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14
Region Tracking Through Image Sequences
 IN PROC. 5TH INT. CONF. ON COMPUTER VISION
, 1995
"... This paper describes a new approach to the tracking of complex shapes through image sequences, that combines deformable region models and deformable contours. A new deformable region model is presented: its optimisation is based on texture correlation and is constrained by the use of a motion model, ..."
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Cited by 49 (5 self)
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This paper describes a new approach to the tracking of complex shapes through image sequences, that combines deformable region models and deformable contours. A new deformable region model is presented: its optimisation is based on texture correlation and is constrained by the use of a motion model, such as rigid, affine or homographic. The use of texture information (versus edge information) noticeably improves the tracking performances of deformable models in the presence of texture. Then the region contour is refined using an edgebased deformable model, in order to better deal with specularities and non planar objects. The method is illustrated and validated by experimental results on real images.
The Geometry and Matching of Lines and Curves Over Multiple Views
"... This paper describes the geometry of imaged curves in two and three views. Multiview relationships are developed for lines, conics and nonalgebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography in ..."
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Cited by 43 (1 self)
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This paper describes the geometry of imaged curves in two and three views. Multiview relationships are developed for lines, conics and nonalgebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography induced by this plane for transfer from one image to another. It is shown that given the fundamental matrix between two views, and images of the curve in each view, then the plane of a conic may be determined up to a two fold ambiguity, but local curvature of a curve uniquely determines the plane. It is then shown that given the trifocal tensor between three views, this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third. Simple expressions are developed for the plane and homography in each case.
Solving Markov random fields using semi definite programming
 In: AISTATS. (2003
"... This paper explores a new generic method for matching, when there are conditional dependencies between the matches. It allows different sorts of features to be matched in the same global optimization framework. The method is based on a binary Markov random field model which is defined on the product ..."
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Cited by 22 (4 self)
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This paper explores a new generic method for matching, when there are conditional dependencies between the matches. It allows different sorts of features to be matched in the same global optimization framework. The method is based on a binary Markov random field model which is defined on the product space of matches, and is shown to be equivalent to 01 quadratic programming, and the MAXCUT graph problem. In general these problem are complete. However our approach takes inspiration from the celebrated result of Goemans and Williamson (1995) that finds a polynomial time 0.879 approximation to several complete, using semidefinite programming. The method is demonstrated for the problem of curve matching. 1
The Intrinsic Structure of Optic Flow Incorporating Measurement Duality
 International Journal of Computer Vision
, 1997
"... The purpose of this report 1 is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scalespace paradigm. It is argued that the design of optic flow based applicati ..."
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Cited by 20 (13 self)
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The purpose of this report 1 is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scalespace paradigm. It is argued that the design of optic flow based applications may benefit from a manifest separation between factual image structure on the one hand, and goalspecific details and hypotheses about image flow formation on the other. The approach is based on a physical symmetry principle known as gauge invariance. Dataindependent models can be incorporated by means of admissible gauge conditions, each of which may single out a distinct solution, but all of which must be compatible with the evidence supported by the image data. The theory is illustrated by examples and verified by simulations, and performance is compared to several techniques reported in the literature. 1 Introduction The conventional "spacetime" representation of a movie as...
ScaleSpaces and Affine Curvature
, 1995
"... We present a new way to compute the affine curvature of plane curves. We explain how an affine scalespace can be used to gain one order of derivation in the numerical approximation of affine curvature. We outline our implementation and compare our results with previous ones. This paper ends by showi ..."
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Cited by 7 (1 self)
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We present a new way to compute the affine curvature of plane curves. We explain how an affine scalespace can be used to gain one order of derivation in the numerical approximation of affine curvature. We outline our implementation and compare our results with previous ones. This paper ends by showing a simple application in pattern recognition using affine curvature. Keywords: Geometry, Invariants, Pattern Recognition. Introduction A great amount of work in object recognition deals with semidifferential affine or projective invariants [7]. Local invariants seem much more difficult to obtain because of the large orders of derivatives required; for example, the affine curvature is a fourth order quantity, the projective curvature a seventh order one, which makes their actual computation quite a challenge, to say the least. Among the numerous applications of scalespaces, this paper presents a surprising one: one can use the affine scalespace to compute the affine curvature of a pla...
Sufficient image structure for 3D motion and shape estimation
 Proc. 3rd European Conf. on Computer Vision
, 1994
"... We derive sufficient conditions on image structure that permits determination of 3D motion parameters and depth from motion relative a rigid surface in front of the camera. We assume that only the first order spatiotemporal derivative or of the image is given and that the image intensity is cont ..."
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Cited by 7 (0 self)
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We derive sufficient conditions on image structure that permits determination of 3D motion parameters and depth from motion relative a rigid surface in front of the camera. We assume that only the first order spatiotemporal derivative or of the image is given and that the image intensity is continuously differentiable everywhere or that image contours are continuously differentiable. This means that only the component of the image motion field orthogonal to isointensity contours, the so called normal flow, can be measured. By defining a tangent line at a point as the line orthogonal to the gradient or normal the sufficiency condition on image structure can be stated as: If each point (x; y) in the infinitely extended image plane is the intersection of at least 6 tangent lines, it is possible to compute unique 3D motion and positive depth from first order spatio temporal derivatives, except for specific combinations of surface texture and depth. The exceptions are specific texture patterns for any surface, for which the problem is inherently ambiguous, e.g. the so called "barberpole". These patterns have the property that there exist a relative motion to the surface such that the image flow field lines are aligned with the contours of the image.
