Dolors Ayala

Topology-reducing surface simplification using a discrete solid representation

This paper presents a new approach for generating coarse-level approximations of topologically complex models. Dramatic topology reduction is achieved by converting a 3D model to and from a volumetric representation. Our approach produces valid, error-bounded models and supports the creation of approximations that do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Several simple to implement versions of our approach are presented and discussed. We show that these methods perform significantly better than other surface-based approaches when simplifying topologically-rich models such as scene parts and complex mechanical assemblies.

Orthogonal polyhedra as geometric bounds in constructive solid geometry

Set membership classification and, specifically, the evaluation of a CSG tree are problems of a certain complexity. Several techniques to speed up these processes have been proposed such as Active Zones, Geometric Bounds and the Extended Convex Differences Tree. Boxes are the most common geometric bounds studied but other bounds such as spheres, convex hulls and prisms have also been proposed. In this work we propose orthogonal polyhedra as geometric bounds in the CSG model. CSG primitives are approximated by orthogonal polyhedra and the orthogonal bound of the object is obtained by applying the corresponding boolean algebra. A specific model for orthogonal polyhedra is presented that allows a simple and robust boolean operations algorithm between orthogonal polyhedra. This algorithm has linear complexity (is based on a merging process) and avoids floating-point computation.

3D reconstruction and quantification of porous structures

In this paper, we describe the methodology that we have designed to quantify the pores distribution in bone implants and the empirical results that we have obtained with BioCAD designed scaffolds, microCT and confocal microscopy data. Our method is based on 3D digital topology properties of the porous structure. We segment the 3D images into three regions: exterior, bone and pore space. Next, we divide the pore space into pores and connection paths. We compute a graph of the pore space such that each node of the graph represents a pore, and an arc between two nodes indicates that the two pores are path-connected. On the basis of the graph and the segmented model, we are able to compute several properties of the material such as global porosity, effective porosity and radial pore distribution.

Fast neighborhood operations for images and volume data sets

Abstract This paper presents a new approach to carry out erosion, dilation and connected component labeling. We use the extreme vertices model, an orthogonal polyhedra representation, to describe binary images and volume data sets in a very efficient way. Our proposal does not use a voxel-based approach but deals with the inner sections of the object. It allows to treat images and volumes indistinctly using the same algorithm and data structure with no overhead of memory and can be applied to manifold as well as non-manifold data. The connected component labeling algorithm actually detects non-manifold zones and permits to break or not the objects at these zones by an user-specified parameter.

Converting Orthogonal Polyhedra from Extreme Vertices Model to B-Rep and to Alternating Sum of Volumes

In recent published papers we presented the Extreme Vertices Model (EVM), a concise and complete model for representing orthogonal polyhedra and pseudopolyhedra (OPP). This model exploits the simplicity of its domain by allowing robust and simple algorithms for set-membership classification and Boolean operations that do not need to perform floating-point operations.

Efficient algorithms for boundary extraction of 2D and 3D orthogonal pseudomanifolds

In this paper we present algorithms to extract the boundary representation of orthogonal polygons and polyhedra, either manifold or pseudomanifold. The algorithms we develop reconstruct not only the polygons of the boundaries but also the hole-face inclusion relationship. Our algorithms have a simple input so they can be used to convert many different kinds of models to B-Rep. In the 2D case, the input is the set of vertices, and in the 3D case, some small additional information must be supplied for every vertex. All proposed algorithms run in O(nlogn) time and use O(n) space, where n is the number of vertices of the input. Moreover, we explain how to use our proposal to extract the boundary from the well-known voxel and octree models as well as from three vertex-based models found in the related literature: the neighbourhood, the EVM, and the weighted vertex list models.

VolumeEVM: A new approach for surface/volume integration

Volume visualization is a very active research area in the field of scientific visualization. The main techniques of volume visualization are surface rendering and direct volume rendering. In recent works, the extreme vertices model (EVM) has been used as an intermediate model to visualize and manipulate volume data using a surface rendering approach. However, the ability to integrate the advantages of surface rendering approaches with the superiority in visual exploration of volume rendering would allow one to obtain a very complete framework for visualization and manipulation of volume data. In this paper, the VolumeEVM is presented as an enhanced EVM-based model. It incorporates the volumetric information required to achieve a nearly direct volume visualization technique. Thus, a new surface/volume integrated model is defined based on the EVM encoding. Also, an algorithm following the splatting technique and using the VolumeEVM has been devised.

EVM: A Complete Solid Model for Surface Rendering

The Extreme Vertices Model (EVM) has been presented as a concise and complete model for orthogonal pseudo-polyhedra (OPP) in the solid modeling field. This model exploits the simplicity of its domain by allowing robust and simple implementations. In this paper we use the EVM to represent and process images and volume data sets. We will prove that the EVM works as an efficient scheme of representation for binary volumes as well as a powerful block-form surface renderer which avoids the redundancy of primitives on the extracted isosurface. In addition, to achieve more realism, the normal vectors at vertices can be added to the model. Furthermore, an efficient tessellator of non-convex orthogonal faces is presented. Useful operating and manipulating tools can be implemented over the EVM, like editing operations via Boolean operators, non voxel-based morphological operations and an improved connected component labeling algorithm. The well-composedness property of the volume can be detected easily.

A connected-component-labeling-based approach to virtual porosimetry

Analyzing the pore-size distribution of porous materials, made up of an aggregation of interconnected pores, is a demanding task. Mercury intrusion porosimetry (MIP) is a physical method that intrudes mercury into a sample at increasing pressures to obtain a pore-size histogram. This method has been simulated in-silice with several approaches requiring prior computation of a skeleton. We present a new approach to simulate MIP that does not require skeleton computation. Our method is an iterative process that considers the diameters corresponding to pressures. At each iteration, geometric tests detect throats for the corresponding diameter and a CCL process collects the region invaded by the mercury. Additionally, a new decomposition model called CUDB, is used. This is suitable for computing the throats and performs better with the CCL algorithm than a voxel model. Our approach obtains the pore-size distribution of the porous medium, and the corresponding pore graph.

Exploration of porous structures with illustrative visualizations

The analysis of porous structures from CT images is emerging as a new computer graphics application that is useful in diverse scientific fields such as BioCAD and geology. These structures are very complex and difficult to analyze visually when they are presented with traditional rendering techniques. In this paper, we describe a visualization application based on illustrative techniques for rendering porous structures. We provide various interactive pore selection mechanisms and visualization styles that allow users to better perceive the connectivity between pores and how they are distributed by radii throughout the structure. The application also shows simulations of fluid intrusion or extrusion through the structure, and it allows users to navigate inside. We describe our application and discuss the experimental results with phantom models, BioCAD scaffolds, implants and rock samples. Graphical AbstractWe describe a porous structures visualization application based on illustrative techniques. It provides pore selection mechanisms, different visualization styles, simulations of fluid intrusion, and navigations inside. Display Omitted Research Highlights? The analysis of porous structures can be enhanced using a graphical model. ? A volume model of the structure alone is difficult to explore. ? The combination of a graph connectivity and a volume model provides tools to efficiently explore pore structures. ? The use of illustrative techniques such as cut-away, ghosting, edge enhancement and colormaps provides clues on the pore size and the topological distances between pores.