Shape Descriptors for Image Analysis
Singular Perturbations For Heart Image Segmentation Tracking
In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.
Spline Subdivision Schemes for Compact Sets. A Survey
Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, IsraelAttempts at extending spline subdivision schemes to operate on compact sets are reviewed. The aim is to develop a procedure for approximating a set-valued function with compact images from a finite set of its samples. This is motivated by the problem of reconstructing a 3D object from...
Subjective surfaces and Riemannian mean curvature flow of graphs.
The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition
Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.
The effect of Gaussian blurring on the extraction of peaks and pits from digital elevation models.
The structure-from-motion reconstruction pipeline – a survey with focus on short image sequences
The problem addressed in this paper is the reconstruction of an object in the form of a realistically textured 3D model from images taken with an uncalibrated camera. We especially focus on reconstructions from short image sequences. By means of a description of an easy to use system, which is able to accomplish this in a fast and reliable way, we give a survey of all steps of the reconstruction pipeline. For the purpose of developing a coherent reconstruction system it is necessary to integrate...
The tree of shapes of an image
In [30], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation...
The tree of shapes of an image
In [CITE], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation problem...
Theoretical foundation of the weighted Laplace inpainting problem
Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers...
Topological optimization with the -Laplacian operator and an application in image processing.
Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...
Universally typical sets for ergodic sources of multidimensional data
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an with...
Variational approximation for detecting point-like target problems
The aim of this paper is to provide a rigorous variational formulation for the detection of points in 2-d biological images. To this purpose we introduce a new functional whose minimizers give the points we want to detect. Then we define an approximating sequence of functionals for which we prove the Γ-convergence to the initial one.
Variational approximation for detecting point-like target problems*
The aim of this paper is to provide a rigorous variational formulation for the detection of points in 2-d biological images. To this purpose we introduce a new functional whose minimizers give the points we want to detect. Then we define an approximating sequence of functionals for which we prove the Γ-convergence to the initial one.
Visual simultaneous localisation and map-building supported by structured landmarks
Visual simultaneous localisation and map-building systems which take advantage of some landmarks other than point-wise environment features are not frequently reported. In the following paper the method of using the operational map of robot surrounding, which is complemented with visible structured passive landmarks, is described. These landmarks are used to improve self-localisation accuracy of the robot camera and to reduce the size of the Kalman-filter state-vector with respect to the vector...
Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising.