Gunnar Sparr

Computer Vision — ECCV 2002

We present a novel algorithm for recovering a smooth manifold of unknown dimension and topology from a set of points known to belong to it. Numerous applications in computer vision can be naturally interpreted as instanciations of this fundamental problem. Recently, a non-iterative discrete approach, tensor voting, has been introduced to solve this problem and has been applied successfully to various applications. As an alternative, we propose a variational formulation of this problem in the continuous setting and derive an iterative algorithm which approximates its solutions. This method and tensor voting are somewhat the differential and integral form of one another. Although iterative methods are slower in general, the strength of the suggested method is that it can easily be applied when the ambient space is not Euclidean, which is important in many applications. The algorithm consists in solving a partial differential equation that performs a special anisotropic diffusion on an implicit representation of the known set of points. This results in connecting isolated neighbouring points. This approach is very simple, mathematically sound, robust and powerful since it handles in a homogeneous way manifolds of arbitrary dimension and topology, embedded in Euclidean or non-Euclidean spaces, with or without border. We shall present this approach and demonstrate both its benefits and shortcomings in two different contexts: (i) data visual analysis, (ii) skin detection in color images.

An Iterative Factorization Method for Projective Structure and Motion from Image Sequences

Abstract In this article a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace and factorization methods and is derived from both ordinary coordinate representations and camera matrices and from a so-called depth and shape analysis. In addition, no initial phase is needed to start the algorithm. It starts directly with the first two images and incorporates new images as soon as new corresponding points are obtained. The performance of the algorithm is shown on both simulated and real data. Moreover, the two different approaches, one using camera matrices and the other using the concepts of affine shape and depth, are unified into a general theory of structure and motion from image sequences.

Simultaneous reconstruction of scene structure and camera locations from uncalibrated image sequences

The paper deals with the structure-motion problem for images of point configurations taken by uncalibrated cameras. Using a parametrisation by affine shape and kinetic depth, a complete and explicit characterisation of the imaging geometry is given, including the shape of the object configuration and the positions of the cameras relative to the scene. No epipolar geometry is used. It is shown that not only the projective but also the affine structure of the scene can be recovered when knowing the relative placement of five of the camera centres (four if they are coplanar). Variational algorithms for reconstruction and motion are presented, thus avoiding numerically unstable solving of algebraic equations. Any number of points in any number of images can be treated simultaneously and uniformly, without preselection of reference points. The performances of the algorithms are illustrated on simulations and experiments.

Depth computations from polyhedral images

A method is developed for the computation of depth maps, modulo scale, from one single image of a polyhedral scene. Only affine shape properties of the scene and image are used, hence no metrical information. Results from simple experiments show good performance, both what concerns exactness and robustness. It is also shown how the underlying theory may be used to single out and characterise certain singular situations that may occur in machine interpretation of line drawings.

A Common Framework for Kinetic Depth, Reconstruction and Motion for Deformable Objects

In this paper, problems related to depth, reconstruction and motion from a pair of projective images are studied under weak assumptions. Only relative information within each image is used, nothing about their interrelations or about camera calibration. Objects in the scene may be deformed between the imaging instants, provided that the deformations can be described locally by affine transformations. It is shown how the problems can be treated by a common method, based on a novel interpretation of a theorem in projective geometry of M. Chasles, and the notion of “affine shape”. No epipolar geometry is used. The method also enables the computation of the “depth flow”, i.e. a relative velocity in the direction of the ray of sight.

Recursive structure and motion from image sequences using shape and depth spaces

A novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace methods and is derived from both ordinary coordinate representations and camera matrices and from a so called depth and shape analysis. Furthermore, no initial phase is needed to start up the algorithm. It starts directly with the first two images and incorporates new images as soon as new corresponding points are obtained. The performance of the algorithm is shown on simulated data. Moreover, the two different approaches, one using camera matrices and the other using the concepts of affine shape and depth, are unified into a general theory of structure and motion from image sequences.

ANALYTICAL AND NUMERICAL DESCRIPTION OF THE SETTLING PROCESS IN THE ACTIVATED SLUDGE OPERATION

The secondary clarifier or settler is crucial for the whole activated sludge operation. Consequently, it is important to obtain a reliable analytical model as well as a useful numerical method, which can be used in the automatic control of the settling process. Discontinuities (shocks) appear physically, and an analytical description as well as a stable numerical algorithm must be able to handle these discontinuities. A model based on the Kynch theory of sedimentation is used, where the settling flux is a function only of the local concentration and is assumed to have one inflexion point. For such non-convex flux functions, the settling process is qualitatively the same, independent of further assumptions on the shapes of the settling functions. Using the theory of nonlinear conservation laws, the main results obtained are: how to calculate transient and asymptotic behavior; how to control the concentration profile of the settler, in particular the depth of the sludge blanket, for a given load; and, a numerical algorithm which automatically preserves shocks and gives the physically correct solution according to the analytical treatment. The algorithm can be applied on any flux function (with more than one inflexion point). (Less)

A fast and highly automated approach to myocardial motion analysis using phase contrast magnetic resonance imaging

To develop a fast and highly automated method for calculating two‐dimensional myocardial motion and deformation using velocity encoded magnetic resonance imaging.

Automated interpretation of ventilation-perfusion lung scintigrams for the diagnosis of pulmonary embolism using artificial neural networks.

Abstract.The purpose of this study was to develop a completely automated method for the interpretation of ventilation-perfusion (V-P) lung scintigrams used in the diagnosis of pulmonary embolism. An artificial neural network was trained for the diagnosis of pulmonary embolism using 18 automatically obtained features from each set of V-P scintigrams. The techniques used to process the images included their alignment to templates, the construction of quotient images based on the ventilation and perfusion images, and the calculation of measures describing V-P mismatches in the quotient images. The templates represented lungs of normal size and shape without any pathological changes. Images that could not be properly aligned to the templates were detected and excluded automatically. After exclusion of those V-P scintigrams not properly aligned to the templates, 478 V-P scintigrams remained in a training group of consecutive patients with suspected pulmonary embolism, and a further 87 V-P scintigrams formed a separate test group comprising patients who had undergone pulmonary angiography. The performance of the neural network, measured as the area under the receiver operating characteristic curve, was 0.87 (95% confidence limits 0.82–0.92) in the training group and 0.79 (0.69–0.88) in the test group. It is concluded that a completely automated method can be used for the interpretation of V-P scintigrams. The performance of this method is similar to others previously presented, whereby features were extracted manually.

Spline-Based Cardiac Motion Tracking Using Velocity-Encoded Magnetic Resonance Imaging

This paper deals with the problem of tracking cardiac motion and deformation using velocity-encoded magnetic resonance imaging. We expand upon an earlier described method and fit a spatiotemporal motion model to measured velocity data. We investigate several different spatial elements both qualitatively and quantitatively using phantom measurements and data from human subjects. In addition, we also use optical flow estimation by the Horn-Schunk method as complementary data in regions where the velocity measurements are noisy. Our results show that it is possible to obtain good motion tracking accuracy in phantoms with relatively few spatial elements, if the type of element is properly chosen. The use of optical flow can correct some measurement artifacts but may give an underestimation of the magnitude of the deformation. In human subjects the different spatial elements perform quantitatively in a similar way but qualitative differences exists, as shown by a semiquantitative visual scoring of the different methods.