Dissertations / Theses on the topic 'Shapes'

I do not know what inspires me to use geometric shapes in my artwork. It may have started when I took my first jewelry and metalworking class in college. For one assignment, I had to find an artist and make an artwork that was inspired by his artworks. I choose is Sol Lewitt because I simply liked his opened cubes. Since I started studying in Jewelry and Metalwork and Sculpture at the University of Iowa, I my artworks are still based on geometric shapes. I enjoy them because they are shapes that I see around me everyday; such as textbooks, chairs, doors etc. In my thesis, I will explain my artworks and the techniques that I used, why I made them, what inspired me. My first semester, I just made containers which were based on geometric shapes. After that my ideas and concepts evolved to a simple object based on geometric shapes with no function. A simple geometric object without a function is better for exploring beautiful geometric. Firstly, I find a subject that I can use my ideas and concepts on. It can be something that I see everyday such as myself, faucet, jewelry etc. Sometimes, I find an interesting thing in textbooks, magazines and catalogs. Other times, I find them when I buy materials for my artworks; just shopping at the hardware. There are many things around me that I could use to create my artworks. I just choose some of them to make art and finish assignments.

Situated in the environmental humanities, Land is Shaped as Land Shapes: A Material Ecocritical Autoethnography is an interdisciplinary doctoral project grounded in the permacultural site of Thar dö Ling in rural north-western Sicily, Italy. Within a theoretical and methodological framework inspired by ecocriticism, new materialism, posthumanism, and a personal land ethic, the research crafted a “collage methodology” to enact a reading and writing of the permacultural site, combining six months of autoethnographic fieldwork with material ecocritical analysis. Conceiving permaculture design as a type of more-than-human communication that can favour multispecies and elemental mutual relationality, the site is interpreted as a more-than-human inscription where to gather (another word for “read”) a shared narrative of regeneration. Following feminist and environmental humanist invitations for “storying” and “worlding” as ethical works of living and relating with more-than-human worlds, this thesis is written within an elemental and multispecies frame offering different temporal and spatial scales, from multiple perspectives. The collage methodology draws dimensions of my personal memories and familial inheritances into relation with immersive fieldwork and situated memories, to write a collage of the Thar dö Ling permacultural site in coemergence with multiple narrative agencies and design abilities. Within this research, storying and worlding are recognised as more-than-human collective practices to draw attention to the narrative agencies and design abilities of other beings, nonbeings and elements composing both the permacultural site and the thesis. Collaging a composition of multiple temporal and spatial dimensions, agencies and partial encounters, this material ecocritical autoethnography is expressed as a process of reading, gathering, and writing the more-than-human threads within the Thar dö Ling fieldwork site. This thesis comprises seven chapters, of which four are the autoethnographic parts dedicated to the fieldwork site’s recollection. Before encountering them, two chapters lay ground for this doctoral project, offering the intimate and larger context in which the research has coemerged, as well as the theoretical and methodological foundations. Across the autoethnographic chapters, the reader is invited to move within the permacultural site, guided by the topic-places of water, plants, food and waste as situated materialities emerging from the landscape in which Thar dö Ling exists. In conclusion, there is hope.
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Hum, Lang & Soc Sc
Arts, Education and Law
Full Text

Shape computations are a formal representation that specify particular aspects of the design process with reference to form. They are defined according to shape grammars, where manipulations of pictorial representations of designs are formalised by shapes and rules applied to those shapes. They have frequently been applied in architecture in order to formalise the stylistic properties of a given corpus of designs, and also to generate new designs within those styles. However, applications in more general design fields have been limited. This is largely due to the initial definitions of the shape grammar formalism which are restricted to rectilinear shapes composed of lines, planes or solids. In architecture such shapes are common but in many design fields, for example industrial design, shapes of a more freeform nature are prevalent. Accordingly, the research described in this thesis is concerned with extending the applicability of the shape grammar formalism such that it enables computation with freeform shapes. Shape computations utilise rules in order to manipulate subshapes of a design within formal algebras. These algebras are specified according to embedding properties and have previously been defined for rectilinear shapes. In this thesis the embedding properties of freeform shapes are explored and the algebras are extended in order to formalise computations with such shapes. Based on these algebras, shape operations are specified and algorithms are introduced that enable the application of rules to shapes composed of freeform B´ezier curves. Implementation of the algorithms enables the application of shape grammars to shapes of a more freeform nature than was previously possible. Within this thesis shape grammar implementations are introduced in order to explore both theoretical issues that arise when considering computation with freeform shapes and practical issues concerning the application of shape computation as a model for design and as a mode for generating freeform shapes.

