Shape Matching By Part Alignment Using Extended Chordal Axis Transform

International audienceOne of the main challenges in shape matching is overcoming intra–class variation where objects that are conceptually similar have significant geometric dissimilarity. The key to a solution around this problem is incorporating the structure of the object in the shape descriptor which can be described by a connectivity graph customarily extracted from its skeleton. In a slightly different perspective, the structure may also be viewed as the arrangement of protruding parts along its boundary. This arrangement does not only convey the protruding part's ordering along the anti clockwise direction, but also relates these parts on different levels of detail. In this paper, we propose a shape matching method that estimates the distance between two objects by conducting a part-to-part matching analysis between their visual protruding parts. We start by a skeleton-based segmentation of the shape inspired by the Chordal Axis Transform. Then, we extract the segments that represent the protruding parts in its silhouette on varied levels of detail. Each one of these parts is described by a feature vector. A shape is thus described by the feature vectors of its parts in addition to their angular and linear proximities to each other. Using dynamic programming, our algorithm finds a minimal cost correspondence between parts. Our experimental evaluations validate the proposition that part correspondence allows conceptual matching of precisely dissimilar shapes

Sketch-based 3D Object Retrieval Using Two Views and Visual Part Alignment

International audienceHand drawn figures are the imprints of shapes in human's mind. How a human expresses a shape is a consequence of how he or she visualizes it. A query-by-sketch 3D object retrieval application is closely tied to this concept from two aspects. First, describing sketches must involve elements in a figure that matter most to a human. Second, the representative 2D projection of the target 3D objects must be limited to ''the canonical views'' from a human cognition perspective. We advocate for these two rules by presenting a new approach for sketch-based 3D object retrieval that describes a 2D shape by the visual protruding parts of its silhouette. Furthermore, the proposed approach computes estimations of ''part occlusion'' and ''symmetry'' in 2D shapes in a new paradigm for viewpoint selection that represents 3D objects by only the two views corresponding to the minimum value of each

Representation and Detection of Shapes in Images

We present a set of techniques that can be used to represent and detect shapes in images. Our methods revolve around a particular shape representation based on the description of objects using triangulated polygons. This representation is similar to the medial axis transform and has important properties from a computational perspective. The first problem we consider is the detection of non-rigid objects in images using deformable models. We present an efficient algorithm to solve this problem in a wide range of situations, and show examples in both natural and medical images. We also consider the problem of learning an accurate non-rigid shape model for a class of objects from examples. We show how to learn good models while constraining them to the form required by the detection algorithm. Finally, we consider the problem of low-level image segmentation and grouping. We describe a stochastic grammar that generates arbitrary triangulated polygons while capturing Gestalt principles of shape regularity. This grammar is used as a prior model over random shapes in a low level algorithm that detects objects in images

Robust and Optimal Methods for Geometric Sensor Data Alignment

Geometric sensor data alignment - the problem of finding the rigid transformation that correctly aligns two sets of sensor data without prior knowledge of how the data correspond - is a fundamental task in computer vision and robotics. It is inconvenient then that outliers and non-convexity are inherent to the problem and present significant challenges for alignment algorithms. Outliers are highly prevalent in sets of sensor data, particularly when the sets overlap incompletely. Despite this, many alignment objective functions are not robust to outliers, leading to erroneous alignments. In addition, alignment problems are highly non-convex, a property arising from the objective function and the transformation. While finding a local optimum may not be difficult, finding the global optimum is a hard optimisation problem. These key challenges have not been fully and jointly resolved in the existing literature, and so there is a need for robust and optimal solutions to alignment problems. Hence the objective of this thesis is to develop tractable algorithms for geometric sensor data alignment that are robust to outliers and not susceptible to spurious local optima. This thesis makes several significant contributions to the geometric alignment literature, founded on new insights into robust alignment and the geometry of transformations. Firstly, a novel discriminative sensor data representation is proposed that has better viewpoint invariance than generative models and is time and memory efficient without sacrificing model fidelity. Secondly, a novel local optimisation algorithm is developed for nD-nD geometric alignment under a robust distance measure. It manifests a wider region of convergence and a greater robustness to outliers and sampling artefacts than other local optimisation algorithms. Thirdly, the first optimal solution for 3D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms other geometric alignment algorithms on challenging datasets due to its guaranteed optimality and outlier robustness, and has an efficient parallel implementation. Fourthly, the first optimal solution for 2D-3D geometric alignment with an inherently robust objective function is proposed. It outperforms existing approaches on challenging datasets, reliably finding the global optimum, and has an efficient parallel implementation. Finally, another optimal solution is developed for 2D-3D geometric alignment, using a robust surface alignment measure. Ultimately, robust and optimal methods, such as those in this thesis, are necessary to reliably find accurate solutions to geometric sensor data alignment problems

