20 research outputs found
An Interpolatory Subdivision Scheme for Triangular Meshes and Progressive Transmission
4 authors, including: chen ren Guangzhou cool-smart electronical inform
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Surface modelling for 2D imagery
Vector graphics provides powerful tools for drawing scalable 2D imagery. With
the rise of mobile computers, of different types of displays and image resolutions,
vector graphics is receiving an increasing amount of attention. However, vector
graphics is not the leading framework for creating and manipulating 2D imagery.
The reason for this reluctance of employing vector graphical frameworks is that it
is difficult to handle complex behaviour of colour across the 2D domain.
A challenging problem within vector graphics is to define smooth colour functions
across the image. In previous work, two approaches exist. The first approach,
known as diffusion curves, diffuses colours from a set of input curves and points.
The second approach, known as gradient meshes, defines smooth colour functions
from control meshes. These two approaches are incompatible: diffusion curves do
not support the local behaviour provided by gradient meshes and gradient meshes
do not support freeform curves as input. My research aims to narrow the gap between
diffusion curves and gradient meshes.
With this aim in mind, I propose solutions to create control meshes from freeform
curves. I demonstrate that these control meshes can be used to render a vector
primitive similar to diffusion curves using subdivision surfaces. With the use of
subdivision surfaces, instead of a diffusion process, colour gradients can be locally
controlled using colour-gradient curves associated with the input curves.
The advantage of local control is further explored in the setting of vector-centric
image processing. I demonstrate that a certain contrast enhancement profile, known
as the Cornsweet profile, can be modelled via surfaces in images. This approach
does not produce saturation artefacts related with previous filter-based methods.
Additionally, I demonstrate various approaches to artistic filtering, where the artist
locally models given artistic effects.
Gradient meshes are restricted to rectangular topology of the control meshes. I
argue that this restriction hinders the applicability of the approach and its potential
to be used with control meshes extracted from freeform curves. To this end, I
propose a mesh-based vector primitive that supports arbitrary manifold topology of
the mesh
Geometric Structures on Matrix-valued Subdivision Schemes
Surface subdivision schemes are used in computer graphics to generate visually smooth surfaces of arbitrary topology. Applications in computer graphics utilize surface normals and curvature. In this paper, formulas are obtained for the first and second partial derivatives of limit surfaces formed using 1-ring subdivision schemes that have 2 by 2 matrix-valued masks. Consequently, surface normals, and Gaussian and mean curvatures can be derived. Both quadrilateral and triangular schemes are considered and for each scheme both interpolatory and approximating schemes are examined. In each case, we look at both extraordinary and regular vertices. Every 3-D vertex of the refinement polyhedrons also has what is called a corresponding “shape vertex.” The partial derivative formulas consist of linear combinations of surrounding polyhedron vertices as well as their corresponding shape vertices. We are able to derive detailed information on the matrix-valued masks and about the left eigenvectors of the (regular) subdivision matrix. Local parameterizations are done using these left eigenvectors and final formulas for partial derivatives are obtained after we secure detailed information about right eigenvectors of the subdivision matrix. Using specific subdivision schemes, unit normals so obtained are displayed. Also, formulas for initial shape vertices are postulated using discrete unit normals to our original polyhedron. These formulas are tested for reasonableness on surfaces using specific subdivision schemes. Obtaining a specified unit normal at a surface point is examined by changing only these shape vertices. We then describe two applications involving surface normals in the field of computer graphics that can use our results
Active Subdivision Surfaces for the Semiautomatic Segmentation of Biomedical Volumes
International audienceWe present a new family of active surfaces for the semiautomatic segmentation of volumetric objects in 3D biomedical images. We represent our deformable model by a subdivision surface encoded by a small set of control points and generated through a geometric refinement process. The subdivision operator confers important properties to the surface such as smoothness, reproduction of desirable shapes and interpolation of the control points. We deform the subdivision surface through the minimization of suitable gradient-based and region-based energy terms that we have designed for that purpose. In addition, we provide an easy way to combine these energies with convolutional neural networks. Our active subdivision surface satisfies the property of multiresolution, which allows us to adopt a coarse-tofine optimization strategy. This speeds up the computations and decreases its dependence on initialization compared to singleresolution active surfaces. Performance evaluations on both synthetic and real biomedical data show that our active subdivision surface is robust in the presence of noise and outperforms current stateof-the-art methods. In addition, we provide a software that gives full control over the active subdivision surface via an intuitive manipulation of the control points