This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". To give the reader some inkling of what we mean by "shape of space", consider the fact that the shape of a triangle is given solely by its three internal angles; its position and size in ambient space are irrelevant for this ultimately intrinsic description. Analogously, the shape of a 3 dimensional space is given by a metric up to coordinate and conformal changes. Considerations of a relational nature strongly support the development of such dynamical theories of shape. The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1 form (ADM). What is special about this theory is that it does not possess foliation invariance, as does ADM. It replaces that "symmetry" by another: local conformal invariance. In so doing it more accurately reflects a theory of the "shape of space", giving us reason to call it shape dynamics. (SD). Being a very recent development, the consequences of this radical change of perspective on gravity are still largely unexplored. In the first part we will try to present some of the highlights of results so far, and indicate what we can and cannot do with shape dynamics. Because this is a young, rapidly moving field, we have necessarily left out some interesting new results which are not yet in print and were developed alongside the writing of the thesis. The second part of the thesis will develop a gauge theory for "shape of space"--theories. To be more precise, if one admits that the physically relevant bservables are given by shape, our descriptions of Nature carry a lot of redundancy, namely absolute local size and absolute spatial position. This redundancy is related to the action of the infinite-dimensional conformal and diffeomorphism groups on the geometry of space. We will show that the action of these groups can be put into a language of infinite-dimensional gauge theory, taking place in the configuration space of 3+1 gravity. In this context gauge connections acquire new and interesting meanings, and can be used as "relational tools".

Skeletal representations are important shape descriptors which encode topological and geometrical properties of shapes and reduce their dimension. Skeletons are used in several fields of science and attract the attention of many researchers. In the biocad field, the analysis of structural properties such as porosity of biomaterials requires the previous computation of a skeleton. As the size of three-dimensional images become larger, efficient and robust algorithms that extract simple skeletal structures are required. The most popular and prominent skeletal representation is the medial axis, defined as the shape points which have at least two closest points on the shape boundary. Unfortunately, the medial axis is highly sensitive to noise and perturbations of the shape boundary. That is, a small change of the shape boundary may involve a considerable change of its medial axis. Moreover, the exact computation of the medial axis is only possible for a few classes of shapes. For example, the medial axis of polyhedra is composed of non planar surfaces, and its accurate and robust computation is difficult. These problems led to the emergence of approximate medial axis representations. There exists two main approximation methods: the shape is approximated with another shape class or the Euclidean metric is approximated with another metric. The main contribution of this thesis is the combination of a specific shape and metric simplification. The input shape is approximated with an orthogonal shape, which are polygons or polyhedra enclosed by axis-aligned edges or faces, respectively. In the same vein, the Euclidean metric is replaced by the L infinity or Chebyshev metric. Despite the simpler structure of orthogonal shapes, there are few works on skeletal representations applied to orthogonal shapes. Much of the efforts have been devoted to binary images and volumes, which are a subset of orthogonal shapes. Two new skeletal representations based on this paradigm are introduced: the cube skeleton and the scale cube skeleton. The cube skeleton is shown to be composed of straight line segments or planar faces and to be homotopical equivalent to the input shape. The scale cube skeleton is based upon the cube skeleton, and introduces a family of skeletons that are more stable to shape noise and perturbations. In addition, the necessary algorithms to compute the cube skeleton of polygons and polyhedra and the scale cube skeleton of polygons are presented. Several experimental results confirm the efficiency, robustness and practical use of all the presented methods.

Man-made objects are ubiquitous in the real world and in virtual environments. While such objects can be very detailed, capturing every small feature, they are often identified and characterized by a small set of defining curves. Compact, abstracted shape descriptions based on such curves are often visually more appealing than the original models, which can appear to be visually cluttered. We introduce a novel algorithm for abstracting three-dimensional geometric models using characteristic curves or contours as building blocks for the abstraction. Our method robustly handles models with poor connectivity, including the extreme cases of polygon soups, common in models of man-made objects taken from online repositories. In our algorithm, we use a two-step procedure that first approximates the input model using a manifold, closed envelope surface and then extracts from it a hierarchical abstraction curve network along with suitable normal information. The constructed curve networks form a compact, yet powerful, representation for the input shapes, retaining their key shape characteristics while discarding minor details and irregularities.

This thesis is concerned with developing statistical methods for evaluating and comparing molecular shapes. Techniques from statistical shape analysis serve as a basis for our methods. However, as molecules are fuzzy objects of electron clouds which constantly undergo vibrational motions and conformational changes, these techniques should be modified to be more suitable for the distinctive features of molecular shape. The first part of this thesis is concerned with the continuous nature of molecules. Based on molecular properties which have been measured at the atom positions, a continuous field--based representation of a molecule is obtained using methods from spatial statistics. Within the framework of reproducing kernel Hilbert spaces, a similarity index for two molecular shapes is proposed which can then be used for the pairwise alignment of molecules. The alignment is carried out using Markov chain Monte Carlo methods and posterior inference. In the Bayesian setting, it is also possible to introduce additional parameters (mask vectors) which allow for the fact that only part of the molecules may be similar. We apply our methods to a dataset of 31 steroid molecules which fall into three activity classes with respect to the binding activity to a common receptor protein. To investigate which molecular features distinguish the activity classes, we also propose a generalisation of the pairwise method to the simultaneous alignment of several molecules. The second part of this thesis is concerned with the dynamic aspect of molecular shapes. Here, we consider a dataset containing time series of DNA configurations which have been obtained using molecular dynamic simulations. For each considered DNA duplex, both a damaged and an undamaged version are available, and the objective is to investigate whether or not the damage induces a significant difference to the the mean shape of the molecule. To do so, we consider bootstrap hypothesis tests for the equality of mean shapes. In particular, we investigate the use of a computationally inexpensive algorithm which is based on the Procrustes tangent space. Two versions of this algorithm are proposed. The first version is designed for independent configuration matrices while the second version is specifically designed to accommodate temporal dependence of the configurations within each group and is hence more suitable for the DNA data.

