Multiresolution editing for B-spline curves and surfaces

Since 1980 surface modeling has been used in industrial design, CAD and entertainment to create and represent complex forms. Even with this comparatively long history of development, challenges remain in free-form surface modeling. One such challenge is building surface creation and editing techniques that effectively balance the need for local control with the need to control the overall global shape, or sweep of the surface. This dissertation presents a multiresolution approach to the creation of surfaces that allows a designer to more easily manage this balance between local and global control. The techniques presented in this dissertation utilize a wavelet decomposition of B-spline curves and surfaces to allow a designer to easily develop the basic shape using lower level representations, and then seamlessly switch to higher level representations to achieve fine control over local features. The algorithms described in the dissertation are implemented in an interactive software system that is used to demonstrate their effectiveness in comparison to existing methods

Perancangan Dan Pembuatan Perangkat Lunak Visualisasi Obyek Tiga Dimensi Dengan Hierarchical B-Splines

Untuk merepresentasikan obyek yang terbentuk dari kurva dan permukaan irregular harus dipakai persamaan polinomial parametrik seperti polinom B-Splines. Polinom ini dapat dipakai untuk merepresentasikan dan memanipulasi kurva dan permukaan berbentuk bebas (free form). Beberapa sistem pemodelan dan animasi grafika komputer tiga dimensi manggunakan representasi B-splines untuk kurva dan permukaan karena properti-properti geometrik yang dimiliki seperti kehalusan (smoothness) dan pengontrolan terhadap kontinyuitas parametrik Cfl antar bag ian. Fungsi-fungsi spline memainkan aturan dasar pada beberapa analisa numerik dan pemodelan geometrik. Daerah hierarchical spline didefinisikan sebagai liniar span dari tensor produk B-spline dari grid level yang berbeda. Ide dasar dari metode ini sama dengan pendekatan-pendekatan sebelumnya, khususnya untuk konstruksi dari wavelets spline. Wavelets adalah tool matematik untuk fungsi-fungsi dekomposisi secara hierarchi, yang memungkinkan sebuah fungsi untuk dideskripsikan ke dalam bagian-bagian dari keseluruhan permukaan, dan detail yangdimiliki terbentuk dari permukaan luas ke permukaan sempit.Disini akan diberikan mekanisme seleksi untuk B-Splines, yang menjaminkebebasan liniet dengan menyertakan kontrol lokal secara lengkap dari penghalusan yang dapat dilakukan dengan menambah beberapa B-splines. Penyelesaian ruang spline rata mempunyai persamaan kegunaan dengan pendekatan polinomial diskontinyu. Selain itu, hirarki dasar B-Splines adalah stabil lemah, dimana kestabilannya tumbuh secara konstan seperti O(n), dimanadalah jumlah level-level grid. Lebih jauh lagi, disini akan didefinisikan quasi interpolant yang didasarkan pada adaptasi prinsip seleksi dan yang menyelesaikan pendekatan lokal optimal. Multilevel dan hirarki ruang B-spline ini sangat sesuai untuk approksimasi dan interpolasi data yang diacak. Approksimasi secara iterasi untuk algoritma dimana ruang spline dapat diadaptasi secara lokal ke dalam data yang diberikan. Tugas akhir ini mengembangkan metode untuk mengotomatisasi pembuatan permukaan B-spline dari himpunan (set) titik kontrol. Hasif dari permukaan hierarachi yang dibuat secara akurat dan ekonomis akan menghasilkan kembali sebuah mesh, yang bebas dari undulasi yang berlebihan pada level-level intermediate dan menghasilkan sebuah gambaran multiresolusi yang tepat untuk animasi dan pemodelan interaktif

Some Basis Function Methods for Surface Approximation

This thesis considers issues in surface reconstruction such as identifying approximation methods that work well for certain applications and developing efficient methods to compute and manipulate these approximations. The first part of the thesis illustrates a new fast evaluation scheme to efficiently calculate thin-plate splines in two dimensions. In the fast multipole method scheme, exponential expansions/approximations are used as an intermediate step in converting far field series to local polynomial approximations. The contributions here are extending the scheme to the thin-plate spline and a new error analysis. The error analysis covers the practically important case where truncated series are used throughout, and through off line computation of error constants gives sharp error bounds. In the second part of this thesis, we investigates fitting a surface to an object using blobby models as a coarse level approximation. The aim is to achieve a given quality of approximation with relatively few parameters. This process involves an optimization procedure where a number of blobs (ellipses or ellipsoids) are separately fitted to a cloud of points. Then the optimized blobs are combined to yield an implicit surface approximating the cloud of points. The results for our test cases in 2 and 3 dimensions are very encouraging. For many applications, the coarse level blobby model itself will be sufficient. For example adding texture on top of the blobby surface can give a surprisingly realistic image. The last part of the thesis describes a method to reconstruct surfaces with known discontinuities. We fit a surface to the data points by performing a scattered data interpolation using compactly supported RBFs with respect to a geodesic distance. Techniques from computational geometry such as the visibility graph are used to compute the shortest Euclidean distance between two points, avoiding any obstacles. Results have shown that discontinuities on the surface were clearly reconstructed, and th

Ensembles de niveaux robustes au speckle et recalage B-spline: application à la segmentation et l'analyse du mouvement cardiaque par des images ultrasons

L'analyse du mouvement local des parois du cœur dans des images ultrasonores est souvent utilisée pour diagnostiquer certaines malformations cardiaques. Malheureusement, cette modalité produit des images caractérisées par un niveau élevé de speckle, rendant difficile la détection des cavités. La thèse présente une méthode d'estimation du mouvement des cavités dans des images 2D. Nous proposons un nouveau modèle de level sets pour segmenter l'image. Ce modèle s'appuie sur une fonction d'arrêt adaptée au speckle. Celle-ci se démarque des fonctions habituelles en remplaçant le gradient par le coefficient de variation, une statistique robuste aux bruits multiplicatifs. De plus, nous renforçant cette fonction par un classificateur perceptron multicouche rendant plus fiable la détection de contours. Les résultats obtenus montrent un apport significatif en précision. L'estimation du mouvement se fait par un processus de recalage adaptatif qui calcule une B-spline hiérarchique. Cette méthode prend en entrée les courbes produites par la segmentation et estime la déformation en appliquant successivement l'algorithme ICP, une optimisation aux moindres carrés, et un raffinage hiérarchique. L'expérimentation montre que ce modèle aboutit à une approximation précise des déformations 2D des parois du cœu

ONLINE HIERARCHICAL MODELS FOR SURFACE RECONSTRUCTION

Applications based on three-dimensional object models are today very common, and can be found in many fields as design, archeology, medicine, and entertainment. A digital 3D model can be obtained by means of physical object measurements performed by using a 3D scanner. In this approach, an important step of the 3D model building process consists of creating the object's surface representation from a cloud of noisy points sampled on the object itself. This process can be viewed as the estimation of a function from a finite subset of its points. Both in statistics and machine learning this is known as a regression problem. Machine learning views the function estimation as a learning problem to be addressed by using computational intelligence techniques: the points represent a set of examples and the surface to be reconstructed represents the law that has generated them. On the other hand, in many applications the cloud of sampled points may become available only progressively during system operation. The conventional approaches to regression are therefore not suited to deal efficiently with this operating condition. The aim of the thesis is to introduce innovative approaches to the regression problem suited for achieving high reconstruction accuracy, while limiting the computational complexity, and appropriate for online operation. Two classical computational intelligence paradigms have been considered as basic tools to address the regression problem: namely the Radial Basis Functions and the Support Vector Machines. The original and innovative aspect introduced by this thesis is the extension of these tools toward a multi-scale incremental structure, based on hierarchical schemes and suited for online operation. This allows for obtaining modular, scalable, accurate and efficient modeling procedures with training algorithms appropriate for dealing with online learning. Radial Basis Function Networks have a fast configuration procedure that, operating locally, does not require iterative algorithms. On the other side, the computational complexity of the configuration procedure of Support Vector Machines is independent from the number of input variables. These two approaches have been considered in order to analyze advantages and limits of each of them due to the differences in their intrinsic nature

Multiresolution Surface Reconstruction For Hierarchical B-splines

This paper presents a method for automatically generating a hierarchical B-spline surface from an initial set of control points. Given an existing mesh of control points , a mesh with half the resolution , is constructed by simultaneously approximating the finer mesh while minimizing a smoothness constraint using weighted least squares. Curvature measures of are used to identify features that need only be represented in the finer mesh. The resulting hierarchical surface accurately and economically reproduces the original mesh, is free from excessive undulations in the intermediate levels and produces a multiresolution representation suitable for animation and interactive modelling. 1 Introduction Many 3D computer graphics modelling and animation systems use a B-spline representation for curves and surfaces because of their geometric properties such as smoothness and controllable C n parametric continuity between patches. However, the tensor product nature of the underlying paramete..