C. A. Rothwell, A. Zisserman, J. L. Mundy, and D. A. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proceedings 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... of matches between model and image features (e.g. Clark et al. 13] Fischler and Bolles [17] Ayache and Faugeras [5] Horaud [25] Huttenlocher and Ullman [27] Other approaches use indexing to match more than the minimal number before looking for confirming features (e.g. Rothwell et al. [38], Thompson and Mundy [43] Lamdan et al. 32] Jacobs [29] Most recognition systems take an ad hoc approach to the problem of accounting for the effects of sensing error on the projected positions of unmatched model features. Some systems match projected model features to image features if they ....

....system might attempt to add matches, and use these additional matches to narrow the area in which it must search for still more consistent matches. Additionally, the algorithm from Section 6 may be useful in methods that match image to model features by indexing, and then verify these matches [32, 14, 29, 43, 38, 45]. In these approaches, some model features are matched to image features to determine a model pose, and then this pose is used to find matches for additional model features. Our results show exactly where to search for these matches when we have matched three image and model points. As mentioned ....

Rothwell C., A. Zisserman, J. Mundy, and D. Forsyth, "Efficient Model Library Access by Projectively Invariant Indexing Functions," IEEE Conf. on Computer Vision and Pattern Recognition, pp. 109-114, 1992.

....# w j satisfy Eq. 19) also # P i # T and # T #1 # w j satisfy Eq. 19) for any 4 4 nonsingular matrix # T# A projective reconstruction can be computed starting from point correspondences only, without any a priori knowledge [18 25] Despite that it conveys some useful information [26,27], we would like to obtain a Euclidean reconstruction, a very special one that differs from the true reconstruction by an unknown similarity transformation. This is composed by a rigid displacement (due to the arbitrary choice of the world reference frame) plus a uniform change of scale (due to the ....

C. Rothwell, A. Zisserman, J. Mundy, D. Forsyth, Efficient model library access by projectively invariant indexing functions, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1992.

....the time complexity could not be further reduced. It has been shown [1, 2, 3] however, that no invariants exist for general 3D point sets. Because of this, many methods have developed special case invariants by placing constraints on feature sets, for example, that all features lie in a plane [4, 5, 6, 7, 8]. We believe this approach is too restrictive for the 3D from 2D recognition problem, and has meant that a wealth of shape information from non invariant groupings has been unavailable to the indexing mechanism. Hash tables also turn out to be problematic when one considers indexing in ....

....and hash tables for indexing. Forsythe et al. 4] outlined several types of projective invariant feature for indexing planar objects viewed in arbitrary 3D orientations. Their experiments were carried out using a 2D index space generated by pairs of coplanar conic sections. Rothwell et al.[7], used 4D indices defined by area moments of planar curves, that were first transformed into canonical reference frames. In each of these methods, the dimensionality of the spaces and the number of models were too small for the inefficiency of hashing to be critical. The geometric hashing ....

C.A. Rothwell, A. Zisserman, J.L. Mundy, and D.A. Forsyth, "Efficient model library access by projectively invariant indexing functions," in Proceedings CVPR '92, 1992, pp. 109--114.

....f P i Tg and f T Gamma1 w j g satisfy (19) for any 4 Theta 4 nonsingular matrix T. A projective reconstruction can be computed starting from points correspondences only, without any a priori knowledge [13, 14, 15, 16, 17, 18] Despite it conveys some useful in6 formations [19, 20], we would like to obtain an Euclidean reconstruction, a very special one that differs from the true reconstruction by a similarity transformation. This is composed by a rigid displacement (due to the arbitrary choice of the world reference frame) plus a a uniform change of scale (due to the ....

C. Rothwell, A. Zisserman, J. Mundy, and D. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 1992.

....invariant and two parallel lines in space will project to two almost parallel lines over a large range of view angles, provided that they are not to long. During the last few years considerable interest has been devoted to the study of projective invariants. In the work by Rothwell et al. [Rothwell et al. 1991] a number of invariants are used, the first are two invariants that can be calculated using 5 coplanar lines, the second is an invariant that can be calculated using a conic and two lines lying in the same plane, and finally an invariant that can be calculated using two coplanar conics is used. ....

C. A. Rothwell, A. P. Zisserman, J. L. Mundy, and D. A. Forsyth. "Efficient Model Library Access by Projectively Invariant Indexing Functions ". In Proc. IEEE Comp. Soc. Conf. on Computer Vision and Pattern Recognition, 1991.