The similarity between two shapes is typically calculated by measuring how well the properties and the spatial organization of the primitives forming the shapes agree. But, when this calculations are done independent from the context, i.e. the whole set of shapes in the experiments, a priori significance to the primitives is assigned, which may cause problematic similarity measures. A possible way of using context information in similarity measure between shape A and shape B is using the category information of shape B in calculations. In this study, shapes are represented as depth-1 shape trees and the dissimilarity between two shapes is computed by using an approximate tree matching algorithm. The category information is created as the union of shape trees that are in the same category and this information guides the matching process between a query shape and a shape whose category is known.

This thesis deals with enumerative combinatorics applied to three different objects related to partition shapes, namely tableaux, restricted words, and Bruhat intervals. The main scientific contributions are the following. Paper I: Let the sign of a standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. A conjecture by Richard Stanley says that the sum of the signs of all SYTs with n squares is 2^[n/2]. We prove a generalisation of this conjecture using the Robinson-Schensted correspondence and a new concept called chess tableaux. The proof is built on a remarkably simple relation between the sign of a permutation pi and the signs of its RS-corresponding tableaux P and Q, namely sgn(pi) = (−1)^v sgn(P)sgn(Q), where v is the number of disjoint vertical dominoes that fit in the partition shape of P and Q. The sign-imbalance of a partition shape is defined as the sum of the signs of all standard Young tableaux of that shape. As a further application of the sign-transferring formula above, we also prove a sharpening of another conjecture by Stanley concerning weighted sums of squares of sign-imbalances. Paper II: We generalise some of the results in paper I to skew tableaux. More precisely, we examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a surprisingly simple generalisation of the ordinary non-skew formula above. As an application, we find vanishing weighted sums of squares of sign-imbalances, thereby generalising a variant of Stanley’s second conjecture. Paper III: The following special case of a conjecture by Loehr and Warrington was proved by Ekhad, Vatter, and Zeilberger: There are 10^n zero-sum words of length 5n in the alphabet {+3,−2} such that no consecutive subword begins with +3, ends with −2, and sums to −2. We give a simple bijective proof of the conjecture in its original and more general setting where 3 and 2 are replaced by any relatively prime positive integers a and b, 10^n is replaced by ((a+b) choose a)^n, and 5n is replaced by (a+b)n. To do this we reformulate the problem in terms of cylindrical lattice walks which can be interpreted as the south-east border of certain partition shapes. Paper IV: We characterise the permutations pi such that the elements in the closed lower Bruhat interval [id,pi] of the symmetric group correspond to non-capturing rook configurations on a skew Ferrers board. These intervals turn out to be exactly those whose flag manifolds are defined by inclusions, as defined by Gasharov and Reiner. The characterisation connects Poincaré polynomials (rank-generating functions) of Bruhat intervals with q-rook polynomials, and we are able to compute the Poincaré polynomial of some particularly interesting intervals in the finite Weyl groups A_n and B_n. The expressions involve q-Stirling numbers of the second kind, and for the group A_n putting q = 1 yields the poly-Bernoulli numbers defined by Kaneko.
Ämnet för denna avhandling är enumerativ kombinatorik tillämpad på tre olika objekt med anknytning till partitionsformer, nämligen tablåer, begränsade ord och bruhatintervall. Dom viktigaste vetenskapliga bidragen är följande. Artikel I: Låt tecknet av en standardtablå vara tecknet hos permutationen man får om man läser tablån rad för rad från vänster till höger, som en bok. En förmodan av Richard Stanley säjer att teckensumman av alla standardtablåer med n rutor är 2^[n/2]. Vi visar en generalisering av denna förmodan med hjälp av Robinson-Schensted-korrespondensen och ett nytt begrepp som vi kallar schacktablåer. Beviset bygger på ett anmärkningsvärt enkelt samband mellan tecknet hos en permutation pi och tecknen hos dess RS-motsvarande tablåer P och Q, nämligen sgn(pi)=(-1)^v sgn(P)sgn(Q), där v är antalet disjunkta vertikala dominobrickor som får plats i partitionsformen hos P och Q. Teckenobalansen hos en partitionsform definieras som teckensumman av alla standardtablåer av den formen. Som en ytterligare tillämpning av formeln för teckenöverföring ovan bevisar vi också en starkare variant av en annan förmodan av Stanley som handlar om viktade summor av kvadrerade teckenobalanser. Artikel II: Vi generaliserar några av resultaten i artikel I till skeva tablåer. Närmare bestämt undersöker vi hur teckenegenskapen överförs av Sagan och Stanleys skeva Robinson-Schensted-korrespondens. Resultatet är en förvånansvärt enkel generalisering av den vanliga ickeskeva formeln ovan. Som en tillämpning visar vi att vissa viktade summor av kvadrerade teckenobalanser blir noll, vilket leder till en generalisering av en variant av Stanleys andra förmodan. Artikel III: Följande specialfall av en förmodan av Loehr och Warrington bevisades av Ekhad, Vatter och Zeilberger: Det finns 10^n ord med summan noll av längd 5n i alfabetet {+3,-2} sådana att inget sammanhängande delord börjar med +3, slutar med -2 och har summan -2. Vi ger ett enkelt bevis för denna förmodan i dess ursprungliga allmännare utförande där 3 och 2 byts ut mot vilka som helst relativt prima positiva heltal a och b, 10^n byts ut mot ((a+b) över a)^n och 5n mot (a+b)n. För att göra detta formulerar vi problemet i termer av cylindriska latticestigar som kan tolkas som den sydöstra gränslinjen för vissa partitionsformer. Artikel IV: Vi karakteriserar dom permutationer pi sådana att elementen i det slutna bruhatintervallet [id,pi] i symmetriska gruppen motsvarar ickeslående tornplaceringar på ett skevt ferrersbräde. Dessa intervall visar sej vara precis dom vars flaggmångfalder är definierade av inklusioner, ett begrepp introducerat av Gasharov och Reiner. Karakteriseringen skapar en länk mellan poincarépolynom (ranggenererande funktioner) för bruhatintervall och q-tornpolynom, och vi kan beräkna poincarépolynomet för några särskilt intressanta intervall i dom ändliga weylgrupperna A_n och B_n. Uttrycken innehåller q-stirlingtal av andra sorten, och sätter man q=1 för grupp A_n så får man Kanekos poly-bernoullital.
QC 20100818

