When considering probabilistic pattern recognition methods, especially methods based on Bayesian analysis, the
probabilistic distribution is of the utmost importance. However, despite the fact that the geometry associated with the
probability distribution constitutes essential background information, it is often not ascertained. This paper discusses
how the standard Euclidian geometry should be generalized to the Riemannian geometry when a curvature is observed in
the distribution. To this end, the probability distribution is defined for curved geometry. In order to calculate the
probability distribution, a Lagrangian and a Hamiltonian constructed from curvature invariants are associated with the
Riemannian geometry and a generalized hybrid Monte Carlo sampling is introduced. Finally, we consider the
calculation of the probability distribution and the expectation in Riemannian space with path integrals, which allows a
direct extension of the concept of probability to curved space.
Distance is a fundamental concept when considering the information retrieval and cluster analysis of 3D information.
That is, a large number of information retrieval descriptor comparison and cluster analysis algorithms are built around
the very concept of the distance, such as the Mahalanobis or Manhattan distances, between points. Although not always
explicitly stated, a significant proportion of these distances are, by nature, Euclidian. This implies that it is assumed that
the data distribution, from a geometrical point of view, may be associated with a Euclidian flat space. In this paper, we
draw attention to the fact that this association is, in many situations, not appropriate. Rather, the data should often be
characterised by a Riemannian curved space. It is shown how to construct such a curved space and how to analyse its
geometry from a topological point of view. The paper also illustrates how, in curved space, the distance between two
points may be calculated. In addition, the consequences for information retrieval and cluster analysis algorithms are
discussed.
The modelling of complex objects and sites involve the acquisition of a large number of texture maps and range images;
each one of them representing a particular viewing angle. These views must be combined and registered in order to
create an accurate model of the original. The complexity of the resultant models, and consequently the number of views
required, has increased tremendously over the past decade. Furthermore major projects involve multinational and
multilingual teams, each with different underlying methodologies. In such conditions, it is difficult to make sense of the
annotation and to determine which views should be registered together. We propose a new approach in which similar
views are found by content-based indexing and retrieval of textures (2D) and range images (3D). The views are
described automatically, according to their appearance and their 3D geometry. A search engine allows retrieving
similar and related views for registration.
KEYWORDS: 3D modeling, Cameras, Data modeling, Laser scanners, RGB color model, Calibration, 3D displays, 3D image processing, Imaging systems, Stereoscopy
The National Research Council of Canada (NRC) has developed a range of 3D imaging technology tools, which have been applied to a wide range of museum and heritage recording applications. The technology suite includes the development of high-resolution laser scanner systems as well as software for the preparation of accurate 3D models and for the display, analysis and comparison of 3D data. This paper will offer an overview of the technology and its museum and heritage applications with particular reference to the 3D examination of paintings and recording of archaeological sites.
The present paper proposes a virtual environment for visualizing virtualized cultural and historical sites. The proposed environment is based on a distributed asynchronous architecture and supports stereo vision and tiled wall display. The system is mobile and can run from two laptops. This virtual environment addresses the problems of intellectual property protection and multimedia information retrieval through encryptation and content-based management respectively. Experimental results with a fully textured 3D model of the Crypt of Santa Cristina in Italy are presented, evaluating the performances of the proposed virtual environment.
The Virtual Boutique is made out of three modules: the decor, the market and the search engine. The decor is the physical space occupied by the Virtual Boutique. It can reproduce any existing boutique. For this purpose, photogrammetry is used. A set of pictures of a real boutique or space is taken and a virtual 3D representation of this space is calculated from them. Calculations are performed with software developed at NRC. This representation consists of meshes and texture maps. The camera used in the acquisition process determines the resolution of the texture maps. Decorative elements are added like painting, computer generated objects and scanned objects. The objects are scanned with laser scanner developed at NRC. This scanner allows simultaneous acquisition of range and color information based on white laser beam triangulation. The second module, the market, is made out of all the merchandises and the manipulators, which are used to manipulate and compare the objects. The third module, the search engine, can search the inventory based on an object shown by the customer in order to retrieve similar objects base don shape and color. The items of interest are displayed in the boutique by reconfiguring the market space, which mean that the boutique can be continuously customized according to the customer's needs. The Virtual Boutique is entirely written in Java 3D and can run in mono and stereo mode and has been optimized in order to allow high quality rendering.
KEYWORDS: Modulation, Image processing, Cameras, 3D image processing, Colorimetry, Light sources and illumination, Image segmentation, Sensors, Chlorine, RGB color model
Correlation methods for polychromatic range image recognition are presented. First, the range and the color are compared and the use of the hue images is discussed. The advantages and disadvantages in combining the range and the color information are analyzed. Single-channel and double-channel approaches are presented. The ability of both recognition methods to be invariant under translation in the xy plane and along the z axis are demonstrated. The codification of the range and the hue images using phase-coding, sine-coding and hybrid coding make possible the fully translation invariance. The double-channel is introduced using sine-coding images in the correlation process. Finally, the combination of those two channels is performed in order to improve the discrimination capability of the system. Digital results are shown.
A method for invariant pattern recognition of range images by means of the phase Fourier transform is introduced. The phase Fourier transform may be used for the segmentation of connected planar and quadric surfaces. The method is generalized to nonconnected planar surfaces through the use of the concept of the characteristic normal. An invariant representation under changes of position, scale, and orientation for the characteristic normals is defined. This representation is used as the input for a feedforward neural network. Examples of applications are given, and finally the method is applied to the problems of classification and occlusion.
We introduce a method for segmentation of planes and quadrics of a three-dimensional range image using the phase Fourier transform. We extend our previous method for contour determination and simultaneous detection of edges and quadrics. We consider optical and electronic implementations. Using the phase Fourier transform, we address the issue of invariant pattern recognition for segmented and non-segmented three-dimensional images. We show results obtained with a parallel computer.
We introduce a new approach for the segmentation of planes and quadrics of a 3-D range image using the Fourier transform of the phase image. We show how it is possible to get a spectrum that contains the planes only and another one that contains the quadrics only. We determine the invariant properties of these spectra and show how our method is suitable for real-time applications.
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