Local and Hierarchical Refinement for Subdivision Gradient Meshes
Gradient mesh design tools allow users to create detailed scalable images, traditionally through the creation and manipulation of a (dense) mesh with regular rectangular topology. Through recent advances it is now possible to allow gradient meshes to have arbitrary manifold topology, using a modified Catmull-Clark subdivision scheme to define the resultant geometry and colour [LKSD17]. We present two novel methods to allow local and hierarchical refinement of both colour and geometry for such subdivision gradient meshes. Our methods leverage the mesh properties that the particular subdivision scheme ensures. In both methods, the artists enjoy all the standard capabilities of manipulating the mesh and the associated colour gradients at the coarsest level as well as locally at refined levels. Further novel features include interpolation of both position and colour of the vertices of the input meshes, local detail follows coarser-level edits, and support for sharp colour transitions, all at any level in the hierarchy offered by subdivision
Non-linear subdivision of univariate signals and discrete surfaces
During the last 20 years, the joint expansion of computing power, computer graphics, networking capabilities and multiresolution analysis have stimulated several research domains, and developed the need for new types of data such as 3D models, i.e. discrete surfaces. In the intersection between multiresolution analysis and computer graphics, subdivision methods, i.e. iterative refinement procedures of curves or surfaces, have a non-negligible place, since they are a basic component needed to adapt existing multiresolution techniques dedicated to signals and images to more complicated data such as discrete surfaces represented by polygonal meshes. Such representations are of great interest since they make polygonal meshes nearly as exible as higher level 3D model representations, such as piecewise polynomial based surfaces (e.g. NURBS, B-splines...). The generalization of subdivision methods from univariate data to polygonal meshes is relatively simple in case of a regular mesh but becomes less straightforward when handling irregularities. Moreover, in the linear univariate case, obtaining a smoother limit curve is achieved by increasing the size of the support of the subdivision scheme, which is not a trivial operation in the case of a surface subdivision scheme without a priori assumptions on the mesh. While many linear subdivision methods are available, the studies concerning more general non-linear methods are relatively sparse, whereas such techniques could be used to achieve better results without increasing the size support. The goal of this study is to propose and to analyze a binary non-linear interpolatory subdivision method. The proposed technique uses local polar coordinates to compute the positions of the newly inserted points. It is shown that the method converges toward continuous limit functions. The proposed univariate scheme is extended to triangular meshes, possibly with boundaries. In order to evaluate characteristics of the proposed scheme which are not proved analytically, numerical estimates to study convergence, regularity of the limit function and approximation order are studied and validated using known linear schemes of identical support. The convergence criterion is adapted to surface subdivision via a Hausdorff distance-based metric. The evolution of Gaussian and mean curvature of limit surfaces is also studied and compared against theoretical values when available. An application of surface subdivision to build a multiresolution representation of 3D models is also studied. In particular, the efficiency of such a representation for compression and in terms of rate-distortion of such a representation is shown. An alternate to the initial SPIHT-based encoding, based on the JPEG 2000 image compression standard method. This method makes possible partial decoding of the compressed model in both SNR-progressive and level-progressive ways, while adding only a minimal overhead when compared to SPIHT
Non-linear subdivision using local spherical coordinates
In this paper, we present an original non-linear subdivision scheme suitable for univariate data, plane curves and discrete triangulated surfaces, while keeping the complexity acceptable. The proposed technique is compared to linear subdivision methods having an identical support. Numerical criteria are proposed to verify basic properties, such as convergence of the scheme and the regularity of the limit function