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 122-141).
Motion capture has revolutionized entertainment and influenced fields as diverse as the arts, sports, and medicine. This is despite the limitation that it tracks only a small set of surface points. On the other hand, 3D scanning techniques digitize complete surfaces of static objects, but are not applicable to moving shapes. I present methods that overcome both limitations, and can obtain the moving geometry of dynamic shapes (such as people and clothes in motion) and analyze it in order to advance computer animation. Further understanding of dynamic shapes will enable various industries to enhance virtual characters, advance robot locomotion, improve sports performance, and aid in medical rehabilitation, thus directly affecting our daily lives. My methods efficiently recover much of the expressiveness of dynamic shapes from the silhouettes alone. Furthermore, the reconstruction quality is greatly improved by including surface orientations (normals). In order to make reconstruction more practical, I strive to capture dynamic shapes in their natural environment, which I do by using hybrid inertial and acoustic sensors. After capture, the reconstructed dynamic shapes are analyzed in order to enhance their utility. My algorithms then allow animators to generate novel motions, such as transferring facial performances from one actor onto another using multi-linear models. The presented research provides some of the first and most accurate reconstructions of complex moving surfaces, and is among the few approaches that establish a relationship between different dynamic shapes.
by Daniel Vlasic.
Ph.D.

Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 53-59).
Given a 3D shape, humans are capable of telling whether it looks natural. This shape priors, namely the perception of whether a shape looks realistic, are formed over years of our interactions with surrounding 3D objects, and go beyond simple definition of objects. In this thesis, we propose two models, 3D Generative Adversarial Network and ShapeHD, to learn shape priors from existing 3D shapes via generative-adversarial modeling, pushing the limits of shape generation, single-view shape completion and reconstruction. For shape generation, we demonstrate that our 3D-GAN generates high-quality 3D objects, and our unsupervisedly learned features achieve impressive performance on 3D object recognition, comparable with those of supervised learning methods; for single-view shape completion and reconstruction, we show that ShapeHD recovers fine details for 3D shapes, and outperforms state-of-the-art by a large margin on both tasks.
by Chengkai Zhang.
M. Eng.

Compact representations of three dimensional objects are very often used in computer graphics to create effective ways to analyse, manipulate and transmit 3D models. Their ability to abstract from the concrete shapes and expose their structure is important in a number of applications, spanning from computer animation, to medicine, to physical simulations. This thesis will investigate new methods for the generation of compact shape representations. In the first part, the problem of computing optimal PolyCube base complexes will be considered. PolyCubes are orthogonal polyhedra used in computer graphics to map both surfaces and volumes. Their ability to resemble the original models and at the same time expose a very simple and regular structure is important in a number of applications, such as texture mapping, spline fitting and hex-meshing. The second part will focus on medial descriptors. In particular, two new algorithms for the generation of curve-skeletons will be presented. These methods are completely based on the visual appearance of the input, therefore they are independent from the type, number and quality of the primitives used to describe a shape, determining, thus, an advancement to the state of the art in the field.

