PRISM :: Browsing by Author "Samavati, Faramarz"

Browsing by Author "Samavati, Faramarz"

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Open Access
√3 Multiresolution by Local Least Squares: The Diagrammatic Approach
(2015-10-19) Bartels, Richard; Mahdavi-Amiri, Ali; Samavati, Faramarz
In [2, 3, 20, 21] the authors explored a construction to produce multiresolutions from given subdivisions. Certain assumptions carried through that work, two of which we wish to challenge: (1) that multiresolutions for irregular meshes have to be constructed on the fly rather than being prepared beforehand and (2) that the connectivity graph of the coarse mesh would have to be a subgraph of the connectivity graph of the fine mesh. Kobbelt's √3 subdivision [11] lets us engage both of these assumptions. With respect to (2), the √3, post-subdivision connectivity graph shares no interior edges with the pre-subdivision connectivity graph. With respect to (1), we observe that subdivision does not produce an arbitrary connectivity graph. Rather, there are local regularities that subdivision imposes on the fine mesh that are exploitable to establish, in advance, the decomposition and reconstruction filters of a multiresolution for an irregular coarse mesh.
Open Access
ACM: Atlas of Connectivity Maps
(2015-05-05) Mahdavi-Amiri, Ali; Samavati, Faramarz
Semiregular models are an important subset of the graphical models used in computer graphics. They are typically obtained by applying repetitive regular refinements on an initial arbitrary model and, as a result, their connectivity exhibits a high degree of regularity. Although data structures exist for regular or irregular models, a data structure designed to take advantage of this semiregularity is desirable. We introduce such a data structure called the atlas of connectivity maps (ACM), which efficiently represents semiregular models resulting from various types of refinements. This atlas maps the connectivity information of vertices and faces onto separate 2D domains called connectivity maps, and handles connectivity queries within each connectivity map using simple algebraic operations or between connectivity maps using a set of linear transformations. We demonstrate the effectiveness of ACM for use in subdivision, multiresolution, and Digital Earth applications. In addition, the generality of ACM has been examined on a variety of face-types (e.g. triangles, hexagons, quads) as well as uniform and adaptive refinements. We compare the performance of ACM to various data structures including the standard half-edge, and show that the performance of ACM is better than these available data structures in supporting important queries such as neighborhood finding and hierarchical traversal.
Open Access
Balanced Multiresolution for Symmetric/Antisymmetric Filters
(2014-05-13) Hasan, Mahmudul; Samavati, Faramarz; Costa Sousa, Mario
Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this article can establish a balanced multiresolution scheme for images, allowing their balanced decomposition and subsequent perfect reconstruction without the use of any extraordinary boundary filters. We define balanced multiresolution such that it allows balanced decomposition i.e. decomposition of a high-resolution image into a low-resolution image and corresponding details of equal size. Such a balanced decomposition makes on-demand reconstruction of regions of interest efficient in both computational load and implementation aspects. We find this balanced decomposition and perfect reconstruction based on an appropriate combination of symmetric/antisymmetric extensions near the image and detail boundaries. In our method, exploiting such extensions correlates to performing sample (pixel/voxel) split operations. Our general approach is demonstrated for some commonly used symmetric /antisymmetric multiresolution filters. We also show the application of such a balanced multiresolution scheme in real-time focus+context visualization.
