Reconstruction-based recognition of scenes with translationally repeated quadrics
01 Jun 2001-IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE Computer Society)-Vol. 23, Iss: 6, pp 617-632
TL;DR: Experimental results on synthetic and real images, establish the discriminatory power and stability of the proposed invariant-based recognition strategy for discriminating images of monuments which are characterized by translationally repeated domes modeled as quadrics.
Abstract: This paper addresses the problem of invariant-based recognition of quadric configurations from a single image. These configurations consist of a pair of rigidly connected translationally repeated quadric surfaces. This problem is approached via a reconstruction framework. A new mathematical framework, using relative affine structure, on the lines of Luong and Vieville (1996), has been proposed. Using this mathematical framework, translationally repeated objects have been projectively reconstructed, from a single image, with four image point correspondences of the distinguished points on the object and its translate. This has been used to obtain a reconstruction of a pair of translationally repeated quadrics. We have proposed joint projective invariants of a pair of proper quadrics. For the purpose of recognition of quadric configurations, we compute these invariants for the pair of reconstructed quadrics. Experimental results on synthetic and real images, establish the discriminatory power and stability of the proposed invariant-based recognition strategy. As a specific example, we have applied this technique for discriminating images of monuments which are characterized by translationally repeated domes modeled as quadrics.
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TL;DR: This paper surveys important approaches to active 3-D object recognition and reviews existing approaches towards another important application of an active sensor namely, that of scene analysis and interpretation.
138 citations
Cites background from "Reconstruction-based recognition of..."
..., canal surfaces [9,10] rotational symmetry [8,11,3], repeated structures (bilateral symmetry, translational repetition) [3,12,13]....
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TL;DR: A prototype implementation of a cooperative agent-based multimedia retrieval architecture that integrates a set of dissimilar collections of multimedia data on Indian cultural heritage and a comparison of the retrieval results with some existing Internet search tools proves the effectiveness of the architecture.
Abstract: We present the planning scheme for a cooperative agent-based multimedia retrieval architecture that integrates a heterogeneous set of repositories into a coherent information system. The agents in the system collaborate in context of a conceptual query to formulate unique retrieval strategies for the different collections. The retrieval plan makes need-based use of independent content analysis tools available on the network. The retrieval strategies for the repositories so formulated satisfy the specified constraints on quality of results and the response time requirements. The retrieval plan is reactively updated based on the retrieval performance at the individual repositories. We present some experimental results to show the effectiveness of the planning scheme for repositories with different characteristics and the scalability of the architecture. We present a prototype implementation of this architecture that integrates a set of dissimilar collections of multimedia data on Indian cultural heritage. A comparison of the retrieval results with some existing Internet search tools proves the effectiveness of the architecture.
15 citations
Additional excerpts
...Index Terms—Reactive planning, distributed planning, multimedia retrieval, distributed retrieval, agent-based systems....
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01 Apr 2005
TL;DR: This paper presents a new online scheme for the recognition and pose estimation of a large isolated 3D object, which may not entirely fit in a camera's field of view, and uses a probabilistic reasoning framework for recognition and next-view planning.
Abstract: Most model-based three-dimensional (3D) object recognition systems use information from a single view of an object. However, a single view may not contain sufficient features to recognize it unambiguously. Further, two objects may have all views in common with respect to a given feature set, and may be distinguished only through a sequence of views. A further complication arises when in an image, we do not have a complete view of an object. This paper presents a new online scheme for the recognition and pose estimation of a large isolated 3D object, which may not entirely fit in a camera's field of view. We consider an uncalibrated projective camera, and consider the case when the internal parameters of the camera may be varied either unintentionally, or on purpose. The scheme uses a probabilistic reasoning framework for recognition and next-view planning. We show results of successful recognition and pose estimation even in cases of a high degree of interpretation ambiguity associated with the initial view.
15 citations
Journal Article•
TL;DR: The 3D scene distance constraints are used to recover 3D models from a single view in this paper, and the proposed technique can be applied in a wide variety of scenes that contain points, lines, and planaror freeform sur-faces.
Abstract: SUMMARY We propose a new method to recover scene points from asingle calibrated view using a subset of distances among the points. Thispaperfirstintroducestheproblemanditsrelationship withtheperspective n point problem. Then the number of distances required to uniquely recoverscene points are explored. The result is then developed into a practicalvision algorithm to calculate the initial points’ coordinates using distanceconstraints. Finally SQP (Sequential Quadratic Programming) is used tooptimize the initial estimations. It can minimize a cost function defined asthe sum of squared reprojection errors while keeping the specified distanceconstraints strictly satisfied. Both simulation data and real scene imageshave been used to test the proposed method, and good results have beenobtained. key words: perspective n point problem, single view reconstruction, sensi-tivity analysis, sequential quadratic programming 1. Introduction Traditional image-based 3D reconstruction methods usemultiple views to extract 3D geometry. However, when re-constructing scene structures with only one photograph orretrieving dynamic scene properties shot by one video cam-era, only a single view exists. To recover 3D scene struc-ture from a single view, 3D scene constraints need to beutilized[1]. A variety of 3D scene geometry constraintshavebeenidentifiedandusedincomputervisionalgorithms.Traditional constraints have used vanishing points, planesand geometric invariants constraints[2]–[4]. Some workhas used the constraint of multiple objects of the same typein the scene separated by a simple translation[5]. How-ever,thesegeometryconstraintsarelimitedtocertainmodeltypes,forexample, scenescomposedofplanesorothersim-ple primitives.The 3D scene distance constraints are used to recover3D models from a single view in this paper. Since 3D scenedistance constraints exist in almost every kind of scenes,the proposed technique can be applied in a wide variety ofscenes that contain points, lines, and planaror freeform sur-faces. In multiple view cases, 3D scene distance constrainthas been applied in motion capture applications to upgradeaffine reconstruction to a metric one[6]. In single view re-construction applications, the 3D scene distance constraintshave not been effectively utilized so far.The closest work to ours is the traditional perspective
3 citations
01 Dec 2015
TL;DR: A framework for retrieving metric information of featureless cylindrical pellet imaged through stereo vision by considering the isometry property, relative affine structure which is an invariant that depends on the depth of the point is employed.