Computational modeling of part relations of shapes is a challenging problem that has been addressed by many researchers since sixties. The most important source of the difficulty is the continuous nature of shapes, which makes the expression of shape very difficult in terms of discrete parts. When discrete parts are combined, they fuse and yield new parts, i.e. parts emerge. There is a number of methods that support emergent part detection. However all of these methods are based on strong assumptions in terms of what constitute a part. There is a need for a generic solution that treats a shape independently of any restriction resulting from analytical, geometrical, or logical abstractions. To this end, we have developed two novel strategies, which can be used both separately and jointly. Both strategies are relatable to the algebraic formalization of shape grammars (by Stiny). In the course of this thesis work, we have introduced a novel data structure called Over-Complete Graph to address the problem of part embedding in the existence of discrete registration marks
and we have developed a novel and robust method for the automatic selection of registration marks. Both developments are certainly useful for other visual problems. On the application side, we have tested our techniques on puzzling Seljuk patterns (from Kayseri) to demonstrate how the developed techniques give way to computational creativity. Apart from the techniques we have developed, the most important contribution of our work is that shapes are treated as perceived wholes rather than composed, as compellingly demonstrated by Seljuk pattern experiments.

Comparing contours is an important problem in content-based image retrieval and object recognition. While humans can easily assess the similarity of two contours, a generic algorithm for approximating this ‘perceptual distance’ has proved elusive. We argue that a multiscale approach is required for this task and introduce a conceptually simple yet highly effective segment-based algorithm (Hierarchical Procrustes Matching (HPM)) which outperforms existing techniques on benchmark retrieval tests. Whereas HPM is designed to match complete contours, many real-world applications of shape matching involve partial occlusion and clutter. Probabilistic approaches to shape matching are particularly well-equipped to handle these problems, yet previous work in this area has focused on matching unordered point sets rather than contours. After reviewing the basic ideas behind probabilistic matching, we show how it can be extended to handle both contours and part-based shapes. In the final chapters of the thesis, we move from pair wise matching to the more complex problem of modelling shape classes. We present linear and nonlinear generative probabilistic models for both contours and unordered point sets and apply these to a variety of data sets. A particularly interesting finding is that the nonlinear contour model performs very well on a benchmark correspondence test relative to state-of-the-art alternatives.

The evolution of technology in the textile industry reached the design of embroidery patterns for machine embroidery. In order to create quality designs the shapes to be embroidered need to be segmented into regions that define different parts. One of the objectives of our research is to develop a method to automatically segment the shapes and by doing so making the process faster and easier. Shape analysis is necessary to find a suitable method for this purpose. It includes the study of different ways to represent shapes. In this thesis we focus on shape representation through its skeleton. We make use of a shape's skeleton and the shape's boundary through the so-called feature transform to decide how to segment a shape and where to place the segment boundaries. The direction of stitches is another important specification in an embroidery design. We develop a technique to select the stitch orientation by defining direction lines using the skeleton curves and information from the boundary. We compute the intersections of segment boundaries and direction lines with the shape boundary for the final definition of the direction line segments. We demonstrate that our shape segmentation technique and the automatic placement of direction lines produce sufficient constrains for automated embroidery designs. We show examples for lettering, basic shapes, as well as simple and complex logos.

