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49
Extracting Projective Structure from Single Perspective Views of 3D Point Sets
 Views of 3D Point Sets Proc. of 4:th ICCV
, 1993
"... A number of recent papers have argued that invariants do not exist for three dimensional point sets in general position [3, 4, 13]. This has often been misinterpreted to mean that invariants cannot be computed for any three dimensional structure. This paper proves by example that although the genera ..."
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Cited by 57 (11 self)
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A number of recent papers have argued that invariants do not exist for three dimensional point sets in general position [3, 4, 13]. This has often been misinterpreted to mean that invariants cannot be computed for any three dimensional structure. This paper proves by example that although the general statement is true, invariants do exist for structured three dimensional point sets. Projective invariants are derived for two classes of object: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: firstly they can be used for recognition; secondly they can be used to compute projective structure. Examples of invariants computed from real images are given. 1 Introduction Exploiting structure modulo a projectivity has recently been shown to simplify a number of vision tasks such as model based recognition [1, 7, 10, 11, 1...
Driving Vision by Topology
 IN PROC. INTERNATIONAL SYMPOSIUM ON COMPUTER VISION
, 1994
"... Recently, vision research has centred on both the extraction and organization of geometric features, and on geometric relations. It is largely assumed that topological structure, that is linked edgel chains and junctions, cannot be extracted reliably from image intensity data. In this paper we demon ..."
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Cited by 34 (2 self)
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Recently, vision research has centred on both the extraction and organization of geometric features, and on geometric relations. It is largely assumed that topological structure, that is linked edgel chains and junctions, cannot be extracted reliably from image intensity data. In this paper we demonstrate that this view is overly pessimistic and that visual tasks, such as perceptual grouping, can be carried out much more efficiently and reliably if wellformed topological structures are available. The widespread assumption that edge detectors produce incomplete and erroneous topological relations, such as the image projection of polyhedral faceedgevertex structures, is shown to be false by analyzing the causes for failure in traditional edge detectors. These deficiencies can largely be overcome, and we show that a good compromise between topological completeness and geometric accuracy can be achieved. Furthermore, edge detection should not be carried out in isolation. The resulti...
Geometry and Algebra of Multiple Projective Transformations
, 1995
"... In this thesis several dioeerent cases of reconstruction of 3D objects from a number of 2D images, obtained by projective transformations, are considered. Firstly, the case where the images are taken by uncalibrated cameras, making it possible to reconstruct the object up to projective transformatio ..."
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Cited by 32 (8 self)
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In this thesis several dioeerent cases of reconstruction of 3D objects from a number of 2D images, obtained by projective transformations, are considered. Firstly, the case where the images are taken by uncalibrated cameras, making it possible to reconstruct the object up to projective transformations, is described. The minimal cases of two images of seven points and three images of six points are solved, giving threefold solutions in both cases. Then linear methods for the cases where more points or more images are available are given, using multilinear constraints, based on a canonical representation of the multiple view geometry. The case of a continuous stream of images is also treated, giving multilinear constraints on the image coordinates and their derivatives. Secondly, the algebraic properties of the multilinear functions and the ideals generated by them are investigated. The main result is that the ideal generated by the bilinearities for three views have a primary decomposit...
3D Object Recognition using Invariance
, 1994
"... The systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years. Invariance overcomes one of the fundamental difficulties in recognising objects from images: that the appearance of an object depends on viewpo ..."
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Cited by 31 (5 self)
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The systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years. Invariance overcomes one of the fundamental difficulties in recognising objects from images: that the appearance of an object depends on viewpoint. This problem is entirely avoided if the geometric description is unaffected by the imaging transformation. Such invariant descriptions can be measured from images without any prior knowledge of the position, orientation and calibration of the camera. These invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification. Object models can be acquired directly from images, allowing efficient construction of model libraries without manual intervention. A significant part of the paper is a summary of recent results on the construction of ...
Recovering reflectance and illumination in a world of painted polyhedra
 Proceedings of the 1993 International Conference on Computer Vision
, 1993
"... To be immune to variations in illumination, a vision system needs to be able to decompose images into their illumination and surface reflectance components. Although this problem is greatly underconstrained, the human visual system is able to solve it in diverse situations. Most computational studie ..."
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Cited by 23 (1 self)
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To be immune to variations in illumination, a vision system needs to be able to decompose images into their illumination and surface reflectance components. Although this problem is greatly underconstrained, the human visual system is able to solve it in diverse situations. Most computational studies thus far have been concerned with strategies for solving the problem in the restricted domain of 2D Mondrians. This domain has the simplifying characteristic of permitting discontinuities only in the reflectance distribution while the illumination distribution is constrained to vary smoothly. Such approaches prove inadequate in a 3D world of painted polyhedra which allows for the existence of discontinuities in both the reflectance and illumination distributions. We propose a twostage computational strategy for interpreting images acquired in such a domain. 1 2
Identification of Faces in a 2D Line Drawing Projection of a Wireframe Object
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... An important key to reconstructing a threedimensional object depicted by a twodimensional line drawing projection is face identification. Identification of edge circuits in a 2D projection corresponding to actual faces of a 3D object becomes complex when the projected object is in wireframe rep ..."
