Style-based exploration of illustration datasets

Searching by style in illustration data sets is a particular problem in Information Retrieval which has received little attention so far. One of its main problems is that the perception of style is highly subjective, which makes labeling styles a very difficult task. Despite being difficult to predict computationally, certain properties such as colorfulness, line style or shading can be successfully captured by existing style metrics. However, there is little knowledge about how we distinguish between different styles and how these metrics can be used to guide users in style-based interactions. In this paper, we propose several contributions towards a better comprehension of illustration style and its usefulness for data exploration and retrieval. First, we provide new insights about how we perceive style in illustration. Second, we evaluate a handmade style clustering of clip art pieces with an existing style metric to analyze how this metric aligns with expert knowledge. Finally, we propose a method for efficient navigation and exploration of large clip art data sets which takes into account both semantic labeling of the data and its style. Our approach combines hierarchical clustering with dimensionality reduction techniques, and strategic sampling to obtain intuitive visualizations and useful visualizations.     

Line-based sunken relief generation from a 3D mesh

Sunken relief is an art form made by cutting the relief sculpture itself into a flat surface with a shallow overall depth. This paper focuses on the problem of direct generation of line-based sunken relief from a 3D mesh. We show how to extract, post-process and organize the messy feature lines in regular forms, applicable for lines engraving on the sculpture surfaces. We further describe how to construct a smooth height field from the input object, and derive a continuous pitting corrosion method to generate the cutting paths. The whole framework is conducted in object-space, making it flexible for stroke stylization and depth control of the engraving lines. We demonstrate the results with several impressive renderings and photographs used to illustrate the paper itself.     

A new 3D-matching method of nonrigid and partially similar models using curve analysis

The 3D-shape matching problem plays a crucial role in many applications, such as indexing or modeling, by example. Here, we present a novel approach to matching 3D objects in the presence of nonrigid transformation and partially similar models. In this paper, we use the representation of surfaces by 3D curves extracted around feature points. Indeed, surfaces are represented with a collection of closed curves, and tools from shape analysis of curves are applied to analyze and to compare curves. The belief functions are used to define a global distance between 3D objects. The experimental results obtained on the TOSCA and the SHREC07 data sets show that the system performs efficiently in retrieving similar 3D models.     

OpenGL绘制NURBS曲线曲面的应用研究

本文介绍了NURBS的基本概念及用OpenGL绘制NUPBS的一般编程思路，并通过实例详细叙述了如何在VisualC 中用OpenGL绘制NURBS的一般过程。     

Stylized Vector Art from 3D Models with Region Support

We describe a rendering system that converts a 3D meshed model into the stylized 2D filled‐region vector‐art commonly found in clip‐art libraries. To properly define filled regions, we analyze and combine accurate but jagged face‐normal contours with smooth but inaccurate interpolated vertex normal contours, and construct a new smooth shadow contour that properly surrounds the actual jagged shadow contour. We decompose region definition into geometric and topological components, using machine precision for geometry processing and raster‐precision to accelerate topological queries. We extend programmable stylization to simplify, smooth and stylize filled regions. The result renders 10K‐face meshes into custom clip‐art in seconds.     

Line-Art and its Mathematical Models

In this paper,the authors describe the principles of Straight Line Strokes illustration,present the mathematical model of the principles,and show how a great number of lines can be implemented as main part of an automated drawing system named Line-Art.Different from traditional drawing art.Line-Art enerates pictures without curves,colors,ink marks,brushes,and oil paint,but only with Straight Line Strokes.Generated pictures are composed,clipped,and plotted.The paper also introduces how to use the initial value problem of the ordinary differential equation to describe a drawing art,e.g.Line-Art.     

Three-dimensional face recognition using shapes of facial curves

We study shapes of facial surfaces for the purpose of face recognition. The main idea is to 1) represent surfaces by unions of level curves, called facial curves, of the depth function and 2) compare shapes of surfaces implicitly using shapes of facial curves. The latter is performed using a differential geometric approach that computes geodesic lengths between closed curves on a shape manifold. These ideas are demonstrated using a nearest-neighbor classifier on two 3D face databases: Florida State University and Notre Dame, highlighting a good recognition performance     

A Linear Variational System for Modelling From Curves

We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve‐based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.     

