An Investigation into 2D and 3D Shapes Perception

Numerous research results support the finding that a product\u27s visual appearance is important. In particular, end products or services that have a direct product-user interaction have to be developed in accordance with the taste of the user and the market. The user-centered product should be designed and created according to both the technical requirements and the customer needs, but it should also differentiate itself from the competition. The shape of a product, whether we observe it in 2D or 3D, should communicate various intangible meanings. Our aim was to investigate whether the meaning of bipolar adjectives varies when observing samples of 2D and 3D shapes. The study was conducted using 2D shape contour samples and interactive 3D extruded models that could be rotated in virtual space. In order to determine the relationship between the shape and the user\u27s perception of it, Kansei engineering methodology was used. We collected data with Semantic differential survey using five level Likert scale. The results revealed minor deviations in the users’ perceptions of the 2D and 3D sample shapes

Structuring 3D Medial Skeletons: A Comparative Study

International audienceMedial skeletons provide an effective alternative to boundary or volumetric representations for applications that focus on shape structure. This capability is provided by the skeletal structure, i.e., the curves and surfaces computed from centers of maximally inscribed balls by a process called structuration. Many several structuration methods exist, all having various challenges in terms of delivering a high-quality medial skeleton. This paper provides a first overview of existing structuration methods. We formally define the skeletal structure by giving its theoretical properties, and use these properties to propose quality criteria for structurations. We next review existing structuration methods and compare them using the established criteria. The obtained insights help both practitioners in choosing a suitable structuration method and researchers in further perfecting such methods

3D shape matching and registration : a probabilistic perspective

Dense correspondence is a key area in computer vision and medical image analysis. It has applications in registration and shape analysis. In this thesis, we develop a technique to recover dense correspondences between the surfaces of neuroanatomical objects over heterogeneous populations of individuals. We recover dense correspondences based on 3D shape matching. In this thesis, the 3D shape matching problem is formulated under the framework of Markov Random Fields (MRFs). We represent the surfaces of neuroanatomical objects as genus zero voxel-based meshes. The surface meshes are projected into a Markov random field space. The projection carries both geometric and topological information in terms of Gaussian curvature and mesh neighbourhood from the original space to the random field space. Gaussian curvature is projected to the nodes of the MRF, and the mesh neighbourhood structure is projected to the edges. 3D shape matching between two surface meshes is then performed by solving an energy function minimisation problem formulated with MRFs. The outcome of the 3D shape matching is dense point-to-point correspondences. However, the minimisation of the energy function is NP hard. In this thesis, we use belief propagation to perform the probabilistic inference for 3D shape matching. A sparse update loopy belief propagation algorithm adapted to the 3D shape matching is proposed to obtain an approximate global solution for the 3D shape matching problem. The sparse update loopy belief propagation algorithm demonstrates significant efficiency gain compared to standard belief propagation. The computational complexity and convergence property analysis for the sparse update loopy belief propagation algorithm are also conducted in the thesis. We also investigate randomised algorithms to minimise the energy function. In order to enhance the shape matching rate and increase the inlier support set, we propose a novel clamping technique. The clamping technique is realized by combining the loopy belief propagation message updating rule with the feedback from 3D rigid body registration. By using this clamping technique, the correct shape matching rate is increased significantly. Finally, we investigate 3D shape registration techniques based on the 3D shape matching result. Based on the point-to-point dense correspondences obtained from the 3D shape matching, a three-point based transformation estimation technique is combined with the RANdom SAmple Consensus (RANSAC) algorithm to obtain the inlier support set. The global registration approach is purely dependent on point-wise correspondences between two meshed surfaces. It has the advantage that the need for orientation initialisation is eliminated and that all shapes of spherical topology. The comparison of our MRF based 3D registration approach with a state-of-the-art registration algorithm, the first order ellipsoid template, is conducted in the experiments. These show dense correspondence for pairs of hippocampi from two different data sets, each of around 20 60+ year old healthy individuals