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Cited by 20 (5 self)
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An important key to reconstructing a threedimensional object depicted by a twodimensional line drawing projection is face identification. Identification of edge circuits in a 2D projection corresponding to actual faces of a 3D object becomes complex when the projected object is in wireframe representation. This representation is commonly encountered in drawings made during the conceptual design stage of mechanical parts. When nonmanifold objects are considered, the situation becomes even more complex. This paper discusses the principles underlying face identification and presents an algorithm capable of performing this identification. Faceedgevertex relationships applicable to nonmanifold objects are also proposed. Examples from a working implementation are given. Index Terms  Line drawing interpretation, face identification, line labeling, 3D object reconstruction, nonmanifold geometry, image understanding. 1.
Creating solid models from single 2D sketches
, 1995
"... We describe a method of constructing a Brep solid model from a single hiddenline removed sketch view of a 3D object. The main steps of our approach are as follows. The sketch is first tidied in 2D (to remove digitisation errors). Line labelling is used to deduce the initial topology of the object ..."
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Cited by 19 (4 self)
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We describe a method of constructing a Brep solid model from a single hiddenline removed sketch view of a 3D object. The main steps of our approach are as follows. The sketch is first tidied in 2D (to remove digitisation errors). Line labelling is used to deduce the initial topology of the object and to locate hidden faces. Constraints are then produced from the line labelling and features in the drawing (such as probable symmetry) involving the unknown face coefficients and point depths. A least squares solution is found to the linear system and any grossly incompatible equations are rejected. Vertices are recalculated as the intersections of the faces to ensure we have a reconstructible solid. Any incomplete faces are then completed as far as possible from neighbouring faces, producing a solid model from the initial sketch, if successful. The current software works for polyhedral objects with trihedral vertices.
Object recognition in the geometric era: A retrospective
 Toward CategoryLevel Object Recognition, volume 4170 of Lecture Notes in Computer Science
, 2006
"... Abstract. Recent advances in object recognition have emphasized the integration of intensityderived features such as affine patches with associated geometric constraints leading to impressive performance in complex scenes. Over the four previous decades, the central paradigm of recognition was base ..."
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Cited by 19 (0 self)
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Abstract. Recent advances in object recognition have emphasized the integration of intensityderived features such as affine patches with associated geometric constraints leading to impressive performance in complex scenes. Over the four previous decades, the central paradigm of recognition was based on formal geometric object descriptions with a focus on the properties of such descriptions under perspective image formation. This paper will review the key advances of the geometric era and investigate the underlying causes of the movement away from formal geometry and prior models towards the use of statistical learning methods based on appearance features. 1
Combinatorial Geometry for Shape Representation and Indexing
 In Object Representation in Computer Vision
, 1996
"... . Combinatorial geometry is the study of order and incidence properties of groups of geometric features. Ordering properties for point sets in 2D and 3D can be seen as a generalization of ordering properties in 1D and incidences are configurations of features that are nongeneric such as collinea ..."
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Cited by 16 (2 self)
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. Combinatorial geometry is the study of order and incidence properties of groups of geometric features. Ordering properties for point sets in 2D and 3D can be seen as a generalization of ordering properties in 1D and incidences are configurations of features that are nongeneric such as collinearity of points. By defining qualitative shape properties using combinatorial geometry we get a common framework for metric and qualitative representations. Order and incidence form a natural hierarchy together with metric representations in terms of increasing abstraction Metric ==? Order ==? Incidence The problem of recognition can be structured in a similar hierarchy ranging from the recognition of specific objects from specific viewpoints ,using calibrated cameras to that of calibration free, view independent recognition of generic objects. Order and incidence relations have invariance properties that make them especially interesting for general recognition problems. We present an algorit...
A Freehand Sketching Interface for Progressive Construction and Analysis of 3D Objects
, 2004
"... The possibility of using freehand sketching as the language for interactive design is a longstanding goal. The ability to sketch a 3D object, predict its performance, and redesign it interactively using physicsbased feedback would bring the power of stateoftheart analysis tools into the critical ..."
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Cited by 14 (2 self)
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The possibility of using freehand sketching as the language for interactive design is a longstanding goal. The ability to sketch a 3D object, predict its performance, and redesign it interactively using physicsbased feedback would bring the power of stateoftheart analysis tools into the critical, early design phase. The enormous potential of sketchbased interfaces is widely recognized, and has been broadly pursued. The practical use of such attempts has remained limited because these interfaces have been primarily 2D, loosing much of the benefit of mainstream 3D analysis potential. In order to become truly 3D, the spatial geometry must be automatically – and quickly – reconstructed from a single 2D sketch in near realtime. Once reconstructed, it can be converted into a model for simulation, and the simulation results interpreted back into the sketch. This paper presents a system that performs that reconstructs a 3D object from a freehand sketch, and uses the reconstructed object as the basis for a physical simulation. The system represents a first step towards fully interactive physicsbased 3D design.