Representation and shape matching of 3-D objects

Journal ArticleA three-dimensional scene analysis system for the shape matching of real world 3-D objects is presented. Various issues related to representation and modeling of 3-D objects are addressed. A new method for the approximation of 3-D objects by a set of planar faces is discussed. The major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the imitation of the previous work in 3-D scene analysis. The method is a sequential region growing algorithm. It is not applied to range images, but rather to a set of 3-D model of an object is obtained

Formenvergleich in höheren Dimensionen

Cover and Contents 1 Introduction 1.1 Overview 1.2 Credits 2 Preliminaries 2.1 Representation of Shapes 2.2 Distance Measures 2.3 Miscellaneous 3 Hausdorff Distance Under Translations 3.1 Overview 3.2 Basic Properties of \delta;->H 3.3 Matching Points to Sites 3.4 Matching Two Sets of Sites 3.5 Approximate Algorithms 4 Matching Special Shape Classes Under Translations 4.1 Matching Terrains 4.2 Matching Convex Polyhedra 5 Matching Curves with respect to the Fréchet Distance 5.1 Basic Properties of the Fréchet Distance 5.2 Polygonal Curves Under Translations 5.3 Polygonal Curves Under Affine Transformations 5.4 Variants 6 Matching a Polygonal Curve in a Graph of Curves 6.1 Problem Statement 6.2 Algorithm 6.3 Variants Bibliography Index A Zusammenfassung B LebenslaufThe comparison of geometric shapes is a task which naturally arises in many applications, such as in computer vision, computer aided design, robotics, medical imaging, etc. Usually geometric shapes are represented by a number of simple objects (sites) that either describe the boundary of the shape, or the whole shape itself. Sites are often chosen to be linear objects, such as line segments, triangles, or simplices in general, since linear objects are easier to handle in algorithms. But sometimes also patches of algebraic curves or surfaces, such as circular arcs or portions of spheres or cylinders are of interest. In order to compare two shapes we need to have a notion of similarity or dissimilarity, which arises from the desired application. There is a large variety of different similarity measures. Popular similarity notions are, for example, the Hausdorff distance, the area of symmetric difference, or especially for curves the turn-angle distance, or the Fréchet distance. The application usually supplies a distance measure, and furthermore a set of allowed transformations, and the task is to find a transformation that, when applied to the first object, minimizes the distance to the second one. Typical transformation classes are translations, rotations, and rigid motions (which are combinations of translations and rotations). The contribution of this thesis consists of several algorithms for matching simplicial shapes in dimensions d >= 2. The shapes are either represented as sets of simplicial objects or as polygonal curves with a given parametrization. The considered distance measures are mainly the Hausdorff distance and the Fréchet distance. In the literature most matching algorithms either attack two-dimensional problems, or consider finite point sets in higher dimensions. In the first half of this thesis we present results for the Hausdorff distance in d >= 2 dimensions under translations, for a rather general notion of simplicial shapes, as well as for some special shape classes which allow to speed up the computations. In the second half of this thesis we investigate the Fréchet distance for polygonal curves. The Fréchet distance is a natural distance measure for curves, but has not been investigated much in the literature. We present the first algorithms to optimize the Fréchet distance under various transformation classes for polygonal curves in arbitrary dimensions. In the last chapter we consider a partial matching variant in which a geometric graph and another curve are given, and we show how to find a polygonal path in the graph which minimizes the Fréchet distance to the curve.Das Vergleichen zweier geometrischer Formen ist eine Aufgabe, die aus vielerlei Anwendungen natürlich hervorgeht. Einige Anwendungen sind Computer Vision, Computer Graphik, Computer Aided Design, Robotics, medizinische Bilderverarbeitung, etc. Normalerweise werden geometrische Formen aus einfacheren Objekten zusammengesetzt, die entweder den Rand der Form oder die ganze Form ansich beschreiben. Oft verwendet werden lineare Objekte wie Strecken, Dreicke, oder Simplizes in höheren Dimensionen. Um zwei Formen zu vergleichen braucht man zunächst einen Ähnlichkeits- oder Abstandsbegriff zwischen zwei Formen, der in der Regel aus der jeweiligen Anwendung hervorgeht. Naturgemäß gibt es eine große Vielfalt solcher Abstandsmaße; eines der natürlichsten ist der Hausdorff-Abstand. Weiterhin gibt die Anwendung in der Regel eine Menge von Transformationen vor, und möchte eine Transformation finden, die, angewandt auf die erste Form, den Abstand zur zweiten Form minimiert. Diese Aufgabe wird als Matching bezeichnet. Oft verwendete Transformationsklassen sind zum Beispiel Translationen, Rotationen und starre Bewegungen (Kombinationen von Translationen und Rotationen). Diese Arbeit beschäftigt sich mit dem Matching von geometrischen Formen in Dimensionen d >= 2, die aus stückweise linearen Objekten bestehen. Die Formen sind entweder als Mengen solcher Objekte, oder als Polygonzüge, die als parametrisierte Kurven aufgefaßt werden, beschrieben. Als Abstandsmaße werden hauptsächlich der Hausdorff-Abstand und der Fréchet-Abstand betrachtet. Bisherige Ergebnisse für das Matching von Formen behandeln in der Regel entweder zweidimensionale Formen, oder Punktmengen in höheren Dimensionen. Die erste Hälfte dieser Dissertation präsentiert Ergebnisse für den Hausdorff- Abstand in d >= 2 Dimensionen unter Translationen für einen allgemein gehaltenen Formenbegriff, sowie für einige spezielle Klassen geometrischer Formen, die eine schnellere Berechnung erlauben. Die zweite Hälfte der Dissertation beschäftigt sich mit dem Matching von parametrisierten Kurven bezüglich des Fréchet-Abstandes. Obwohl der Fréchet-Abstand ein natürliches Abstandsmaß für Kurven darstellt, gibt es bisher diesbezüglich wenig Ergebnisse in der Literatur. Für parametrisierte Kurven in d >= 2 Dimensionen wird in dieser Dissertation ein Matching-Algorithmus vorgestellt, der unter Translationen und relativ allgemein gehaltenen Teilmengen der affinen Abbildungen den Fréchet-Abstand minimiert. Als letztes Ergebnis wird eine weitere Matching-Variante bezüglich des Fréchet-Abstandes vorgestellt, in der eine Teilkurve in in einem eingebetteten planaren Graphens gefunden werden soll, die den Fréchet-Abstand zu einer gegebenen Kurve minimiert

