Orientation, sphericity and roundness evaluation of particles using alternative 3D representations

Sphericity and roundness indices have been used mainly in geology to analyze the shape of particles. In this paper, geometric methods are proposed as an alternative to evaluate the orientation, sphericity and roundness indices of 3D objects. In contrast to previous works based on digital images, which use the voxel model, we represent the particles with the Extreme Vertices Model, a very concise representation for binary volumes. We define the orientation with three mutually orthogonal unit vectors. Then, some sphericity indices based on length measurement of the three representative axes of the particle can be computed. In addition, we propose a ray-casting-like approach to evaluate a 3D roundness index. This method provides roundness measurements that are highly correlated with those provided by the Krumbein's chart and other previous approach. Finally, as an example we apply the presented methods to analyze the sphericity and roundness of a real silica nano dataset.Postprint (published version

Fast connected component labeling algorithm: a non voxel-based approach

This paper presents a new approach to achieve connected component labeling on both binary images and volumes by using the Extreme Vertices Model (EVM), a representation model for orthogonal polyhedra, applied to digital images and volume datasets recently. In contrast with previous techniques, this method does not use a voxel-based approach but deals with the inner sections of the object.Postprint (published version

Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)

The alternating sum of volumes (ASV) decomposition is a widely used technique for converting a B-Rep into a CSG model. The obtained CSG tree has convex primitives at its leaf nodes, while the contents of its internal nodes alternate between the set union and difference operators. This work first shows that the obtained CSG tree T can also be expressed as the regularized Exclusive-OR operation among all the convex primitives at the leaf nodes of T, regardless the structure and internal nodes of T. This is an important result in the case in which EVM represented orthogonal polyhedra are used because in this model the Exclusive-OR operation runs much faster than set union and difference operations. Therefore this work applies this result to EVM represented orthogonal polyhedra. It also presents experimental results that corroborate the theoretical results and includes some practical uses for the ASV decomposition of orthogonal polyhedra.Postprint (published version

VolumeEVM: A new surface/volume integrated model

Volume visualization is a very active research area in the field of scien-tific visualization. The Extreme Vertices Model (EVM) has proven to be a complete intermediate model to visualize and manipulate volume data using a surface rendering approach. However, the ability to integrate the advantages of surface rendering approach with the superiority in visual exploration of the volume rendering would actually produce a very complete visualization and edition system for volume data. Therefore, we decided to define an enhanced EVM-based model which incorporates the volumetric information required to achieved a nearly direct volume visualization technique. Thus, VolumeEVM was designed maintaining the same EVM-based data structure plus a sorted list of density values corresponding to the EVM-based VoIs interior voxels. A function which relates interior voxels of the EVM with the set of densities was mandatory to be defined. This report presents the definition of this new surface/volume integrated model based on the well known EVM encoding and propose implementations of the main software-based direct volume rendering techniques through the proposed model.Postprint (published version

Compact union of disjoint boxes: An efficient decomposition model for binary volumes

This paper presents in detail the CompactUnion of Disjoint Boxes (CUDB), a decomposition modelfor binary volumes that has been recently but brieflyintroduced. This model is an improved version of aprevious model called Ordered Union of Disjoint Boxes(OUDB). We show here, several desirable features thatthis model has versus OUDB, such as less unitary basicelements (boxes) and thus, a better efficiency in someneighborhood operations. We present algorithms forconversion to and from other models, and for basiccomputations as area (2D) or volume (3D). We alsopresent an efficient algorithm for connected-componentlabeling (CCL) that does not follow the classical two-passstrategy. Finally we present an algorithm for collision (oradjacency) detection in static environments. We test theefficiency of CUDB versus existing models with severaldatasets.Peer ReviewedPostprint (published version

Two triangulations methods based on edge refinement

In this paper two curvature adaptive methods of surface triangulation are presented. Both methods are based on edge refinement to obtain a triangulation compatible with the curvature requirements. The first method applies an incremental and constrained Delaunay triangulation and uses curvature bounds to determine if an edge of the triangulation is admissible. The second method uses this function also in the edge refinement process, i.e. in the computation of the location of a refining point, and in the re-triangulation needed after the insertion of this refining point. Results are presented, comparing both approachesPostprint (published version

CUDB: An improved decomposition model for orthogonal pseudo-polyhedra

We present a new decomposition model for Orthogonal Pseudo-Polyhedra (OPP): the Compact Union of Disjoint Boxes. This model is an improved version of the Ordered Union of Disjoint Boxes model. Our model has many desirable features versus the OUDB, such as less storage size and a better efficiency in the connected-component labeling (CCL) process. CCL is a very important operation for manipulating volume data where multiple disconnected components that compose a volume need to be identify. We present the algorithms for conversion to and from the Extreme Vertices Model, which is closely related to the OUDB, and for CCL. The performance of the CUDB is experimentally analyzed with 2D and 3D datasets.Postprint (published version

Improved plane-sweep based algorithm for boundary extraction of 3D images

There exist several approaches to extract the boundary of a 3D image. Most of them represent the extracted boundary as a collection of a large number of little triangular or quadrangular faces whereas few approaches give general orthogonal faces (with any number of edges and with possible holes). One of these approaches is based on a secondary model EVM and focusses mainly on the process to obtain the orientation of the output primitives (edges and faces). Actually, this algorithm obtains, for each plane, a set of oriented edges that have to be rearranged as contours and these contours have to be classified in order to have the corresponding inclusion relationships. These last two processes are performed in a simple brute force way. In this paper, we present an improved algorithm that processes all the edges of a plane and, following a plane-sweep based method, obtains the contours and the inclusion relationships.Postprint (published version

Solving point and plane vs. orthogonal polyhedra using the extreme vertices model (EVM)

In a previous work, Orthogonal Polyhedra (OP) were proposed as geometric bounds in CSG. Primitives in the CSG model were approximated by their respective bounding boxes. The polyhedrical bound for the CSG object was obtained by applying the corresponding Boolean Algebra to those boxes. Also in that paper, a specific and very concise model for representing and handling OP was presented: the Extreme Vertices Model (EVM). The EVM allows simple and robust algorithms for performing the most usual and demanding tasks. This paper deals with the classification of point, and plane vs. OP. These operations can be done on the EVM in linear time. Furthermore, a very important feature of EVM algorithms is that, even though their input data (i.e., vertices' coordinates) can be floating-point values, no time-consuming floating-point arithmetic is ever performed (except when explicitly noted), so there are absolutely no propagation errors due to partial results (which do not exist). All results are obtained by just classifying and selecting vertices' coordinates of the initial data.Postprint (published version

An improved boundary extraction algorithm using a plane-sweep technique

Extracting the boundary of a 3D or a 2D image is a fundamental operation in several image processing related fields. In other fields as NC-data generation, obtaining the cutting areas of sculptured surfaces can be performed by first representing the surface using a regular grid model which is equivalent to a 2D binary image. There exist several approaches to extract the boundary of a 3D image. Most of them represent the extracted boundary as a collection of a large number of little triangular or quadrangular faces whereas few approaches give general orthogonal contours with the corresponding inclusion relationships. One of these approaches is based on a secondary model EVM and allows to obtain the orientation of the output primitives (edges and faces). It actually obtains, for each plane of the resulting B-Rep model, a set of oriented edges that have to be rearranged as contours and these contours have to be classified in order to have the corresponding inclusion relationships. These last two processes are performed in a simple brute force way. In this paper, we present an improved algorithm that processes all the edges of a plane and, following a plane-sweep based method, obtains the contours and the inclusion relationships. The presented algorithm can also be applied to extract the boundary of a 2D image.Postprint (published version