Open Access
Balanced Multiresolution in Multilevel Focus+Context Visualization
(2018-08-22) Hasan, Mahmudul; Samavati, Faramarz; Costa Sousa, Mário; Mudur, Sudhir Pandurang; Gavrilova, Marina L.; Jacob, Christian J.; Katz, Larry
Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this thesis can establish a balanced multiresolution (BMR) scheme for images, allowing their balanced decomposition and subsequent perfect reconstruction without the use of any extraordinary boundary filters. We define balanced multiresolution such that it allows balanced decomposition i.e. decomposition of a high-resolution image into a low-resolution image and corresponding details of equal size. Several applications of such a decomposition result in a balanced wavelet transform (BWT) that makes on-demand reconstruction of regions of interest (ROIs) efficient in both computational load and implementation aspects. We find such decomposition and perfect reconstruction based on an appropriate combination of symmetric/antisymmetric extensions near the image and detail boundaries. In our method, exploiting such extensions correlates to performing sample (pixel/voxel) split operations. We demonstrate our general approach for some commonly used symmetric/antisymmetric multiresolution filters. We also show the application of such a balanced multiresolution scheme in constructing an interactive multilevel focus+context visualization framework for the navigation and exploration of large-scale 2D and 3D images. Typically, the given filters are floating-point values, so our BWTs reversibly map integers to floating-point i.e. real values. We extend our balanced multiresolution framework further to construct reversible integer-to-integer BWTs from a given symmetric/antisymmetric decomposition filter vector of width less or equal to four. In our approach, we adjust the linear combination of fine samples suggested by the given decomposition vector using optimal sample split operations in combination with a rounding operation. Such adjustments translate an affine integer combination of fine samples to obtain an integer coarse sample, which closely approximates the floating-point coarse sample suggested by the given decomposition filter vector. The associated translation vectors give us the detail samples. Furthermore, when necessary, we construct every other detail sample differently in order to ensure local perfect reconstruction. Compared to their integer-to-real counterparts, the resulting reversible integer-to-integer BWTs occupy less memory, offer better compressibility, and do not require sample quantization for rendering purposes.
Open Access
CINAPACT-Splines: A Family of Infnite Smooth, Accurate and Compactly Supported Splines
(2015-09-01) Akram, Bita; Alim, Usman; Samavati, Faramarz
We introduce a class of compactly supported C infinite kernels (CINAPACT-splines) whose integer translates form a shift-invariant reconstruction space that can be tuned to achieve any order of accuracy. CINAPACT-splines resemble traditional B-splines in that higher orders of accuracy are achieved by successive convolutions with a B-spline of degree zero. Unlike B-splines however, the starting point for CINAPACT-splines is a compactly supported bump function that has been properly normalized so that it fulfills the partition of unity criterion. We explore the properties of CINAPACT-splines in reconstructing volumetric data sampled on regular grids. We show that CINAPACT-splines provide similar reconstruction quality and cost compared to some well-established filters, while being infinitely smooth. We further explore the advantages of our filter by implementing a curvature-based transfer function using second derivatives of the filter to demonstrate feature lines of a function. We apply the same technique using filters of smaller support and less cost.
Open Access
Compactly Supported Biorthogonal Wavelet Constructions on the A-star Lattice and their Application to Visualization
(2017) Horacsek, Joshua; Alim, Usman; Alim, Usman; Samavati, Faramarz; Nielsen, John; Li, Zongpeng
In this dissertation, a family of compact biorthogonal wavelet filter banks that are tailored to the geometry of the A-star lattice are derived. Our application of interest is on the three dimensional A-star or {\em body centered cubic} (BCC) lattice. While the BCC lattice has been shown to have superior approximation properties for volumetric data when compared to the Cartesian cubic (CC) lattice, there has been little work in the way of designing wavelet filter banks that respect the geometry of the BCC lattice. Since wavelets have applications in signal de-noising, compression, and sparse signal reconstruction, these filter banks are an important tool that addresses some of the scalability concerns presented by the BCC lattice. We use these filters in the context of volumetric data compression and reconstruction and qualitatively evaluate our results by rendering images of isosurfaces from compressed data.
Open Access
Cover-it: An Interactive System for Covering 3D Printed Objects
(2014-11-03) Mahdavi-Amiri, Ali; Whittingham, Philip; Samavati, Faramarz
The ubiquity of 3D printers has made it possible to print various types of objects, from toys to mechanical objects. However, most available 3D printers are single or double colors. Even printers that can produce objects with multiple colors do not offer the ability to cover the object with a desired material, such as a piece of cloth or fur. In this paper, we propose a system that produces simple 2D patches that can be used as a reference to cover the 3D printed object. The 2D patches are created by optimizing a fitness function that measures a number of criteria such as planarity of patches, smoothness of patch boundaries, and visibility of the seams on the 3D print. The system allows for user interactions to correct and modify the patches, and provides guidelines on how to wrap the printed object via small curves illustrating the patch boundaries etched on the printed object as well as an animation showing how the 2D patches should be folded together.