3D object recognition using invariants of 2D projection curves

This paper presents a new method for recognizing 3D objects based on the comparison of invariants of their 2D projection curves. We show that Euclidean equivalent 3D surfaces imply affine equivalent 2D projection curves that are obtained from the projection of cross-section curves of the surfaces onto the coordinate planes. Planes used to extract cross-section curves are chosen to be orthogonal to the principal axes of the defining surfaces. Projection curves are represented using implicit polynomial equations. Affine algebraic and geometric invariants of projection curves are constructed and compared under a variety of distance measures. Results are verified by several experiments with objects from different classes and within the same class.     

Curve Fitting in Architecture

It used to be popular to draw geometric figures on images of paintings or buildings, and to propose them as an “analysis” of the observed work, but the tradition lost some credit due to exaggerated (golden section) interpretations. So, how sure can an art or mathematics teacher be when he wants to propose the profile of a nuclear plant as an example of a hyperboloid, or proportions in paintings as an illustration of the presence of number series? Or, if Gaudi intended to show chain curves in his work, can the naked eye actually notice the difference between these curves and parabolas? The present paper suggests applying the “least squares method”, developed in celestial mechanics and since applied in various fields, to art and architecture, especially since modern software makes computational difficulties nonexistent. Some prefer jumping immediately to modern computer machinery for visual recognition, but such mathematical overkill may turn artistic minds further away from the (beloved!) tradition of geometric interpretations.     

Detection of loops and singularities of surface intersections

Two surface patches intersecting each other generally at a set of points (singularities), form open curves or closed loops. While open curves are easily located by following the boundary curves of the two patches, closed loops and singularities pose a robustness challenge since such points or loops can easily be missed by any subdivision or marching-based intersection algorithms, especially when the intersecting patches are flat and ill-positioned. This paper presents a topological method to detect the existence of closed loops or singularities when two flat surface patches intersect each other. The algorithm is based on an oriented distance function defined between two intersecting surfaces. The distance function is evaluated in a vector field to identify the existence of singular points of the distance function since these singular points indicate possible existence of closed intersection loops. The algorithm detects the existence rather than the absence of closed loops and singularities. This algorithm requires general C² parametric surfaces.     

Orthogonal Decomposition of Non-Uniform Bspline Spaces using Wavelets

We take advantage of ideas of an orthogonal wavelet complement to produce multiresolution orthogonal decomposition of nonuniform Bspline (NUB) spaces. The editing of NUB curves and surfaces can be handled at different levels of resolutions. Applying Multiresolution decomposition to possibly C¹ discontinuous surfaces, one can preserve the general shape on one hand and local features on the other of the free-form models, including geometric discontinuities. The Multiresolution decomposition of the NUB tensor product surface is computed via the symbolic computation of inner products of Bspline basis functions. To find a closed form representation for the inner product of the Bspline basis functions, an equivalent interpolation problem is solved. As an example for the strength of the Multiresolution decomposition, a tool demonstrating the Multiresolution editing capabilities of NUB surfaces was developed and is presented as part of this work, allowing interactive 3D editing of NUB free-form surfaces.     

Multiresolution for Closed Curves and Surfaces Using Wavelets

Multiresolution modeling is becoming a powerful tool for fast display, and geometric data compression and transmission of complex shapes. Most of the existing literatures investigating the multiresolution for B-spline curves and surfaces are concentrated on open ones. In this paper, we focus on the multiresolution representations and editing of closed B-spline curves and surfaces using wavelets. A repetition approach is adopted for the multiresolution analysis of closed B-spline curves and surfaces. Since the closed curve or surface itself is periodic, it can overcome the drawback brought by the repetition method, i.e. introducing the discontinuities at the boundaries. Based on the models at different multiresolution levels, the multiresolution editing methods of closed curves and surfaces are introduced. Users can edit the overall shape of a closed one while preserving its details, or change its details without affecting its overall shape.     