Abstract: In the present work, we propose a framework for retrieving metric information of featureless cylindrical pellet imaged through stereo vision. Considering the isometry property, relative affine structure which is an invariant that depends on the depth of the point is employed for obtaining the information. This method skips considering vanishing points for depth estimation, and hence the errors are reduced remarkably as no points are assumed to be at infinity. Real world measurements are taken and the metrics of a selected reference point is assumed to be known. With these minimal information the mapping between the images using the relative affine structure is carried out that enables the 3D reconstruction. This work also blends the concepts of 360 degree rotational symmetry and orthogonal planes with the stereo vision that has minimized the error percentage. The results presented by the theory will have an impact on the design of 3D reconstruction systems for computer vision and its applications.
1 citations
Cites background from "Reconstruction-based recognition of..."
...Computational symmetry and group theory are the fields that contributed for image analysis and retrieving structure from scenes of real world [1][3][6][9]....
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References
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Proceedings Article•
31 Dec 1993TL;DR: Results from constrained optimization some results from algebraic geometry differential geometry are shown.
Abstract: Projective geometry modelling and calibrating cameras edge detection representing geometric primitives and their uncertainty stereo vision determining discrete motion from points and lines tracking tokens over time motion fields of curves interpolating and approximating three-dimensional data recognizing and locating objects and places answers to problems. Appendices: constrained optimization some results from algebraic geometry differential geometry.
2,744 citations
"Reconstruction-based recognition of..." refers background in this paper
...This has lead to the convergence of the single view [13], [14] and multiple view-based approaches [7], [20]....
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TL;DR: In this paper, the authors proposed a method for fitting conic sections to scattered data, which permits an extension to conic splines around extended digitized curves, expediting a smooth reconstruction of their curvature.
568 citations
"Reconstruction-based recognition of..." refers background or methods in this paper
...For all images, the conics were fitted interactively by using Bookstein's algorithm [1] (Fig....
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...The strategy would fail in cases when the outline conics are occluded (occlusion to some extent is permissible by Bookstein's algorithm [1]), or if it is not possible to pick image point correspondences, they are not in general position in the image or the points lie on the outline conic....
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TL;DR: A model-based vision system that recognizes curved plane objects irrespective of their pose is demonstrated and the stability of a range of invariant descriptors to measurement error is treated in detail.
Abstract: Invariant descriptors are shape descriptors that are unaffected by object pose, by perspective projection, or by the intrinsic parameters of the camera. These descriptors can be constructed using the methods of invariant theory, which are briefly surveyed. A range of applications of invariant descriptors in 3D model-based vision is demonstrated. First, a model-based vision system that recognizes curved plane objects irrespective of their pose is demonstrated. Curves are not reduced to polyhedral approximations but are handled as objects in their own right. Models are generated directly from image data. Once objects have been recognized, their pose can be computed. Invariant descriptors for 3D objects with plane faces are described. All these ideas are demonstrated using images of real scenes. The stability of a range of invariant descriptors to measurement error is treated in detail. >
451 citations
"Reconstruction-based recognition of..." refers methods in this paper
...As a specific example, we have applied this technique for discriminating images of monuments which are characterized by translationally repeated domes modeled as quadrics....
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222 citations
Additional excerpts
...Index TermsÐ3D objects, reconstruction, recognition, projective invariants, translationally repeated objects, quadrics. æ...
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01 Jun 1994
TL;DR: It is shown how a special decomposition of general projection matrices, called canonic, enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations.
Abstract: We show how a special decomposition of general projection matrices, called canonic enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations. These representations are minimal and capture completely the properties of each level of description considered: Euclidean (in the context of calibration, and in the context of structure from motion, which we distinguish clearly), affine, and projective, that we also relate to each other. In the last case, a new decomposition of the well-known fundamental matrix is obtained. Dependencies, which appear when three or more views are available, are studied in the context of the canonic decomposition, and new composition formulas are established, as well as the link between local (ie for pairs of views) representations and global (ie for a sequence of images) representations.
188 citations
"Reconstruction-based recognition of..." refers background in this paper
...…6 0 and centre of perspectivity (COP) in homogeneous coordinates given by ÿPÿ1p 1 : Let eP P p and eP 0 P 0 p0 represent two cameras in the equivalent stereo framework with respective center of perspectivities given by COP1 ÿP ÿ1p 1 and COP2 ÿP 0ÿ1p0 1 and having respective image planes R1 and R2....
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...Shashua [21], [22] has handled affine structure as a special case of relative affine structure....
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...Index TermsÐ3D objects, reconstruction, recognition, projective invariants, translationally repeated objects, quadrics. æ...
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