On surfaces in digital topology

In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework for digital topology has been proposed. This framework offers the possibility of transfering, in an easy way, definitions, statements and proofs from continuous topology to digital topology. In particular, it provides a straightforward definition of n-dimensional digital manifold. In this paper we prove that the class of digital 2-manifolds without boundary in the grid Z3 agrees with the class of (26, 6)-surfaces defined by Kong-Roscoe and other authors. As a consequence, the separation theorem for digital surfaces stated in D.G. Morgenthaler, A. Rosenfeld. Surfaces in threedimensional digital images. Information and Control, 51 (1981), 227-247] and G.M. Reed. On the Characterization of Simple Closed Surfaces in Three-dimensional Digital Images. Computer Graphics and Image Processing, 25 (1984), 226-235 is obtained.Dirección General de Investigación Científica y TécnicaUniversidad de La Rioj

A background-priority discrete boundary triangulation method

Discrete boundary triangulation methods generate triangular meshes through the centers of the boundary voxels of a volumetric object. At some voxel configurations it may be arbitrary whether a part of the volume should be included in the object or could be classified as background. Consequently, important details such as concave and convex edges and corners are not consistently preserved in the describing geometry. We present a "background priority" version of an existing "object priority" algorithm [6]. We show that the ad hoc configurations of the well-known Discretized Marching Cubes algorithm [13] can be derived from our method and that a combined triangulation with "object priority" and "background priority" better would preserve object details

Digital pseudomanifolds, digital weakmanifolds and Jordan–Brouwer separation theorem

AbstractIn this paper we introduce the new notion of n-pseudomanifold and n-weakmanifold in an (n+1)-digital image using (2(n+1),3(n+1)−1)-adjacency. For these classes, we prove the digital version of the Jordan–Brouwer separation theorem. To accomplish this objective, we construct a polyhedral representation of the (n+1)-digital image based on a cubical complex decomposition which enables us to translate some results from polyhedral topology into the digital space. Our main result extends the class of “thin” objects that are defined locally and verifying the Jordan–Brouwer separation theorem

Strong separating (k, k)−surfaces on Z3

For each adjacency pair (k, k) != (6, 6), k, k ∈ {6, 18, 26}, we introduce a new family Skk of surfaces in the discrete space Z3 that strictly contains several families of surfaces previously defined, and other objects considered as surfaces, in the literature. Actually, Skk characterizes the strongly k−separating objects of the family of digital surfaces, defined by means of continuous analogues, of the universal (k, k)−spaces introduced in [6]

A boundary representation for extracting sharp surfaces from regularly-gridded 3d objects

Geometry extraction from volume data is important in many applications. On a regular 3d grid, current approaches do not consistently preserve object details such as sharp corners and edges of 26-connected objects. We describe a boundary representation in which we geometrically constrain the connectivity, so that such details can be maintained. Application of our model for object surfacing compares favorable to current surfacing methods

Sketching-based Skeleton Extraction

Articulated character animation can be performed by manually creating and rigging a skeleton into an unfolded 3D mesh model. Such tasks are not trivial, as they require a substantial amount of training and practice. Although methods have been proposed to help automatic extraction of skeleton structure, they may not guarantee that the resulting skeleton can help to produce animations according to user manipulation. We present a sketching-based skeleton extraction method to create a user desired skeleton structure which is used in 3D model animation. This method takes user sketching as an input, and based on the mesh segmentation result of a 3D mesh model, generates a skeleton for articulated character animation. In our system, we assume that a user will properly sketch bones by roughly following the mesh model structure. The user is expected to sketch independently on different regions of a mesh model for creating separate bones. For each sketched stroke, we project it into the mesh model so that it becomes the medial axis of its corresponding mesh model region from the current viewer perspective. We call this projected stroke a “sketched bone”. After pre-processing user sketched bones, we cluster them into groups. This process is critical as user sketching can be done from any orientation of a mesh model. To specify the topology feature for different mesh parts, a user can sketch strokes from different orientations of a mesh model, as there may be duplicate strokes from different orientations for the same mesh part. We need a clustering process to merge similar sketched bones into one bone, which we call a “reference bone”. The clustering process is based on three criteria: orientation, overlapping and locality. Given the reference bones as the input, we adopt a mesh segmentation process to assist our skeleton extraction method. To be specific, we apply the reference bones and the seed triangles to segment the input mesh model into meaningful segments using a multiple-region growing mechanism. The seed triangles, which are collected from the reference bones, are used as the initial seeds in the mesh segmentation process. We have designed a new segmentation metric [1] to form a better segmentation criterion. Then we compute the Level Set Diagrams (LSDs) on each mesh part to extract bones and joints. To construct the final skeleton, we connect bones extracted from all mesh parts together into a single structure. There are three major steps involved: optimizing and smoothing bones, generating joints and forming the skeleton structure. After constructing the skeleton model, we have proposed a new method, which utilizes the Linear Blend Skinning (LBS) technique and the Laplacian mesh deformation technique together to perform skeleton-driven animation. Traditional LBS techniques may have self-intersection problem in regions around segmentation boundaries. Laplacian mesh deformation can preserve the local surface details, which can eliminate the self-intersection problem. In this case, we make use of LBS result as the positional constraint to perform a Laplacian mesh deformation. By using the Laplacian mesh deformation method, we maintain the surface details in segmentation boundary regions. This thesis outlines a novel approach to construct a 3D skeleton model interactively, which can also be used in 3D animation and 3D model matching area. The work is motivated by the observation that either most of the existing automatic skeleton extraction methods lack well-positioned joints specification or the manually generated methods require too much professional training to create a good skeleton structure. We dedicate a novel approach to create 3D model skeleton based on user sketching which specifies articulated skeleton with joints. The experimental results show that our method can produce better skeletons in terms of joint positions and topological structure

Weak lighting functions and strong 26-surfaces

AbstractThe goal of this paper is to introduce the notion of weak lighting function in order to replicate the “continuous perception” associated with strong 26-surfaces. As a consequence, the continuous analogue defined ad hoc by Malgouyres and Bertrand only for these surfaces is extended for arbitrary objects, and the local characterization of finite strong 26-surfaces given in (Malgouyres and Bertrand, Int. J. Pattern Recognition Art. Intell. 13(4) (1999) 465–484) is generalized to possibly infinite surfaces. Moreover, weak lighting functions also replicate the “continuous perception” associated with (α,β)-surfaces, (α,β)≠(6,6), since they are generalizing the lighting functions previously defined by the authors

Segmentação e visualização tridimensional interativa de imagens de ressonancia magnetica

Orientadores: Roberto de Alencar Lotufo, Alexandre Xavier FalcãoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoMestradoEngenharia de ComputaçãoMestre em Engenharia Elétric