Open Access
Data Management Possibilities for Aperture 3 Hexagonal Discrete Global Grid Systems
(2016-08-22) Mahdavi-Amiri, Ali; Alderson, Troy; Samavati, Faramarz
In a Digital Earth framework, data sets are gathered from different sources in three main forms: imagery/elevation, vector, and quantitative data sets. In order to efficiently work with these data sets in a Digital Earth framework, effective methods to represent and transmit these data sets are required. While these representations may be different for each type of data set, they must all preserve the actual data as much as possible in order to accurately address queries. Furthermore, they also need to be compatible with the underlying structure of the Digital Earth framework. In this paper, we describe several data representations for an Aperture 3 Hexagonal Discrete Global Grid System which is a common approach to build a Digital Earth framework. We also discuss how they can be used to transmit data sets or address specific queries.
Open Access
Designing Camera Controls for Map Environments
(2019-01-16) Danyluk, Kurtis; Willett, Wesley J.; Willett, Wesley J.; Sharlin, Ehud; Samavati, Faramarz
We present an exploration of two classes of navigation techniques designed for representations of real-world terrain. The first introduces look-from camera controls, a new style of camera control for touch devices designed with representations of real world-terrain in mind and provides an evaluation of three different implementations of this style of control. The second looks to virtual reality and compares the effectiveness of four existing and common camera control techniques within the context of a representations of real world-terrain. Effective camera controls greatly increase a user’s ability to engage with a virtual environment, and virtual map environments are no different. However, current camera controls are difficult to use within map-like environments, requiring burdensome sequences of interactions or performing poorly within ragged terrain. To examine the effectiveness of different camera controls in this space we conducted two studies in which we asked participants to perform map reading and interaction tasks. In both studies the camera control technique greatly influenced participant engagement and enjoyment within a scene. The first study highlights the effectiveness of look-from camera controls as light-weight additions to direct manipulation controls and provides design guidelines for the construction of look-from camera controls. The second study highlights which existing common navigation techniques are most appropriate within a map-like environment presented in immersive virtual reality and how combinations of these controls can combine the strengths of the controls to cover for the weaknesses of others.
Open Access
Diagrammatic Tools for Generating Biothogonal Multiresolutions
(2003-10-22) Samavati, Faramarz; Bartels, Richard
In a previous work we introduced a construction designed to produce biorthogonal multiresolutions from given subdivisions. This construction was formulated in matrix terms, which is appropriate for curves and tensor-product surfaces. For mesh surfaces of non-tensor connectivity, however, matrix notation is inconvenient. This work introduces diagrams and diagram interactions to replace matricies and matrix multiplication. The diagrams we use are patterns of value-labeled nodes, one type of diagram corresponding to each row or column of one of the matricies of a biorthogonal system. All types of diagrams used in the construction are defined on a common mesh of the multiresolution.
Open Access
Disdyakis Triacontahedron Discrete Global Grid System
(2022-04) Hall, John; Samavati, Faramarz; Runions, Adam; Stefanakis, Emmanuel
The amount of information collected about the Earth has become extremely large. With this information comes the demand for integration, processing, visualization and distribution of this data so that it can be leveraged to solve real‑world problems. To address this issue, a carefully designed information structure is needed to store all of the information about the Earth in a convenient format such that one can easily use it to solve a wide variety of problems. In this thesis, we explore the idea of creating a Discrete Global Grid System (DGGS) using a Disdyakis Triacontahedron (DT) as the initial polyhedron. We have adapted a simple, closed‑form, equal‑area projection to reduce distortion and speed up queries. We have also derived an efficient, closed‑form inverse for this projection that can be used in important DGGS queries. The resulting construction is indexed using an atlas of connectivity maps. Using some simple modular arithmetic, we can then address point to cell, neighborhood and hierarchical queries on the grid, allowing for these queries to be performed in constant time. We have evaluated the angular distortion created by our DGGS by comparing it to a traditional icosahedron DGGS using a similar projection. We demonstrate that our grid reduces angular distortion while allowing for real‑time rendering of data across the globe.