Detecting objects in motion is a fundamental task that the visual system executes in everyday life in order for us to navigate safely through -- and interact with -- the environment. In order to make appropriate responses to moving objects, such as avoiding a moving branch or catching a ball, the visual system needs to precisely calculate the path an object is travelling. To develop computational models for the determination of such motion, we should first determine how accurately the visual system judges the direction of motion of simple shapes. Tracking of 2D features is, in theory, suffIcient to determine the direction of motion of objects in the fronto-parallel plane. However, large perceptual deviations have been observed for single lines containing features when they are in translation along non-cardinal axes. I have found that, surprisingly, such perceptual deviations also exist for progressively more complex shapes with multiple features such as crosses, squares, rectangles and octagons for translation along non-cardinal axes. When motion is on cardinal axes, typically no or only small perceptual deviations are observed. It is proposed that the perceptual deviations are linked with attraction towards static cues. These cues are the symmetry axes of the object and cardinal reference axes. When these axes are not aligned with the direction of motion, observers perceive motion biased towards them giving rise to substantial perceptual biases. I then investigated if these perceptual deviations would vanish or give rise to a non-linear trajectory if the static object axes were made dynamic: for example by changing orientation whiles the object translates. Therefore, several combinations of rotations and translations were tested. Surprisingly, observers perceived a curved trajectory for both cardinal and non-cardinal axes of translation as long as the orientation of the object axis was close to the axis of translation. This suggests that an object in rotation and translation is wrongly perceived to "slide" on a curved trajectory despite the fact that it is actually rotating and translating along a straight line. This illusion is novel and might be a consequence of the fact that objects in nature often travel along their intrinsic axes of symmetry. A visual system that is confronted with making best use of often ambiguous signals may occasionally make incorrect assignments of motion along trajectories that are closer to the object's orientation than they actually are. . Next attention was turned from motion of rigid objects to investigating non- rigidly moving objects. In natural scenes objects often move non-rigidly with different features belonging to the same object moving in different directions. Such non-rigid motions include those of a swimming jellyfish or a beating heart. This study employed a simple stimulus of three (invisible) apertures with a line segment behind the central one and terminated line segments behind the other two which produces the percept of rigidly or non-rigidly moving lines depending on the terminator velocities. It was discovered that when the terminators were moving in similar directions (rigid or marginally non- rigid motions) the central segment was captured and its velocity given by the vector sum of the velocities of the two terminators. In these circumstances, the motion signal of the central segment did not appear to play a significant role. On the other hand, the segment showed resistance to capture and its motion signal did play a significant role when: (1) ·th~· terminators were moving in opposite directions (e.g. one up and to the right and one down and to the right) giving the percept of a contracting or expanding line, (2) the terminators were moving close to the normal of the line segment, (3) when only one terminator was present. Overall these findings suggest that the visual system computes a vector summation of terminator motions, with the motion signal of the central segment not playing a substantial role when the segment is captured but when capture is reduced the motion signal of the segment should appear as an integral part of the motion computation. A simple model, based on the experimental observations, could account for the data and provides a promising, unified computational approach for signal integration across space in the presence of rigid and non-rigid motion. Abstract 11.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.
Includes bibliographical references (p. 79-83).
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.
by Pedro F. Felzenszwalb.
Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 159-167).
In order to gain a deeper understanding of the Standard Model of particle physics and test its limitations, it is necessary to carry out accurate calculations to compare with experimental results. Event shapes provide a convenient way for compressing the extremely complicated data from each collider event into one number. Using eective theories and studying the appropriate limits, it is possible to probe the underlying physics to a high enough precision to extract interesting information from the experimental results. In the initial sections of this work, we use a particular event shape, C-parameter, in order to make a precise measurement of the strong coupling constant, s. First, we compute the e+e- C-parameter distribution using the Soft-Collinear Eective Theory (SCET) with a resummation to N³LL' accuracy of the most singular partonic terms. Our result holds for C in the peak, tail, and far-tail regions. We treat hadronization effects using a field theoretic nonperturbative soft function, with moments [omega]n, and perform a renormalon subtraction while simultaneously including hadron mass effects. We then present a global fit for [alpha]s(mZ), analyzing the available C-parameter data in the resummation region, including center-of-mass energies between Q = 35 and 207 GeV. We simultaneously also fit for the dominant hadronic parameter, [omega]1. The experimental data is compared to our theoretical prediction, which has a perturbative uncertainty for the cross section of ~/= 2:5% at Q = mZ in the relevant t region for [alpha]s(mZ) and [omega]1. We find [alpha]s(mZ) = 0:1123 +/- 0:0015 and [omega]1 = 0:421 +/- 0:063 GeV with X² / =dof = 0:988 for 404 bins of data. These results agree with the prediction of universality for [omega]₁ between thrust and C-parameter within 1-[sigma]. The latter parts of this study are dedicated to taking SCET beyond leading power in order to further increase the possible precision of calculations. On-shell helicity methods provide powerful tools for determining scattering amplitudes, which have a one-to-one correspondence with leading power helicity operators in SCET away from singular regions of phase space. We show that helicity based operators are also useful for enumerating power suppressed SCET operators, which encode subleading amplitude information about singular limits. In particular, we present a complete set of scalar helicity building blocks that are valid for constructing operators at any order in the SCET power expansion. We also describe an interesting angular momentum selection rule that restricts how these building blocks can be assembled.
by Daniel W. Kolodrubetz.
Ph. D.

The effects of gravity on the two-dimensional equilibrium shapes (ES) of crystals and menisci are investigated for different geometries (positions) of the substrate. In the gravity-free case, the equilibrium crystal shape (ECS) is characterized by a scale invariance. The presence of gravity breaks the scale invariance and the resulting ECS changes as the volume of the crystal V is changed. Moreover, the presence of gravity breaks the translational invariance along the direction it acts. Physically realized by the necessity of a support, this is manifested by the existence of an inhomogeneous effective pressure P_eff, which divides the space into two regions, with P_eff either negative or positive. The ECS changes as the crystal passes from one region to another, being concave where P_eff < 0, and convex where P_eff > 0. In all cases it was possible to express the corresponding ECS in terms of the gravity-free one. For the hung crystal, i.e., a crystal pinned to a vertical wall at the top, it is shown that some orientations are missing from the ECS that otherwise will be present in the gravity-free ECS, adsorbed on the same substrate. Thus, facets could disappear from the crystal shape as the volume V or the gravitational acceleration g is increased. A critical volume V_c is found, so that if the crystal volume V exceeds V_c, the crystal cannot be pinned. The ECS can exhibit both concave and convex portions. For a crystal, pinned to a vertical wall at its lower end, we find that it will never develop a concave part. On the other hand, new orientations, absent from the gravity-free crystal, will be present on its ECS. The ES of a free and pinned crystal meniscus is also solved and an expression for the excess (depleted) volume AV is derived. The solution for the crystal meniscus between two walls is also presented. For the pendant crystal, i.e., a crystal hanging from a horizontal support, we find that it can exhibit both concave and convex portions on its ECS. When it develops a concave part, new orientations will appear, compared to the gravity-free case. An intuitive stability criterion is introduced, according to which only crystals wetting the substrate can develop a concave portion before they break. The treatment of a crystal on an inclined substrate shows the complications that arise in determining the ES for a general position of the support as a result of the conflict between the directions associated with gravity and support. An expression for the facet length in the presence of gravity is obtained that is valid for all types of support. For crystal shapes that display a concave portion it offers a very convenient way to experimentally measure step free energies. Thus, by breaking scale invariance, the presence of gravity allows absolute measures of surface energy in contrast to the gravity-free case, where the facet length is proportional to the step free energy by an unknown scale.
Ph. D.

