Discovering Regularity in Point Clouds of Urban Scenes

Despite the apparent chaos of the urban environment, cities are actually replete with regularity. From the grid of streets laid out over the earth, to the lattice of windows thrown up into the sky, periodic regularity abounds in the urban scene. Just as salient, though less uniform, are the self-similar branching patterns of trees and vegetation that line streets and fill parks. We propose novel methods for discovering these regularities in 3D range scans acquired by a time-of-flight laser sensor. The applications of this regularity information are broad, and we present two original algorithms. The first exploits the efficiency of the Fourier transform for the real-time detection of periodicity in building facades. Periodic regularity is discovered online by doing a plane sweep across the scene and analyzing the frequency space of each column in the sweep. The simplicity and online nature of this algorithm allow it to be embedded in scanner hardware, making periodicity detection a built-in feature of future 3D cameras. We demonstrate the usefulness of periodicity in view registration, compression, segmentation, and facade reconstruction. The second algorithm leverages the hierarchical decomposition and locality in space of the wavelet transform to find stochastic parameters for procedural models that succinctly describe vegetation. These procedural models facilitate the generation of virtual worlds for architecture, gaming, and augmented reality. The self-similarity of vegetation can be inferred using multi-resolution analysis to discover the underlying branching patterns. We present a unified framework of these tools, enabling the modeling, transmission, and compression of high-resolution, accurate, and immersive 3D images

Branching Boogaloo: Botanical Adventures in Multi-Mediated Morphologies

FormaLeaf is a software interface for exploring leaf morphology using parallel string rewriting grammars called L-systems. Scanned images of dicotyledonous angiosperm leaves removed from plants around Bard’s campus are displayed on the left and analyzed using the computer vision library OpenCV. Morphometrical information and terminological labels are reported in a side-panel. “Slider mode” allows the user to control the structural template and growth parameters of the generated L-system leaf displayed on the right. “Vision mode” shows the input and generated leaves as the computer ‘sees’ them. “Search mode” attempts to automatically produce a formally defined graphical representation of the input by evaluating the visual similarity of a generated pool of candidate leaves. The system seeks to derive a possible internal structural configuration for venation based purely off a visual analysis of external shape. The iterations of the generated L-system leaves when viewed in succession appear as a hypothetical development sequence. FormaLeaf was written in Processing

Methods for Structural Pattern Recognition: Complexity and Applications

Katedra kybernetik

Model synthesis

Three-dimensional models are extensively used in nearly all types of computer graphics applications. The demand for 3D models is large and growing. However, despite extensive work in modeling for over four decades, model generation remains a labor-intensive and difficult process even with the best available tools. We present a new procedural modeling technique called model synthesis that is designed to generate many classes of objects. Model synthesis is inspired by developments in texture synthesis. Model synthesis is designed to automatically generate a large model that resembles a small example model provided by the user. Every small part of the generated model is identical to a small part of the example model. By altering the example model, a wide variety of objects can be produced. We present several different model synthesis algorithms and analyze their strengths and weaknesses. Discrete model synthesis generates models built out of small building blocks or model pieces. Continuous model synthesis generates models on set of parallel planes. We also show how to incorporate several additional user-defined constraints to control the large-scale structure of the model, to control how the objects are distributed, and to generate symmetric models. The generality of the approach will be demonstrated by showing many models produced using each approach including cities, landscapes, spaceships, and castles. The models contain hundreds of thousands of model pieces and are generated in only a few minutes

Recognition of simple 3-D objects by the use of syntactic pattern recognition

This project is an attempt to supply the existing hardware with adequate software, in order to develop a system capable of recognizing 3-D objects, bounded by simple 2-D planes, which in turn are bounded by straight lines. [Continues.