....also applies to so called quasi invariants, i.e. image descriptors that show non zero but small variation due to change of viewpoint [2] 41] By limiting the object instances to be planar in 3 D, the choice of projectively invariant descriptors actually ensures that view variation is eliminated. [34, 35]. A more general way to overcome view variation is to use multiple cameras and reconstruct the object in 3 D. 32] If this reconstruction is based on projective metrics, the effect of internal camera parameters will be cancelled [10, 14, 28] Introducing multiple cameras means that images have to ....

....of retrieval due to the extensive search that has to be performed. 1.3 Camera Parameter Variation The variation due to changing camera calibration is probably the one that has been most successfully attacked leading to so called calibration free methods for recognition and reconstruction. [10, 14, 28, 34] By choosing a sufficiently general metric for the image descriptors, the effect of internal camera parameter variation can be eliminated. For a linear pinhole camera this requires projective metric but affine metric is sufficient in many cases. The transformation groups euclidean, affine and ....

[Article contains additional citation context not shown here]

Rothwell, C.A., Zisserman, A.P., Mundy, J.L., Forsyth, D.A., Efficient Model Library Access by Projectively Invariant Indexing Functions, In: Proc. CVPR-92, pp. 109-114. (1992)

....be determined by finding the perspective 35 transformation that maps two known conics on the object plane to two conics found in the image plane. Follow up work has investigated invariant indexing functions for other planar feature sets such as a conic and three lines, and five coplanar lines [Rothwell92]. The early successes in object recognition based on planar invariants sparked considerable interest in developing more general 3D to 2D invariants. However, work by Burns shows that there is no holy grail there are no 3D to 2D invariants for general configurations of points in space ....

Rothwell, C.A., Zisserman, A., Mundy, J.L. and Forsythe, D.A. "Efficient Model Library Access by Projectively Invariant Indexing Functions," Proceedings IEEE Computer Vision and Pattern Recognition, Champaign, IL, June 1992, pp. 109--114.

....in all reasonable cases be close in the images. These groupings were then further grouped into larger structures and these structures were used for recognition. During the last few years considerable interest has been devoted to the study of projective invariants. In the work by Rothwell et al. [RZFM91] a number of invariants are used, the first are two invariants that can be calculated using 5 coplanar lines, the second is an invariant that can be calculated using a conic and two lines lying in the same plane, and finally an invariant that can be calculated using two coplanar conics is used. ....

C. A. Rothwell, A. P. Zisserman, D. A. Forsyth, and J. L. Mundy. Efficient model library access by projectively invariant indexing functions. Paper sent to conference, November 1991.

....In the second method local features are extracted from the model and from the image. Subsets of model features are matched to subsets of image features, and this match is used to recover the alignment transformation. This has been done using point features ( 15, 17, 21, 42, 1, 2] line segments ([30, 4, 36]) vertices ( 40] and distinguished points on curves such as inflection points or bitangents ( 24, 37] By relying on local properties, these methods can be more robust than global ones. Typically we must isolate an entire shape to extract its global properties. However, we can often find local ....

Rothwell C., A. Zisserman, J. Mundy, and D. Forsyth, 1992, "Efficient Model Library Access by Projectively Invariant Indexing Functions," IEEE Conference on Computer Vision and Pattern Recognition, pp. 109-114.

....of matching image descriptors to models can be considerable. A way to reduce this is to use index tables where image descriptors are used as indexes to a table containing corresponding model descriptors. These tables can be constructed off line which means that space is traded off for time [1] [2] [6] 7] Another factor affecting the complexity of recognition is the fact that the image of an object depends on the viewpoint of the camera. This has initiated work in finding feature descriptors invariant to viewpoint [1] 2] For configurations of points and lines invariants can in general ....

....off line which means that space is traded off for time [1] 2] 6] 7] Another factor affecting the complexity of recognition is the fact that the image of an object depends on the viewpoint of the camera. This has initiated work in finding feature descriptors invariant to viewpoint [1] [2]. For configurations of points and lines invariants can in general be found only when they are contained in a planar surface. For general configurations of points and lines, any descriptor computed from data in one image will vary with viewpoint. 6] 8] By imposing constraints on the ....

C.A. Rothwell, A.P. Zisserman, J.L. Mundy, D.A. Forsyth, Efficient Model Library Access by Projectively Invariant Indexing Functions, In: Proc. CVPR-92, pp. 109-114 , (1992)

....as shown in Figure 2.2. In the figure, every set of four collinear points joined by a solid line has the same cross ratio. Various constructions can be used to derive related invariants for different geometric configurations, e.g. for five coplanar points [60] or a conic and two coplanar lines [77, 87]. As a general rule, the number of independent invariants of a given structure under a particular transformation group is equal to the dimension (i.e. number of degrees of freedom) of the structure minus the dimension of the transformation [77] Therefore, in the case of the planar perspective ....

C.A. Rothwell, A. Zisserman, J.L. Mundy, and D.A. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proc. IEEE Conf. Computer Vision and Pattern Recognition, pages 109--114, 1992.

.... of matches between model and image features (e.g. Clark et al. 13] Fischler and Bolles [17] Ayache and Faugeras [5] Horaud [25] Huttenlocher and Ullman [27] Other approaches use indexing to match more than the minimal number before looking for confirming features (e.g. Rothwell et al. [38], Thompson and Mundy [43] Lamdan et al. 32] Jacobs [29] Most recognition systems take an ad hoc approach to the problem of accounting for the effects of sensing error on the projected positions of unmatched model features. Some systems match projected model features to image features if they ....

....system might attempt to add matches, and use these additional matches to narrow the area in which it must search for still more consistent matches. Additionally, the algorithm from Section 6 may be useful in methods that match image to model features by indexing, and then verify these matches [32, 14, 29, 43, 38, 45]. In these approaches, some model features are matched to image features to determine a model pose, and then this pose is used to find matches for additional model features. Our results show exactly where to search for these matches when we have matched three image and model points. As mentioned ....

Rothwell C., A. Zisserman, J. Mundy, and D. Forsyth, "Efficient Model Library Access by Projectively Invariant

....et al. FMZB90] create invariant functions from grouped planar curves, such as coplanar pairs of conics or sets of at least 4 coplanar lines. Lambdan and Wolfson [LW88] also restrict to planar faces. They generate affine bases in which the coordinates of points on the face are invariant. [RZMF92] generalize this work to deal with the more general perspective transformation. Such invariants are very useful when available, but many objects will not contain one of these. A second approach ignores invariants, and attempts to store an index value for each possible appearance of a feature set. ....

C.A. Rothwell, A. Zisserman, J.L. Mundy, and D.A. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proceedings CVPR '92, pages 109--114, 1992.

....of indexing is to recover from the index the most similar model shapes to a given image shape. In terms of feature vectors, or points in a feature space, this corresponds to finding a set of nearest neighbours (NN) to a query point. Virtually all previous indexing approaches in model based vision [4, 5, 9, 10, 16, 18, 19] have used hash tables for this task. This is somewhat surprising since it is well known in other communities (e.g. pattern recognition, algorithms) that tree structures do the job much more efficiently. In large part this oversight can be explained by the fact that indexing techniques are ....

....which have used hash tables for indexing. Forsythe, et al. 5] outlined several types of projective invariant features for indexing planar objects viewed in arbitrary 3D orientations. However, their experiments were carried out using a 2D index space generated by pairs of conics. Rothwell, et al.[16], used 4D indices defined by area moments of planar curves, that were first transformed into canonical reference frames. Clemens and Jacobs [4] generated 4D and 6D index spaces from hand grouped point sets. For each of the methods above, the dimensionality of the spaces and the number of models ....

C. Rothwell, A. Zisserman, J. Mundy,andD. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proceedings CVPR '92, pages 109--114, 1992.

....classes of features, each large enough to have distinctive properties (invariants) preserved under the imaging transformation. These invariants can then be used as an index for a model library (examples of various combinations of geometry, imaging transformations, and indexing strategies include [14, 26, 48, 52, 54, 60, 30, 24]) Each case described so far models object geometry exactly. Systems that recognize an object by matching a view to a collection of images of an object proceed in one of two ways. In the first approach, correspondence between image features and features on the model object is either given a ....

Rothwell, C.A., A. Zisserman, J.L. Mundy and D.A. Forsyth, "Efficient Model Library Access by Projectively Invariant Indexing Functions," Computer Vision and Pattern Recognition 92, 109-114, 1992.