Thesis (M.S.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Fire Protection Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

In this document, we consider coreset and total sensitivity for shape fitting problems. The shape fitting problems that are of considerable interest include: (1) (j, k) projective clustering problem, and (2) circle fitting problem on the plane. In (j, k) projective clustering, we are given a finite set of points P in d-dimensional Euclidean space, and the goal is to find a shape, which is a k-tuple j-flats (affine j-subspace), that best fits P. In circle fitting problem, given an input point set P ⊂ ℝ2, the goal is to find a circle that best fits P. In L1-fitting, the cost of fitting P to a shape F is defined as Σp∈p dist(p, F), where dist(p, F) is the cost of assigning P to F, while in F∞-fitting, maxp∈p dist(pF). We focus on L1-fitting. A coreset is a compact representation of the input point set. For a shape fitting problem, a coreset for a point set P is a weighted point set, with the property that the cost of fitting the coreset to a shape F approximates the cost of fitting P to F, for every shape in the family of shapes. Coreset of small (e.g., constant) cardinality is of interest, because one can afford to use off-shelf, perhaps computationally expensive algorithms to solve the geometric optimization problem for the coreset, and a good solution for the coreset is guaranteed to be also good for the original input. Depending on whether the fitting problem is L1 fitting or L∞ fitting, the coreset is L1 coreset or L∞ coreset, respectively. One way to obtain small coreset is via non-uniform sampling, using the framework by [30]. Given a point set P, the “importance" of each point p∈P is quantified by its sensitivity σp(p), and the total sensitivity of P is the summation of sensitivities at every point, Σp∈PσP(p). It is shown that if one samples the point set P according to the probability distribution imposed by the sensitivities, one obtains coresets of size roughly O(�2P). Total sensitivity of a shape fitting problem quantifies the complexity of the shapes, which is the main object being studied in this thesis. We briefly summarize the main results below. We establish the connection between L∞ coreset and L1 coreset. In particular, we show that shape fitting problems with small L∞ coreset also have small L1 coreset. This connection allows us to use existing work on L∞ coreset to obtain small L1 coreset for the aforementioned shape fitting problems (variants of (j,k) projective clustering, and circle fitting). Consequently, we obtain the first near-linear algorithm for integer (j,k) projective clustering in high dimension. We show that the total sensitivity of shape fitting problem in ℝd depends on the intrinsic dimension of the shapes. For many shape fitting problems, the shapes are low-dimensional: for example, in (j,k) projective clustering, each shape is a union of k j-flats, and each k-tuple of j-flats is contained in a subspace of dimension O(jk). This fact allows us to get a dimension-reduction type result for the (j,k)-projective clustering problems. Specifically, for integer (j,k) projective clustering, the upper bounds of the total sensitivity is improved from O((log n)f(d,j,k)) to O((log n)f(j,k)), where f (j, k) is a function depending on only j, and k, and no longer on the possibly large d. We obtain coreset of size O((log n)2), using the connection between L∞ coreset and L1 coreset. We show that circle fitting problem does not admit coreset of size o((log n). In particular, we show a construction of a point set, such that any 1/100-coreset of P has size at least Ω(log n).

A method of locating structural damage is developed and tested to aid in the evaluation of structural health. This method will help minimize the cost of structural inspection and repair by informing engineers of where damage, due a seismic event, has occurred before the removal of finishes for visual inspection. This thesis begins to answer the question “can structural damage be detected solely through analysis of experimentally measured mode shapes?” The work encompasses construction of a test structure, with three braces that can be repeatedly engaged or dis-engaged, thus allowing for testing of a variety of braced configurations. For this thesis, damage is assumed to cause a change in stiffness. Experimental testing is conducted to acquire mode shapes and frequencies for the 6 dominant modes of the test structure. Lastly, the data is analyzed to identify the configuration of braces engaged on the structure. The accuracy of the method is assessed by the number of configurations that it correctly predicts and the confidence of the predictions.