Automatic music genre classification

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Master of Science. 2014.No abstract provided

Exploiting Structural Regularities and Beyond: Vision-based Localization and Mapping in Man-Made Environments

Image-based estimation of camera motion, known as visual odometry (VO), plays a very important role in many robotic applications such as control and navigation of unmanned mobile robots, especially when no external navigation reference signal is available. The core problem of VO is the estimation of the camera’s ego-motion (i.e. tracking) either between successive frames, namely relative pose estimation, or with respect to a global map, namely absolute pose estimation. This thesis aims to develop efficient, accurate and robust VO solutions by taking advantage of structural regularities in man-made environments, such as piece-wise planar structures, Manhattan World and more generally, contours and edges. Furthermore, to handle challenging scenarios that are beyond the limits of classical sensor based VO solutions, we investigate a recently emerging sensor — the event camera and study on event-based mapping — one of the key problems in the event-based VO/SLAM. The main achievements are summarized as follows. First, we revisit an old topic on relative pose estimation: accurately and robustly estimating the fundamental matrix given a collection of independently estimated homograhies. Three classical methods are reviewed and then we show a simple but nontrivial two-step normalization within the direct linear method that achieves similar performance to the less attractive and more computationally intensive hallucinated points based method. Second, an efficient 3D rotation estimation algorithm for depth cameras in piece-wise planar environments is presented. It shows that by using surface normal vectors as an input, planar modes in the corresponding density distribution function can be discovered and continuously tracked using efficient non-parametric estimation techniques. The relative rotation can be estimated by registering entire bundles of planar modes by using robust L1-norm minimization. Third, an efficient alternative to the iterative closest point algorithm for real-time tracking of modern depth cameras in ManhattanWorlds is developed. We exploit the common orthogonal structure of man-made environments in order to decouple the estimation of the rotation and the three degrees of freedom of the translation. The derived camera orientation is absolute and thus free of long-term drift, which in turn benefits the accuracy of the translation estimation as well. Fourth, we look into a more general structural regularity—edges. A real-time VO system that uses Canny edges is proposed for RGB-D cameras. Two novel alternatives to classical distance transforms are developed with great properties that significantly improve the classical Euclidean distance field based methods in terms of efficiency, accuracy and robustness. Finally, to deal with challenging scenarios that go beyond what standard RGB/RGB-D cameras can handle, we investigate the recently emerging event camera and focus on the problem of 3D reconstruction from data captured by a stereo event-camera rig moving in a static scene, such as in the context of stereo Simultaneous Localization and Mapping

Measurement and Characterization of Track Geometry Data: Literature Review and Recommendations for Processing FRA ATIP Program Data

Task Order 86From October 2018 to March 2019, the Federal Railroad Administration sponsored Transportation Technology Center, Inc. to conduct a literature review on the methods of measurement and characterization of track geometry. The goal of the review was to summarize the current state of track geometry measurement and to provide recommendations on methods for processing and characterizing track geometry data collected under FRA\u2019s Automated Track Inspection Program

Statistical shape analysis of large molecular data sets

Protein classification databases are widely used in the prediction of protein structure and function, and amongst these databases the manually-curated Structural Classification of Proteins database (SCOP) is considered to be a gold standard. In SCOP, functional relationships are described by hyperfamily and superfamily categories and structural relationships are described by family, species and protein categories. We present a method to calculate a difference measure between pairs of proteins that can be used to reproduce SCOP2 structural relationship classifications, and that can also be used to reproduce a subset of functional relationship classifications at the superfamily level. Calculating the difference measure requires first finding the best correspondence between atoms in two protein configurations. The problem of finding the best correspondence is known as the unlabelled, partial matching problem. We consider the unlabelled, partial matching problem through a detailed analysis of the approach presented in Green and Mardia (2006). Using this analysis, and applying domain-specific constraints, we develop a new algorithm called GProtA for protein structure alignment. The proposed difference measure is constructed from the root mean squared deviation of the aligned protein structures and a binary similarity measure, where the binary similarity measure takes into account the proportions of atoms matching from each configuration. The GProtA algorithm and difference measure are applied to protein structure data taken from the Protein Data Bank. The difference measure is shown to correctly classify 62 of a set of 72 proteins into the correct SCOP family categories when clustered. Of the remaining 9 proteins, 2 are assigned incorrectly and 7 are considered indeterminate. In addition, a method for deriving characteristic signatures for categories is proposed. The signatures offer a mechanism by which a single comparison can be made to judge similarity to a particular category. Comparison using characteristic signatures is shown to correctly delineate proteins at the family level, including the identification of both families for a subset of proteins described by two family level categories