This article investigates the problem of acquiring 3D object maps of indoor household environments, in particular kitchens. The objects modeled in these maps include cupboards, tables, drawers and shelves, which are of particular importance for a household robotic assistant. Our mapping approach is based on PCD (point cloud data) representations. Sophisticated interpretation methods operating on these representations eliminate noise and resample the data without deleting the important details, and interpret the improved point clouds in terms of rectangular planes and 3D geometric shapes. We detail the steps of our mapping approach and explain the key techniques that make it work. The novel techniques include statistical analysis, persistent histogram features estimation that allows for a consistent registration, resampling with additional robust fitting techniques, and segmentation of the environment into meaningful regions. Key words: environment object model, point cloud data, geometrical reasoning 1

An algorithm for least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters between two or more fully 3D surfaces, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surfaces simultaneously, without using explicit tie points. Besides the mathematical model and execution aspects we pay particular interest to the reduction of the computational expenses. An efficient space partitioning method is implemented in order to speed up the correspondence search, which is the main portion of the computational efforts. The simultaneous matching of sub-surface patches is given as another strategy. It provides a computationally effective solution, since it matches only relevant multi-subpatches rather then the whole overlapping area. A practical example including computation times is given for the demonstration of the method. 1.

3D documentation and visualization of Cultural Heritage objects is an expanding application area. The selection of the right technology for these kinds of applications is very important and strictly related to the project requirements, budget and user’s experience. Active sensors, i.e. triangulation based laser scanners and structured light systems are used for many kinds of 3D object reconstruction tasks and in particular for 3D documentation of cultural heritage objects. This study presents some experiences in the results of two case studies in which a close-range structured light system is used for the 3D digitization. The paper includes all necessary steps of the 3D object modeling pipeline from data acquisition to 3D visualization.

The relative orientation of independently acquired terrestrial laser scan point clouds is an important task. If good starting values are available, well-known iterative algorithms exist to determine the required transformation. In this paper, we describe a method to obtain such starting values fully automatically, which is applicable to scenes containing planar elements. Our method first extracts planar patches in each scan individually and then assigns patch triples across scans in order to compute the rotation and translation component of the relative orientation. We assess the performance of our approach using a set of 20 terrestrial scans acquired systematically at increasing distance. For each scan, we automatically extract the 50 largest planar patches. We show that, although there are 1.15 billion possible patch triple assignments, we are able to compute efficiently a ranked list of possible transformations where the correct transformation is usually within the first few positions. For our test data and three test runs, it has been among the first 53 positions, even for scans with little overlap. Thus, instead of 1.15 billion candidate solutions, the score function needs only to evaluate on the order of 100 candidate solutions, which is an improvement by a factor of 10 7. 1

We present an algorithm for the least squares matching of overlapping 3D surfaces. It estimates the transformation parameters between two or more fully 3D surfaces, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surfaces simultaneously, without using explicit tie points. Besides the mathematical model of the procedure, we discuss the computational aspects. We give practical examples to demonstrate the method.

Athens“. An aim of the project is the 3D documentation of the whole Acropolis, one of the major archaeological sites world-wide included in the UNESCO World Heritage list. The largest part of the monument was digitised with laser scanning, while the main objective of IBM was to model difficult-to- access areas not covered by the scanner but also for comparison with laser scanning for scientific investigations. For the 3D modeling, as the Erechtheion contains some typical architectural elements (like columns, flat walls, etc), some manual measurements were necessary. On the other hand, for some detailed areas automated approaches for dense surface reconstructions are applied. For these parts we compared the image matching results with the surfaces coming from a laser scanner. 1.

We present a novel cosine series representation for encoding fiber bundles consisting of multiple 3D curves. The coordinates of curves are parameterized as coefficients of cosine series expansion. We address the issue of registration, averaging and statistical inference on curves in a unified framework. Unlike traditional splines, the proposed method does not have internal knots and explicitly represents curves as a linear combination of cosine basis functions. This simplicity in the representation enables us to design statistical models, register curves and perform subsequent analysis in a more unified statistical framework. The proposed representation is applied in characterizing abnormal shape of white matter fiber tracts passing through the splenium of the corpus callosum in autistic subjects. For an arbitrary tract, a 19 degree expansion is found to be sufficient to reconstruct the tract with 60 parameters.

new developments in remote sensing, photogrammetry and laser scanning generated new possibilities for acquisition, processing and presentation of different objects at various scales. Beside object modelling, photorealistic texturing is still a challenging task. This paper focuses on a new texture mapping technique, which extends the known 2.5D approaches of texture mapping to 3D objects. A new algorithm will be described, suitable to achieve high quality results by eliminating problems of current approaches e.g. resolution dependency, need of huge amount of memory and handling of colour and brightness differences. A new, vector based visibility analysis, using vector algebra instead of pixel based algorithms will be presented. In the context of texture mapping, the fusion of different texture sources (different images) with different illumination and exposure conditions as well as images with different resolutions is an important task. To achieve best results in terms of homogeneity and level of detail, a multi-image texturing approach was developed, to preserve the fine texture information of the object. To adjust the brightness levels of the image dataset, a global and a local colour adjustment was developed. The software “Blender ” was used to generate high quality images, movies and animations. The result of the investigations and developments is a software system to texture 3D models photorealistically and automatically. All algorithms are discussed in detail. The performance is demonstrated using artificial and real world data sets. 1.

We present a novel unified framework for explicitly parameterizing white fiber tracts. The coordinates of tracts are parameterized using a Fourier series expansion. For an arbitrary tract, a 19 degree cosine expansion is found to be sufficient to reconstruct the tract with an error of about 0.26 mm. By adding specific periodic constraints to open tracts, we can avoid using the sine basis. Then each tract is fully parameterized with 60 parameters, which results in a substantial data reduction. Unlike available spline models, the proposed method does not have internal knots and explicitly represents the tract as a linear combination of basis functions. This simplicity in the representation enables us to design statistical models, register tracts and segment tracts in a unified Hilbert space formulation.

A method for the simultaneous co-registration and georeferencing of multiple 3D pointclouds and associated intensity information is proposed. It is a generalization of the 3D surface matching problem. The simultaneous co-registration provides for a strict solution to the problem, as opposed to sequential pairwise registration. The problem is formulated as the Least Squares matching of overlapping 3D surfaces. The parameters of 3D transformations of multiple surfaces are simultaneously estimated, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances among the surfaces. An observation equation is written for each surface-to-surface correspondence. Each overlapping surface pair contributes a group of observation equations to the design matrix. The parameters are introduced into the system as stochastic variables, as a second type of (fictitious) observations. This extension allows to control the estimated parameters. Intensity information is introduced into the system in the form of quasisurfaces as the third type of observations. Reference points, defining an external (object) coordinate system, which are imaged in additional intensity images, or can be located in the pointcloud, serve as the fourth type of observations. They transform the whole block of “models ” to a unique reference system. Furthermore, the given coordinate values of the control points are treated as observations. This gives the fifth type of observations. The total system is solved by applying the Least Squares technique, provided that sufficiently good initial values for the transformation parameters are given. This method can be applied to data sets generated from aerial as well as terrestrial laser scanning or other pointcloud generating methods. 1.