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Quando a cidade se expande, o que veio primeiro, transporte ou desenvolvimento urbano? Transporte pode ser usado para promover mudanças urbanas? Que tipo de mudanças no ambiente construído podemos esperar dos investimentos em transporte? Transporte é um fator crítico ao se explicar a morfologia de uma área urbana. Ao mesmo tempo que aspectos históricos de transporte podem determinar a forma das cidades, novos investimentos também têm o potencial de alterar o ambiente construído ao redor. O estudo da forma urbana e do transporte urbano é um dos elementos que unem os dois ensaios empíricos que compõem esta tese. Outro aspecto que se repete entre os capítulos deste manuscrito é a análise empírica baseada em São Paulo. Na literatura sobre o desenvolvimento urbano da cidade São Paulo, faltam resultados empíricos que evidenciem a conexão entre o desenvolvimento do transporte rodoviário e da expansão urbana periférica na cidade. No Capítulo 1, usamos modelos de causalidade de Granger e dados históricos sobre transporte e desenvolvimento urbano para medir o co-desenvolvimento desses fatores na cidade entre 1881 e 2013. Os resultados confirmam a hipótese da literatura ao mostrar que a expansão urbana seguiu a implantação do transporte rodoviário, mas esse fenômeno também avançou na direção oposta, com expansão urbana puxando a construção de novas ruas e avenidas. Exploramos como as decisões tomadas na década de 1930 priorizaram o desenvolvimento rodoviário em vez do transporte de massa, que depois disso não foi mais capaz de acompanhar a expansão urbana de São Paulo. No entanto, encontramos evidências de que os investimentos em transporte de massa têm sido historicamente seguidos por significativo adensamento de edificações em áreas adjacentes. No Capítulo 2, desenvolvemos uma análise empírica de curto prazo usando uma gama mais ampla de variáveis para explorar como investimentos recentes em transporte de média e alta capacidade estão alterando regiões paulistanas, com atenção especial a áreas periféricas. Desde a década de 1980, a condição urbana de muitas áreas periféricas melhorou significativamente, e famílias de renda média estão mudando para algumas dessas “periferias melhoradas”. Usamos dados socioeconômicos altamente desagregados espacialmente para 2000 e 2010 e o método econométrico de diferenças-em-diferenças para avaliar o impacto de novos corredores de ônibus, linhas de metrô e estações de trem construídos no início dos anos 2000. Nossos resultados mostram que os ganhos de acessibilidade gerados por essas infraestruturas de transporte público atraíram novos projetos imobiliários, aumentaram o número de empregos per capita e levaram a uma melhor cobertura de alguns serviços públicos nas áreas periféricas vizinhas, contribuindo para sua consolidação urbana. Esse resultado, somado aos mencionados achados históricos, revela o potencial que investimentos em transportes têm para alterar o ambiente construído, seja estimulando a expansão urbana periférica, induzindo adensamento ou contribuindo para a consolidação urbana. O uso de investimentos em transporte público para induzir transformações urbanas recebe mais atenção na medida em que o conceito de desenvolvimento orientado ao transporte sustentável (DOTS) atrai mais adeptos e fica evidente que os planos de transporte e uso do solo urbano devem ser integrados. Os fatores estão inter-relacionados e intervenções públicas coordenadas têm o potencial de produzir resultados sinérgicos. No entanto, investimentos em transporte coletivo estão entre as políticas urbanas mais complexas e apresentam desafios específicos para estudos de políticas públicas, principalmente relacionados à coordenação intra e interfederativa em sua implementação.
When the city sprawls, what came first, transportation or urban development? Can transportation be used to promote urban changes? What kind of changes in the built environment can we expect from transportation investments? Transportation is a critical factor explaining the morphology of an urban area. While historical aspects of transportation can determine the form of cities, new investments may also affect and change the surrounding built environment. The study of urban form and urban transportation is one of the elements that unite the two empirical essays comprising this thesis. Another aspect that recurs among the chapters of this manuscript is empirical analysis based in São Paulo. There is a lack of empirical results evidencing the interconnected development of road transportation and peripheral urban sprawl in São Paulo. In Chapter 1, we used Granger causality models and historical data on transportation and urban development to measure the co-development of these factors in the city between 1881 and 2013. Our findings confirm the hypothesis in the literature by showing that urban sprawl followed road transportation deployment, but this phenomenon also moved in the opposite direction, with sprawl pulling construction of new roadways. We explore how critical juncture decisions made during the 1930’s have prioritized road development instead of mass transit, that after that was no more capable to follow São Paulo’s urban sprawl. Nonetheless, we found evidence that mass transit investments have historically been followed by significant building densification in surrounding areas. In Chapter 2, we developed a short-term empirical analysis using a wider range of variables to explore how recent mass transportation investment is currently changing São Paulo’s neighborhoods, with particular attention to peripheral areas. Since the 1980`s, the urban condition of many peripheral areas has improved significantly, and middle-income families are moving to some of this “upgraded peripheries.” We used highly spatial disaggregated socioeconomic data from 2000 and 2010 and a differences-in-differences econometric method to access the impact of new bus corridors, subway lines, and train stations built in the early 2000s. Our findings show that the accessibility gains generated by these public transportation facilities have attracted new real estate projects, increased the number of jobs per capita, and led to better provision of some public services in surrounding peripheral areas, contributing to their urban consolidation. This result, added to the mentioned historical findings, reveals the potential which transportation investment has to change the built environment, whether by stimulating peripheral urban sprawl, inducing densification, or contributing to urban consolidation. The use of transit investments to induce urban transformations is receiving new attention as the concept of transit oriented development (TOD) attracts more adepts and evident that transportation and urban land use plans must be integrated. The factors are interrelated, and coordinated public interventions therefore have the potential to produce synergistic results. However, mass transit investments are among the most complex urban policies and present specific challenges for public policy studies, primarily related to intra- and inter-federative coordination in their implementation.