Open Access
Equal Area Spherical Subdivision
(2012) Harrison, Erika E.; Samavati, Faramarz
Open Access
Fault-Sketch: A Framework for Modeling Geological Faults and Displacements
(2024-02-15) Banaeizadeh, Arya; Costa Sousa, Mario; Samavati, Faramarz; Costa Sousa, Mario; Samavati, Faramarz; Eaton, David; Yanushkevich, Svetlana
Geological faults, which result from rock fracturing and displacement in the subsurface, play an important role in shaping the Earth's crust. Modeling fault surfaces and their impact on rock formations is, thus, useful for various geological applications. However, due to the complex configurations of faults, the modeling process can become difficult, requiring a framework with a specialized modeling toolkit. The primary challenge in fault modeling lies in properly correlating the geometry of faults with their effects on rock layers and other fault surfaces during displacement. The final models also have to satisfy certain properties to be reusable for further geological analysis. A factor that even if users who have both modeling and geology expertise cannot guarantee to have. To address this, we have developed a series of operators designed for fault modeling. In this manner, we present Fault-Sketch, a Sketch-Based Interface and Modeling (SBIM) framework that tackles the task of fault modeling and captures their influence on various geological structures. This framework enables the creation of surfaces as a result of rock configurations that have previously been largely overlooked in the existing literature. The collection of operators presented in Fault-Sketch are built upon a data structure fit for the purpose of consistently representing fault surfaces and their boundaries together with the influence they cause both on other surfaces and on the volumes they bound. Moreover, the operators are designed to mimic the geologic processes relevant to fault creation and displacement to facilitate their use by domain experts.
Open Access
GFFD: General Free Form Deformations using Partition Unity Parametrics
(2017-04-08) Mahdavi-Amiri, Ali; Samavati, Faramarz
Free Form Deformations (FFD) have been successfully employed to deform 2D or 3D shapes to manipulate them and obtain a desired shape. In this deformation, a lattice of control points is placed on the given shape and by moving control points, the given shape is deformed according to a set of underlying smooth basis function (e.g. BSpline, NURBS). In this paper, we attempt to generalize Free Form Deformations (GFFD) by using more general basis functions called Partition Uniform Parametrics or PUPs. We provide a comparison of GFFD in which PUPs are employed as the basis functions with BSpline, Bezier, and NURBS basis functions. Although this work is in its preliminary stages, we believe that there are many directions to improve and extend the current idea. We eventually discuss these ideas in the paper.
Open Access
Hierarchical Grid Conversion
(2016-04-01) Mahdavi-Amiri, Ali; Harrison, Erika; Samavati, Faramarz
Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, using simple conversions, we can switch between the grid types to take advantages of each grid for better supporting advanced applications. In this paper, we introduce some simple conversions between grids. To describe their usage, we define new regular and semiregular refinements. We also describe how patch-based data structures can be used for hexagonal cells and semiregular refinements.
Open Access
Improving Deep Neural Networks: Optimization, Regularization, and Generative Modeling
(2019-12) Zhang, Zijun; Li, Zongpeng; Samavati, Faramarz; Li, Zongpeng; Denzinger, Jorg; Krishnamurthy, Diwakar
In the past decade, deep learning has revolutionized the fields of computer vision, speech recognition, natural language processing, and continues spreading to many other fields. Therefore, it is important to better understand and improve deep neural networks (DNNs), which serve as the backbone of deep learning. In this thesis, we approach this topic from three different perspectives: optimization, regularization, and generative modeling. Firstly, we address the generalization gap recently observed between adaptive optimization methods, such as Adam, and simple stochastic gradient descent (SGD). We develop a tailored version of Adam for training DNNs, which is shown to close the gap on image classification tasks. Secondly, we identify a side effect of a widely used regularization technique, dropout, and multiplicative noise in general. That is, multiplicative noise tends to increase the correlation between features. We then exploit batch normalization to efficiently remove the correlation effect. Finally, we focus on generative modeling, a fundamental application of DNNs. We propose a framework for training autoencoder-based generative models, with non-adversarial losses and unrestricted neural network architectures.
Open Access
In-situ interaction in AR medical imaging
(2008-06-16T21:46:26Z) Deries, Sebastien; Sharlin, Ehud; Samavati, Faramarz
One application of augmented reality (AR) is AR medical imaging. This technique helps physicians in analyzing medical data and preparing surgical procedures. In this paper we present a preliminary report on our efforts to implement a set of in-situ interaction techniques in AR medical imaging, supporting display and interaction with AR data on the patient's body.We briefly motivate our approach, review the state of the art and explain our ideas about displaying, tracking and interacting with in-situ AR medical data using tangible physical tools. We describe our current work, present our designed tools, scalpel and tweezers, and explain how they are integrated in a motion tracking system.
Open Access
Interactive 3D Content Modeling for Digital Earth
(2015-08-21) Ketabchi Khonsari, Kaveh; Samavati, Faramarz
In this thesis, we present an interactive system for the creation and editing of 3D content for Digital Earth systems, such as Digital Elevation Models, vegetation, bodies of water and man-made structures. The proposed system employs a set of interactive tools to integrate commonly available data sources, such as orthophotos and Digital Elevation Models (DEM), to facilitate the rapid creation and integration of detailed geospatial content. Consequently, our system can be used to enhance the quality of Digital Earth data by enabling the straightforward creation of new 3D landscapes and urban elements.
Open Access
Interactive Data Styling and Multifocal Visualization for a View-Aware Digital Earth
(2016-10-21) Sherlock, Mark; Hasan, Mahmudul; Samavati, Faramarz
A Discrete Global Grid System (DGGS) is a powerful tool for creating the discrete reference models that support geospatial dataset integration, organization, processing, and visualization in a Digital Earth (DE) application. However, the growing size and scale of geospatial datasets present significant obstacles to the interactivity and accessibility of geospatial visualizations. To address this challenge, we present a portable DGGS that runs in web browsers on a client device and efficiently communicates with a server-side DGGS. In our method, the client-side is responsible for triggering queries for missing data, managing the viewing area, and rendering various styles and effects. The server is responsible for generating data representations for DGGS cells in response to queries from clients. The resulting system is capable of interactively displaying multiple simultaneous viewpoints which enable support for multilevel focus+context visualization on the globe. We also provide several real-time data styling techniques that are designed to work efficiently on both the client and server. These methods help make DE more accessible and informative than ever before.
Open Access
Interactive Design of Muqarnas
(2013-01-21) Hamekasi, Nader; Samavati, Faramarz
Muqarnas is an iconic element of Islamic architecture. It exhibits fascinating beauty and captures the attention of viewers via its complicated form and mesmerizing patterns. Generating a 3D model of a muqarnas and designing the patterns to decorate it have applications in architecture, virtual tourism and other areas. Modeling virtual muqarnas can be very challenging, requiring a lot of time and eff ort even from expert modellers. Our goal is to provide an analysis of muqarnas and its decorating patterns as well as a set of methods and tools which can facilitate the modeling of muqarnas. In this thesis, we present a new approach to model muqarnas. Our approach is to consider muqarnas as a transition between layers of di fferent form. We also take advantage of a special type of ceiling plan, called two dimensional pattern plans, as a guide to overcome the complexity of the muqarnas. Using these methods we provide an interactive framework to design muqarnas. Muqarnas structures are frequently decorated with diff erent patterns. Among these patterns, Persian oral patterns are very interesting but poorly studied. We provide a novel method to generate Persian oral patterns to decorate our models. The key idea in this method is to decompose the patterns into the ornaments and the composition and secondly, separating the geometry from the combinatorial properties of the composition. Our implementation of the presented methods is a software tool that can generate complicated muqarnas models. Several examples of virtual models, including models of real buildings as well as new designs made using this software, are shown.