A large number of 3D models are created and available on the Web, since more and more 3D modelling and digitizing tools are developed for ever increasing applications. The techniques for content-based 3D model retrieval then become necessary. In this paper, a visual similarity-based 3D model retrieval system is proposed.

Recognition of three dimensional (3D) objects in noisy and cluttered scenes is a challenging problem in 3D computer vision. One approach that has been successful in past research is the regional shape descriptor. In this paper, we introduce two new regional shape descriptors: 3D shape contexts and harmonic shape contexts. We evaluate the performance of these descriptors on the task of recognizing vehicles in range scans of scenes using a database of 56 cars. We compare the two novel descriptors to an existing descriptor, the spin image, showing that the shape context based descriptors have a higher recognition rate on noisy scenes and that 3D shape contexts outperform the others on cluttered scenes.

Persistent homology is the mathematical core of recent work on shape, including reconstruction, recognition, and matching. Its pertinent information is encapsulated by a pairing of the critical values of a function, visualized by points forming a diagram in the plane. The original algorithm in [10] computes the pairs from an ordering of the simplices in a triangulation and takes worst-case time cubic in the number of simplices. The main result of this paper is an algorithm that maintains the pairing in worst-case linear time per transposition in the ordering. A side-effect of the algorithm’s analysis is an elementary proof of the stability of persistence diagrams [7] in the special case of piecewise-linear functions. We use the algorithm to compute 1-parameter families of diagrams which we apply to the study of protein folding trajectories. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—Geometrical problems and

Elevation maps are a popular data structure for representing the environment of a mobile robot operating outdoors or on not-flat surfaces. Elevation maps store in each cell of a discrete grid the height of the surface at the corresponding place in the environment. However, the use of this 2 1-dimensional representation, is disad-2 vantageous when utilized for mapping with mobile robots operating on the ground, since vertical or overhanging objects cannot be represented appropriately. Furthermore, such objects can lead to registration errors when two elevation maps have to be matched. In this paper, we propose an approach that allows a mobile robot to deal with vertical and overhanging objects in elevation maps. Our approach classifies the points in the environment according to whether they correspond to such objects or not. We also present a variant of the ICP algorithm that utilizes the classification of cells during the data association. Additionally, we describe how the constraints computed by the ICP algorithm can be applied to determine globally consistent alignments. Experiments carried out with a real robot in an outdoor environment demonstrate that our approach yields highly accurate elevation maps even in the case of loops. We furthermore present experimental results demonstrating that our classification increases the robustness of the scan matching process. 1

We propose a novel technique for the registration of 3D point clouds which makes very few assumptions: we avoid any manual rough alignment or the use of landmarks, displacement can be arbitrarily large, and the two point sets can have very little overlap. Crude alignment is achieved by estimation of the 3D-rotation from two Extended Gaussian Images even when the data sets inducing them have partial overlap. The technique is based on the correlation of the two EGIs in the Fourier domain and makes use of the spherical and rotational harmonic transforms. For pairs with low overlap which fail a critical verification step, the rotational alignment can be obtained by the alignment of constellation images generated from the EGIs. Rotationally aligned sets are matched by correlation using the Fourier transform of volumetric functions. A fine alignment is acquired in the final step by running Iterative Closest Points with just few iterations.

A wide-spread use of 3D models in cultural heritage application requires low cost equipment and technically simple modeling procedures. In this context methods for automatic 3D modeling of textured objects will play a central role. Such methods need fully automatic techniques for 3D views registration and for the removal of texture artifacts. This paper proposes a contribution in this direction based on image processing approaches. The proposed procedure is very robust and simple. It does not require special equipment or skill in order to make textured 3D models. The results of this paper, originally conceived to address the costs issues of cultural heritage modeling, can be profitably exploited also in other modeling applications.

We present a dense 3D correspondence finding method that enables spatio-temporally coherent reconstruction of surface animations from multi-view video data. Given as input a sequence of shape-from-silhouette volumes of a moving subject that were reconstructed for each time frame individually, our method establishes dense surface correspondences between subsequent shapes independently of surface discretization. This is achieved in two steps: first, we obtain sparse correspondences from robust optical features between adjacent frames. Second, we generate dense correspondences which serve as map between respective surfaces. By applying this procedure subsequently to all pairs of time steps we can trivially align one shape with all others. Thus, the original input can be reconstructed as a sequence of meshes with constant connectivity and small tangential distortion. We exemplify the performance and accuracy of our method using several synthetic and captured real-world sequences.

Abstract The photorealistic modeling of large-scale scenes, such as urban structures, requires a fusion of range sensing technology and traditional digital photography. This paper presents a system that integrates automated 3D-to-3D and 2D-to-3D registration techniques, with multiview geometry for the photorealistic modeling of urban scenes. The 3D range scans are registered using our automated 3D-to-3D registration method that matches 3D features (linear or circular) in the range images. A subset of the 2D photographs are then aligned with the 3D model using our automated 2D-to-3D registration algorithm that matches linear features between the range scans and the photographs. Finally, the 2D photographs are used to generate a second 3D model of the scene that consists of a sparse 3D point cloud, produced by applying a multiview geometry (structure-from-motion) algorithm directly on a sequence of 2D photographs. The last part of this paper introduces a novel algorithm for automatically recovering the rotation, scale, and translation that

In this thesis we explore and extend the theory of persistent homology, which captures topological features of a function by pairing its critical values. The result is represented by a collection of points in the extended plane called persistence diagram. We start with the question of ridding the function of topological noise as suggested by its persistence diagram. We give an algorithm for hierarchically finding such ε-simplifications on 2-manifolds as well as answer the question of when it is impossible to simplify a function in higher dimensions. We continue by examining time-varying functions. The original algorithm computes the persistence pairing from an ordering of the simplices in a triangulation and takes worstcase time cubic in the number of simplices. We describe how to maintain the pairing in linear time per transposition of consecutive simplices. A side effect of the update algorithm is an elementary proof of the stability of persistence diagrams. We introduce a parametrized family of persistence diagrams called persistence vineyards and illustrate the concept with a vineyard describing a folding of a small peptide. We also base a simple algorithm to compute the rank invariant of a collection of functions on the update procedure.

Accurate and robust registration of multiple threedimensional (3D) views is crucial for creating digital 3D models of real-world scenes. In this paper, we present a framework for evaluating the quality of model hypotheses during the registration phase. We use maximum likelihood estimation to learn a probabilistic model of registration success. This method provides a principled way to combine multiple measures of registration accuracy. Also, we describe a stochastic algorithm for robustly searching the large space of possible models for the best model hypothesis. This new approach can detect situations in which no solution exists, outputting a set of model parts if a single model using all the views cannot be found. We show results for a large collection of automatically modeled scenes and demonstrate that our algorithm works independently of scene size and the type of range sensor. This work is part of a system we have developed to automate the 3D modeling process for a set of 3D views obtained from unknown sensor viewpoints.