.

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