New feature points based on geometric invariants for 3D image registration

We introduce in this paper a new type of feature points of 3D surfaces, based on geometric invariants. We call this new type of feature points the extremal points of the 3D surfaces, and we show that the relative positions of those 3D points are invariant according to 3D rigid transforms (rotation and translation). We show also how to extract those points from 3D images, such as Magnetic Resonance images (MRI) or Cat-Scan images, and also how to use them to perform precise 3D registration. Previously, we described a method, called the Marching Lines algorithm, which allow us to extract the extremal lines, which are geometric invariant 3D curves, as the intersection of two implicit surfaces: the extremal points are the intersection of the extremal lines with a third implicit surface. We present an application of the extremal points extraction to the fully automatic registration of two 3D images of the same patient, taken in two different positions, to show the accuracy and robustness of the extracted extremal points.     

Visual‐inertial curve simultaneous localization and mapping: Creating a sparse structured world without feature points

We present a simultaneous localization and mapping (SLAM) algorithm that uses Bézier curves as static landmark primitives rather than feature points. Our approach allows us to estimate the full six degrees of freedom pose of a robot while providing a structured map that can be used to assist a robot in motion planning and control. We demonstrate how to reconstruct the three‐dimensional (3D) location of curve landmarks from a stereo pair and how to compare the 3D shape of curve landmarks between chronologically sequential stereo frames to solve the data association problem. We also present a method to combine curve landmarks for mapping purposes, resulting in a map with a continuous set of curves that contain fewer landmark states than conventional point‐based SLAM algorithms. We demonstrate our algorithm's effectiveness with numerous experiments, including comparisons to existing state‐of‐the‐art SLAM algorithms.     

On the statistical decorrelation of the 2D discrete wavelet transform coefficients of a wide sense stationary bivariate random process

We present a second order statistical analysis of the 2D Discrete Wavelet Transform (2D DWT) coefficients. The input images are considered as wide sense bivariate random processes. We derive closed form expressions for the wavelet coefficientsʼ correlation functions in all possible scenarios: inter-scale and inter-band, inter-scale and intra-band, intra-scale and inter-band and intra-scale and intra-band. The particularization of the input process to the White Gaussian Noise (WGN) case is considered as well. A special attention is paid to the asymptotical analysis obtained by considering an infinite number of decomposition levels. Simulation results are also reported, confirming the theoretical results obtained. The equations derived, and especially the inter-scale and intra-band dependency of the 2D DWT coefficients, are useful for the design of different signal processing systems as for example image denoising algorithms. We show how to apply our theoretical results for designing state of the art denoising systems which exploit the 2D DWT.     

A framework for digital sunken relief generation based on 3D geometric models

Sunken relief is a special art form of sculpture whereby the depicted shapes are sunk into a given surface. This is traditionally created by laboriously carving materials such as stone. Sunken reliefs often utilize the engraved lines or strokes to strengthen the impressions of a 3D presence and to highlight the features which otherwise are unrevealed. In other types of relief, smooth surfaces and their shadows convey such information in a coherent manner. Existing methods for relief generation are focused on forming a smooth surface with a shallow depth which provides the presence of 3D figures. Such methods unfortunately do not help the art form of sunken reliefs as they omit the presence of feature lines. We propose a framework to produce sunken reliefs from a known 3D geometry, which transforms the 3D objects into three layers of input to incorporate the contour lines seamlessly with the smooth surfaces. The three input layers take the advantages of the geometric information and the visual cues to assist the relief generation. We have modified the existing techniques of line drawings and relief generation, and then combine them organically for this particular purpose.     

DTI in Context: Illustrating Brain Fiber Tracts In Situ

We present an interactive illustrative visualization method inspired by traditional pen‐and‐ink illustration styles. Specifically, we explore how to provide context around DTI fiber tracts in the form of surfaces of the brain, the skull, or other objects such as tumors. These contextual surfaces are derived from either segmentation data or generated using interactive iso‐surface extraction and are rendered with a flexible, slice‐based hatching technique, controlled with ambient occlusion. This technique allows us to produce a consistent and frame‐coherent appearance with precise control over the lines. In addition, we provide context through cutting planes onto which we render gray matter with stippling. Together, our methods not only facilitate the interactive exploration and illustration of brain fibers within their anatomical context but also allow us to produce high‐quality images for print reproduction. We provide evidence for the success of our approach with an informal evaluation with domain experts.