....parameters) perspective projection to the image plane, and an affine transformation of the final image which covers the effects of camera intrinsic parameters. Consequently, projective invariants, which are unaffected with respect to all of these parameters, have a high currency for this domain [40, 50, 55, 57, 58, 60, 70, 71]. Here we summarise the main features of a planar object recognition system that has been developed during the past four years. The projective representation of shape used in the system has the key advantages of simple model acquisition (direct from images) no need for camera calibration or ....

....(e.g. one for the five line invariant, another for the conic pair) Each sub library then has a list of each of the invariant values tagged with an object name, and is structured as a hash table. 2. 4 Recognition examples Only a small number of examples are included since others appear elsewhere [45, 58, 60]. In each case successful recognition is demonstrated by projecting the model outline onto the image. Segmentation for algebraic features is shown in figure 4. The two objects in the scene which are contained in the library are successfully recognised using algebraic invariants computed from these ....

Rothwell, C.A., Zisserman, A., Mundy, J.L. and Forsyth, D.A. "Efficient Model Library Access by Projectively Invariant Indexing Functions", Proc. CVPR92, p.109-114, 1992.

....of the appropriate transformation to be used to index models to produce a selection of recognition hypotheses. These hypotheses are combined as appropriate, and the result is back projected into the image, and verified by inspecting relationships between the back projected outline and image edges [3, 5, 9, 12, 14]. Indexing using projective invariants has been demonstrated for plane objects and simple polyhedral objects, and has been extended with varying success to certain types of surfaces [1, 6, 8, 13, 15] One main disadvantage of this approach is that objects are identified only up to either an affine ....

....this scene with an uncalibrated camera can be obtained by applying an appropriate plane projective transformation to the scene. The goal of a recognition algorithm is from an image of the scene, label each object correctly up to Euclidean equivalence. Indexing using projective invariants (as in [9]) associates with each group of image features a collection of object models (labels) which are projectively equivalent, but Euclidean inequivalent. If only one known object is present, the task is possible only if there is just one possible label for that object. If two or more labels apply, the ....

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Rothwell, C.A., Zisserman, A., Mundy, J.L. and Forsyth, D.A. "Efficient Model Library Access by Projectively Invariant

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Rothwell, C.A., Zisserman, A., Mundy, J.L. & Forsyth, D.A., 1992c. Efficient Model Library Access by Projectively Invariant Indexing. Proc. of CVPR, 109-114.

....texture map acquisition and metric measurements. 1 Introduction It is well known that under perspective imaging a plane is mapped to the image by a plane projective transformation (a homography) 13] This transformation is used in many areas of computer vision including planar object recognition [12], mosaicing [15] and photogrammetry [14] The projective transformation is determined uniquely if the Euclidean world coordinates of four or more image points are known. Once the transformation is determined, Euclidean measurements, such as lengths and angles, can be made on the world plane ....

C. Rothwell, A. Zisserman, J. Mundy, and D. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proc. CVPR, pages 109--114, 1992.

....corresponding points do in fact lie on the epipoles. 4 Discussion 4.1 Applications One application of the invariants described within this paper is for 3D object recognition. The invariants can be used as model indexes to generate recognition hypotheses. We can compare such a system to that of [14]. The hypotheses are verified by projecting the 3D object model into the image, and determining whether there is image support (edges) for the projected outline. To do this a 3D projective model is needed for every object in the library. There are a number of ways that such a model can be ....

Rothwell, C.A., Zisserman, A., Mundy, J.L. and Forsyth, D.A. "Efficient Model Library Access by Projectively Invariant

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Rothwell, C.A., Zisserman, A., Mundy, J.L., and Forsyth, D.A. (1992) "Efficient Model Library Access by Projectively Invariant Indexing Functions," Computer Vision and Pattern Recognition 92, 109-114.

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C. A. Rothwell, A. Zisserman, J. L. Mundy, and D. A. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proceedings 1992.

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C.A. Rothwell, A. Zisserman, J.L. Mundy, and D.A. Forsyth. Efficient model library access by projectively invariant indexing functions. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 109--114, 1992. Referred to in page(s) 19, 20, 20.

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Rothwell, C.A., Zisserman, A.P., Mundy, J.L., Forsyth, D.A., (1992) Efficient Model Library Access by Projectively Invariant Indexing Functions, In: Proc. CVPR-92, pp. 109-114.

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Rothwell, C., Zisserman, A., Mundy, J. L, and Forsyth, D. A, 1992, "Efficient Model Library Access by Projectively Invariant Indexing Functions," IEEE Conf. on Computer Vision and Pattern Recognition: 109--114.

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