Geometrical positioning of a flow diverter in case of aneurysm

Aquest projecte de final de carrera s'emmarca dins un estudi de recerca d'un estudiant de doctorat, Julien Egger de la “Swiss Federal Institute of Technology of Zürich (ETH)”. Té com a finalitat el desenvolupament d’un programa per optimitzar el posicionament virtual d'un desviador de flux (FD) dins d'una artèria en el cas d'un aneurisma, definint un aneurisma com la dilatació de l’artèria causada per la degradació de la paret. També servirà de base per després fer diferents simulacions de flux i així tenir una anàlisi de sensibilitat sobre les diferents característiques del FD, una vegada implementat en un pacient. Concretament, saber com el FD té inflüència sobre l'artèria, en el flux sanguini, ja que l'objectiu d'utilitzar un FD és canviar la direcció del flux per tal d’evitar que entri a l'interior del sac, fet que portaria a un augment del mateix podent-ne provocar l’explosió. A més a més, trobar una solució per resoldre els possibles problemes en cas que no funcioni i per donar més informació als cirurgians sobre el procediment de implementació. Per exemple, pot servir alhora de comparar les diferents opcions en cas d'una bifurcació, en quina direcció ha d'anar el FD? Per provar nous enfocaments pràctics (dos FD un dins l'altre ), etc. Per tant, donada les dades d’un volum en tres dimensions obtingut a partir d’una CT d'un pacient, el mètode desenvolupat en aquest treball té per objectiu el posicionament d'un FD virtual dins de l’artèria. El procediment emprat es pot dividir en els següents subpassos: - Obtenir una representació en 3D de la paret de l'artèria per mitjà de la segmentació. - Trobar la representació matemàtica de la línia central de l'artèria per utilitzar-la com a base per a la descripció geomètrica del desviador. - Donades les característiques del FD considerat, adaptar la geometria al llarg de la línea central per tal que encaixi amb l’artèria. - Exportar i guardar la representació volumètrica del FD en un format determinat, compatible amb els productes comercials utilitzats per a mallats volumètrics i simulació de flux. Per acabar dir que comparacions qualtitatives del posicionament virtual de FD obtingut a partir d’aquest mètode i el posicionament de FD obtingut a partir de dades reals de pacients són presentats en aquest projecte

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

Novel approaches to statistical shape modelling of bone

The femur is the longest bone in the human body and serves the important purposes of load-bearing and allowing bipedal locomotion. Accurate modelling of the variation in shape within the healthy adult population can be useful for a variety of applications: from the mere anatomical description of its features, in order to better understand its function, to more complex tasks such as pathology detection or surgical planning. Statistical Shape Modelling (SSM) is a well-established technique that enables to capture the variability within a set of training shapes and describes it with a reduced set of variables. The aim of this thesis is to evaluate the performance of a SSM based on a point cloud representation of shape, and introduce and test subsequent improvements to the modelling process that can increase its clinical relevance and scope of application. The standard approach to SSM employs a dimension-reducing technique, generally by means of Principal Component Analysis (PCA). However, this approach favours the compactness of the model, thus not focusing on other aspects that may be more relevant to clinical practice. Although rotation of the principal components is commonly performed as a post-processing step in statistical analysis involving PCA, it is not routinely applied in SSM. By applying this class of rotation, the components' effects are more localised, allowing a better interpretation, understanding and classification of pathological deformities. Among other possible representations, the Medial Axis Transform (MAT) could offer a further insight into shape modelling, since it allows the information about thickness to be decoupled from the rest of the shape. SSMs based on this representation can lead to a di erent perspective on the understanding of femoral anatomy and function,and can also enable the reconstruction of the complete anatomy starting from a reduced set of features, with diverse applications in the elds of surgical planning, forensic science and paleontology

Efficient computation of discrete Voronoi diagram and homotopy-preserving simplified medial axis of a 3d polyhedron

The Voronoi diagram is a fundamental geometric data structure and has been well studied in computational geometry and related areas. A Voronoi diagram defined using the Euclidean distance metric is also closely related to the Blum medial axis, a well known skeletal representation. Voronoi diagrams and medial axes have been shown useful for many 3D computations and operations, including proximity queries, motion planning, mesh generation, finite element analysis, and shape analysis. However, their application to complex 3D polyhedral and deformable models has been limited. This is due to the difficulty of computing exact Voronoi diagrams in an efficient and reliable manner. In this dissertation, we bridge this gap by presenting efficient algorithms to compute discrete Voronoi diagrams and simplified medial axes of 3D polyhedral models with geometric and topological guarantees. We apply these algorithms to complex 3D models and use them to perform interactive proximity queries, motion planning and skeletal computations. We present three new results. First, we describe an algorithm to compute 3D distance fields of geometric models by using a linear factorization of Euclidean distance vectors. This formulation maps directly to the linearly interpolating graphics rasterization hardware and enables us to compute distance fields of complex 3D models at interactive rates. We also use clamping and culling algorithms based on properties of Voronoi diagrams to accelerate this computation. We introduce surface distance maps, which are a compact distance vector field representation based on a mesh parameterization of triangulated two-manifolds, and use them to perform proximity computations. Our second main result is an adaptive sampling algorithm to compute an approximate Voronoi diagram that is homotopy equivalent to the exact Voronoi diagram and preserves topological features. We use this algorithm to compute a homotopy-preserving simplified medial axis of complex 3D models. Our third result is a unified approach to perform different proximity queries among multiple deformable models using second order discrete Voronoi diagrams. We introduce a new query called N-body distance query and show that different proximity queries, including collision detection, separation distance and penetration depth can be performed based on Nbody distance query. We compute the second order discrete Voronoi diagram using graphics hardware and use distance bounds to overcome the sampling errors and perform conservative computations. We have applied these queries to various deformable simulations and observed up to an order of magnitude improvement over prior algorithms

The Shock Scaffold for Representing 3D Shape

F. Leymarie and B. Kimia, "The Shock Scaffold for Representing 3D Shape", Proc. of 4th International Workshop on Visual Form (IWVF4). Published in "Visual Form 2001", Lecture Notes in Computer Science (LNCS 2059), Springer-Verlag, pp. 216-229, May 2001