Perceptually Motivated Shape Context Which Uses Shape Interiors

In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

Structured Knowledge Representation for Image Retrieval

We propose a structured approach to the problem of retrieval of images by content and present a description logic that has been devised for the semantic indexing and retrieval of images containing complex objects. As other approaches do, we start from low-level features extracted with image analysis to detect and characterize regions in an image. However, in contrast with feature-based approaches, we provide a syntax to describe segmented regions as basic objects and complex objects as compositions of basic ones. Then we introduce a companion extensional semantics for defining reasoning services, such as retrieval, classification, and subsumption. These services can be used for both exact and approximate matching, using similarity measures. Using our logical approach as a formal specification, we implemented a complete client-server image retrieval system, which allows a user to pose both queries by sketch and queries by example. A set of experiments has been carried out on a testbed of images to assess the retrieval capabilities of the system in comparison with expert users ranking. Results are presented adopting a well-established measure of quality borrowed from textual information retrieval

Object recognition using shape-from-shading

This paper investigates whether surface topography information extracted from intensity images using a recently reported shape-from-shading (SFS) algorithm can be used for the purposes of 3D object recognition. We consider how curvature and shape-index information delivered by this algorithm can be used to recognize objects based on their surface topography. We explore two contrasting object recognition strategies. The first of these is based on a low-level attribute summary and uses histograms of curvature and orientation measurements. The second approach is based on the structural arrangement of constant shape-index maximal patches and their associated region attributes. We show that region curvedness and a string ordering of the regions according to size provides recognition accuracy of about 96 percent. By polling various recognition schemes. including a graph matching method. we show that a recognition rate of 98-99 percent is achievable

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure