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Curve cuspless reconstruction via sub-riemannian geometry

Ugo Boscain, Remco Duits, Francesco Rossi, Yuri Sachkov (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of minimizing ∫ 0 ℓ ξ 2 + K 2 ( s ) d s ∫ 0 ℓ ξ 2 + K 2 ( s )   d s for a planar curve having fixed initial and final positions and directions. The total lengthℓ is free. Here s is the arclength parameter, K(s) is the curvature of the curve and ξ > 0 is a fixed constant. This problem comes from a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem. We prove that if for a certain choice of boundary conditions there...

Detection of moving objects in image sequences using 3D velocity filters

Sam Schauland, Joerg Velten, Anton Kummert (2008)

International Journal of Applied Mathematics and Computer Science

A movement analysis of objects contained in visual scenes can be performed by means of linear multidimensional filters, which have already been analyzed in the past. While the soundness of the results was convincing, interest in those systems declined due to the limited computational power of contemporary computers. Recent advances in design and implementation of integrated circuits and hardware architectures allow realizing velocity filters if the n-D system is carefully adapted to the analyzed...

Efficient generation of 3D surfel maps using RGB-D sensors

Artur Wilkowski, Tomasz Kornuta, Maciej Stefańczyk, Włodzimierz Kasprzak (2016)

International Journal of Applied Mathematics and Computer Science

The article focuses on the problem of building dense 3D occupancy maps using commercial RGB-D sensors and the SLAM approach. In particular, it addresses the problem of 3D map representations, which must be able both to store millions of points and to offer efficient update mechanisms. The proposed solution consists of two such key elements, visual odometry and surfel-based mapping, but it contains substantial improvements: storing the surfel maps in octree form and utilizing a frustum culling-based...

Efficient RGB-D data processing for feature-based self-localization of mobile robots

Marek Kraft, Michał Nowicki, Rudi Penne, Adam Schmidt, Piotr Skrzypczyński (2016)

International Journal of Applied Mathematics and Computer Science

The problem of position and orientation estimation for an active vision sensor that moves with respect to the full six degrees of freedom is considered. The proposed approach is based on point features extracted from RGB-D data. This work focuses on efficient point feature extraction algorithms and on methods for the management of a set of features in a single RGB-D data frame. While the fast, RGB-D-based visual odometry system described in this paper builds upon our previous results as to the general...

From the Slit-Island Method to the Ising model: Analysis of irregular grayscale objects

Przemysław Mazurek, Dorota Oszutowska-Mazurek (2014)

International Journal of Applied Mathematics and Computer Science

The Slit Island Method (SIM) is a technique for the estimation of the fractal dimension of an object by determining the area-perimeter relations for successive slits. The SIM could be applied for image analysis of irregular grayscale objects and their classification using the fractal dimension. It is known that this technique is not functional in some cases. It is emphasized in this paper that for specific objects a negative or an infinite fractal dimension could be obtained. The transformation...

Fusion based analysis of ophthalmologic image data

Jiří Jan, Radim Kolář, Libor Kubečka, Jan Odstrčilík, Jiří Gazárek (2011)

Kybernetika

The paper presents an overview of image analysis activities of the Brno DAR group in the medical application area of retinal imaging. Particularly, illumination correction and SNR enhancement by registered averaging as preprocessing steps are briefly described; further mono- and multimodal registration methods developed for specific types of ophthalmological images, and methods for segmentation of optical disc, retinal vessel tree and autofluorescence areas are presented. Finally, the designed methods...

Fuzzy transforms in image compression and fusion

Irina Perfilieva (2007)

Acta Mathematica Universitatis Ostraviensis

An overview of direct and inverse fuzzy transforms of three types is given and applications to data processing are considered. The construction and some important properties of fuzzy transforms are presented on the theoretical level. Three applications of F -transform to data processing have been chosen: compressional and reconstruction of data, removing noise and data fusion. All of them successively exploit the filtering property of the inverse fuzzy transform.

Image Compression with Schauder Bases

Zbigniew Ciesielski (2001)

Applicationes Mathematicae

As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information. For, each...

Image Interpolation

Vicent Caselles, Simon Masnou, Jean-Michel Morel, Catalina Sbert (1997/1998)

Séminaire Équations aux dérivées partielles

We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The Absolute Minimal Lipschitz Extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range. We...

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