Complexity of Two-Dimensional Patterns

In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of ``regular language'' or ``local rule'' that are equivalent in d=1 lead to distinct classes in d >= 2. We explore the closure properties and computational complexity of these classes, including undecidability and L-, NL- and NP-completeness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in d >= 2 has a periodic point of a given period, and that certain ``local lattice languages'' are not finite-time images or limit sets of any CA. We also show that the entropy of a d-dimensional CA's finite-time image cannot decrease faster than t^{-d} unless it maps every initial condition to a single homogeneous state.Comment: To appear in J. Stat. Phy

Improving Usability in Procedural Modeling

This work presents new approaches and algorithms for procedural modeling geared towards user convenience and improving usability, in order to increase artists’ productivity. Procedural models create geometry for 3D models from sets of rules. Existing approaches that allow to model trees, buildings, and terrain are reviewed and possible improvements are discussed. A new visual programming language for procedural modeling is discussed, where the user connects operators to visual programs called model graphs. These operators create geometry with textures, assign or evaluate variables or control the sequence of operations. When the user moves control points using the mouse in 3D space, the model graph is executed to change the geometry interactively. Thus, model graphs combine the creativity of freehand modeling with the power of programmed modeling while displaying the program structure more clearly than textbased approaches. Usability is increased as a result of these advantages. Also, an interactive editor for botanical trees is demonstrated. In contrast to previous tree modeling systems, we propose linking rules, parameters and geometry to semantic entities. This has the advantage that problems of associating parameters and instances are completely avoided. When an entity is clicked in the viewport, its parameters are displayed immediately, changes are applied to selected entities, and viewport editing operations are reflected in the parameter set. Furthermore, we store the entities in a hierarchical data structure and allow the user to activate recursive traversal via selection options for all editing operations. The user may choose to apply viewport or parameter changes to a single entity or many entities at once, and only the geometry for the affected entities needs to be updated. The proposed user interface simplifies the modeling process and increases productivity. Interactive editing approaches for 3D models often allow more precise control over a model than a global set of parameters that is used to generate a shape. However, usually scripted procedural modeling generates shapes directly from a fixed set of parameters, and interactive editing mostly uses a fixed set of tools. We propose to use scripts not only to generate models, but also for manipulating the models. A base script would set up the state of an object, and tool scripts would modify that state. The base script and the tool scripts generate geometry when necessary. Together, such a collection of scripts forms a template, and templates can be created for various types of objects. We examine how templates simplify the procedural modeling workflow by allowing for editing operations that are context-sensitive, flexible and powerful at the same time. Many algorithms have been published that produce geometry for fictional landscapes. There are algorithms which produce terrain with minimal setup time, allowing to adapt the level of detail as the user zooms into the landscape. However, these approaches lack plausible river networks, and algorithms that create eroded terrain with river networks require a user to supervise creation and minutes or hours of computation. In contrast to that, this work demonstrates an algorithm that creates terrain with plausible river networks and adaptive level of detail with no more than a few seconds of preprocessing. While the system can be configured using parameters, this text focuses on the algorithm that produces the rivers. However, integrating more tools for user-controlled editing of terrain would be possible.Verbesserung der Usability bei prozeduraler Modellierung Ziel der vorliegenden Arbeit ist es, prozedurale Modellierung durch neue neue Ansätze und Algorithmen einfacher, bequemer und anwendungsfreundlicher zu machen, und damit die Produktivität der Künstler zu erhöhen. Diese Anforderungen werden häufig unter dem Stichwort Usability zusammengefasst. Prozedurale Modelle spezifizieren 3D-Modelle über Regeln. Existierende Ansätze für Bäume, Gebäude und Terrain werden untersucht und es werden mögliche Verbesserungen diskutiert. Eine neue visuelle Programmiersprache für prozedurale Modelle wird vorgestellt, bei der Operatoren zu Modellgraphen verschaltet werden. Die Operatoren erzeugen texturierte Geometrie, weisen Variablen zu und werten sie aus, oder sie steuern den Ablauf der Operationen. Wenn der Benutzer Kontrollpunkte im Viewport mit der Maus verschiebt, wird der Modellgraph ausgeführt, um interaktiv neue Geometrie für das Modell zu erzeugen. Modellgraphen kombinieren die kreativen Möglichkeiten des freihändigen Editierens mit der Mächtigkeit der prozeduralen Modellierung. Darüber hinaus sind Modellgraphen eine visuelle Programmiersprache und stellen die Struktur der Algorithmen deutlicher dar als textbasierte Programmiersprachen. Als Resultat dieser Verbesserungen erhöht sich die Usability. Ein interaktiver Editor für botanische Bäume wird ebenfalls vorgestellt. Im Gegensatz zu früheren Ansätzen schlagen wir vor, Regeln, Parameter und Geometrie zu semantischen Entitäten zu verschmelzen. Auf diese Weise werden Zuordnungsprobleme zwischen Parametern und deren Instanzen komplett vermieden. Wenn im Viewport eine Instanz angeklickt wird, werden sofort ihre Parameter angezeigt, alle Änderungen wirken sich direkt auf die betroffenen Instanzen aus, und Änderungen im Viewport werden sofort in den Parametern reflektiert. Darüber hinaus werden die Entitäten in einer hierarchischen Datenstruktur gespeichert und alle Änderungen können rekursiv auf der Hierarchie ausgeführt werden. Dem Benutzer werden Selektionsoptionen zur Verfügung gestellt, über die er Änderungen an den Parametern oder Änderungen im Viewport an einzelnen oder vielen Instanzen gleichzeitig vornehmen kann. Anschließend muss das System nur die Geometrie der betroffenen Instanzen aktualisieren. Auch hier ist das Ziel, das User Interface möglichst an den Bedürfnissen des Benutzers auszurichten, um Vereinfachungen und eine Erhöhung der Produktivität zu erreichen. Interaktive Editieransätze für 3D-Modelle erlauben häufig eine präzisere Kontrolle über ein Modell als ein globaler Parametersatz, der für die Erzeugung des Modells genutzt wird. Trotzdem erzeugen prozedurale Modellierskripte ihre Modelle meist direkt aus einem festen Parametersatz, während interaktive Tools meist mit hartkodierten Operationen arbeiten. Wir schlagen vor, Skripte nicht nur zur Erzeugung der Modelle zu verwenden, sondern auch um die erzeugten Modelle zu editieren. Ein Basisskript soll die Statusinformationen eines Objekts anlegen, während weitere Skripte diesen Status verändern und passende Geometrie erzeugen. Diese Skripte bilden dann ein Template zum Erzeugen einer Klasse von Objekten. Verschiedene Objekttypen können jeweils ihr eigenes Template haben. Wir zeigen, wie Templates den Workflow mit prozeduralen Modellen vereinfachen können, indem Operationen geschaffen werden, die gleichzeitig kontext-sensitiv, mächtig und flexibel sind. Es existiert eine Reihe von Verfahren, um Geometrie für synthetische Landschaften zu erzeugen. Ein Teil der Algorithmen erzeugt Geometrie mit minimaler Vorberechnung und erlaubt es, den Detailgrad der Landschaft interaktiv an die Perspektive anzupassen. Leider fehlen den so erzeugten Landschaften plausible Flussnetze. Algorithmen, die erodiertes Terrain mit Flussnetzen erzeugen, müssen aufwendig vom Benutzer überwacht werden und brauchen Minuten oder Stunden Rechenzeit. Im Gegensatz dazu stellen wir einen Algorithmus vor, der plausible Flussnetze erzeugt, während sich der Betrachter interaktiv durch die Szene bewegt. Das System kann über Parameter gesteuert werden, aber der Fokus liegt auf dem Algorithmus zur Erzeugung der Flüsse. Dennoch wäre es möglich, Tools zum benutzergesteuerten Editieren von Terrain zu integrieren

Graph Theory and Universal Grammar

Tese arquivada ao abrigo da Portaria nº 227/2017 de 25 de Julho-Registo de Grau EstrangeiroIn the last few years, Noam Chomsky (1994; 1995; 2000; 2001) has gone quite far in the direction of simplifying syntax, including eliminating X-bar theory and the levels of D-structure and S-structure entirely, as well as reducing movement rules to a combination of the more primitive operations of Copy and Merge. What remain in the Minimalist Program are the operations Merge and Agree and the levels of LF (Logical Form) and PF (Phonological form). My doctoral thesis attempts to offer an economical theory of syntactic structure from a graph-theoretic point of view (cf. Diestel, 2005), with special emphases on the elimination of category and projection labels and the Inclusiveness Condition (Chomsky 1994). The major influences for the development of such a theory have been Chris Collins’ (2002) seminal paper “Eliminating labels”, John Bowers (2001) unpublished manuscript “Syntactic Relations” and the Cartographic Paradigm (see Belletti, Cinque and Rizzi’s volumes on OUP for a starting point regarding this paradigm). A syntactic structure will be regarded here as a graph consisting of the set of lexical items, the set of relations among them and nothing more