The Local Projective Shape of Smooth Surfaces and their Outlines
, 2003
"... This paper examines projectively invariant local properties of smooth curves and surfaces. Oriented projective differential geometry is proposed as a theoretical framework for establishing such invariants and describing the local shape of surfaces and their outlines. This framework is applied to two ..."
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Cited by 6 (1 self)
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This paper examines projectively invariant local properties of smooth curves and surfaces. Oriented projective differential geometry is proposed as a theoretical framework for establishing such invariants and describing the local shape of surfaces and their outlines. This framework is applied to two problems: a projective proof of Koenderink's famous characterization of convexities, concavities, and inflections of apparent contours; and the determination of the relative orientation of rim tangents at frontier points.
Structure From Translational Observer Motion, Proceedings of the International Workshop on Algebraic Frames for the PerceptionAction Cycle  Trends in the conceptualization, design and implementation of artificial autonomous systems
 Published in Springer, Lecture Notes In Computer Science
, 1999
"... This work presents a unified, globally based geometric framework, using congruence geometry, for the description and computation of structure from motion. It is based on projectively invariant tangent information in a sequence of monocular images, i.e. occluding contours under general perspective. T ..."
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Cited by 4 (3 self)
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This work presents a unified, globally based geometric framework, using congruence geometry, for the description and computation of structure from motion. It is based on projectively invariant tangent information in a sequence of monocular images, i.e. occluding contours under general perspective. The strength of the framework is demonstrated by applying it to the case of translational observer motion, a type of motion that is of great practical importance since it can be easily implemented with the help of various gyroscopic devices. Starting with a brief overview of congruence geometry, we show how it can be applied to vision leading to a classification of the global linegeometric structure of different targetobserver configurations. Then we illustrate how this approach facilitates explicit bookkeeping of what information that is available in any specific situation, making it possible to parametrise what is “knowable ” and what is “unknowable ” from any given observational sequence of images. It also allows a consistent treatment of degenerate target shape and observer motion by supporting globally based discrimination of pointlike, curvelike and surfacelike targets, as well as detection of rectilinear observer motion. We then introduce a simple technique for the computation of the direction of motion (“Focus
Toward Recovering Shape and Motion of 3D Curves from MultiView Image Sequences
 in Proc. Computer Vision and Pattern Recognition Conf
, 1999
"... We introduce a framework for recovering the 3D shape and motion of unknown, arbitrarilymoving curves from two or more image sequences acquired simultaneously from distinct points in space. We use this framework to (1) identify ambiguities in the multiview recovery of (rigid or nonrigid) 3D motion ..."
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Cited by 3 (1 self)
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We introduce a framework for recovering the 3D shape and motion of unknown, arbitrarilymoving curves from two or more image sequences acquired simultaneously from distinct points in space. We use this framework to (1) identify ambiguities in the multiview recovery of (rigid or nonrigid) 3D motion for arbitrary curves, and (2) identify a novel spatiotemporal constraint that couples the problems of 3D shape and 3D motion recovery in the multiview case. We show that this constraint leads to a simple hypothesizeand test algorithm for estimating 3D curve shape and motion simultaneously. Experiments performed with synthetic data suggest that, in addition to recovering 3D curve motion, our approach yields shape estimates of higher accuracy than those obtained when stereo analysis alone is applied to a multiview sequence. 1 Introduction A fundamental problem in computer vision is to recover the 3D shape and motion of unknown dynamic scenes from sequences of images. While this problem h...
Shape and Motion of 3D Curves from MultiView Image Sequences
 In Image Understanding Workshop
, 1998
"... We introduce a framework for recovering the 3D motion and shape of unknown, moving curves from two or more image sequences acquired simultaneously from distinct points in space. We use this framework to (1) identify ambiguities in the multiview recovery of 3D motion for arbitrary curves, and (2) ide ..."
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Cited by 1 (0 self)
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We introduce a framework for recovering the 3D motion and shape of unknown, moving curves from two or more image sequences acquired simultaneously from distinct points in space. We use this framework to (1) identify ambiguities in the multiview recovery of 3D motion for arbitrary curves, and (2) identify a novel spatiotemporal constraint that couples the problems of 3D shape and 3D motion recovery in the multiview case. We show that this constraint leads to a simple algorithm for estimating 3D curve motion and 3D shape simultaneously. Experiments performed with synthetic data suggest that the algorithm allows accurate recovery of 3D curve motion, and yields shape estimates of higher accuracy than those obtained when stereo analysis alone is applied to simultaneous snapshots of a multiview sequence. 1 Introduction A fundamental problem in computer vision is recovering the threedimensional shape and motion of an unknown dynamic scene from sequences of images. While this problem has ...