Recent Reports

"Estat de l'Art en Modelatge de Volum"  

Research Trends in Volume Modelling  

Report Number: LSI-94-14-R
Title: A Volume Visualization Algorithm Using a Coherent Extended Weight Matrix
Author(s): D. Tost, Puig, A., I. Navazo
Date: 1994

 Abstract:

Direct cell-to-cell volume visualization algorithms, also called projective rendering methods, present the advantage of allowing semi-transparencies and, additionally, as they project all the samples, they avoid the voxel-space aliasing. However, they are generally computationally expensive and artifacts may appear in the projection. In this paper, different projective strategies are reviewed and compared. It consists of the computation, in a preprocess, of 16 Extended Generallized Weight (EGW) matrices, based on the voxels geometry and the viewpoint direction. Taking into advatage the voxel-to-voxel coherence, the EGW are applied incrementally to each voxel as footprints to be composited with the image buffer, according to the voxel shade and opacity values. It is shown that the method avoids all artifacts, and that it has a low computational cost because it does not require any geometric computation in the projection process. It is specially suitable for voxel representations and image space resolutions such that the projection of a single voxel covers more than one pixel.  

Abstract:
In order to enhance the cerebral blood vessels in the visualization, in this report, the specific problems of the medical diagnosis of vascular structures and the requirements of the visualization are presented. The most suitable shading model to outline the vessel features is defines and a new visualization method is proposed which keeps a low computational cost. This method provides a general solution to visualize volume objects and it is based on the splatting approach using spatial coherence. First, a pre-process is performed in which the visualization parameters that are independent from the viewpoint are computed, next the number of samples to be projected is reduced and finally advantage is taken of the coherence between successive samples projection. The coherence can be used also on the ray-casting strategy. Thus, the costs of these approachs are analyzed and compared. Some implementations are done in order to shown its results.
 

Abstract:
Cerebral vascular diseases are complex to analyze directly from the input data captions offered by Computer Tomographies and Magnetic Resonances because the cerebral blood vessels are small and narrow. In this report, the reconstruction and the modelling of cerebral vascular structures are addressed. First, the medical issues on diagnosis are studied and the requirements of the problem are defined. A symbolic model of the cerebral blood vessels, which provides information of the semantics, the topology, the geometry and the volume of the vascular map is proposed and evaluated. In addition, from an input discrete representation, a seed algorithm of construction of these model which analyzes the characteristiques of the blood vessel MAT (Medial Axis Transform), its regular features as well as its anomalies is analyzed and evaluated. 

Report Number: LSI-98-22-R
Title: Discrete Medial Axis Transform for Discrete Objects
Author(s): Puig, A.
Date: April 2
Nr. of pages: 26
Source file: Postscript/gzip, 160 K

Abstract:
The Medial Axis Transform $MAT$ was defined by Blum as an alternate description of the shape of a continuous object. The $MAT$ is the closure of the set of centers of maximal balls which can fit inside the object. A ball is maximal if it is not contained by any other such ball. This model provides dimensionality reduction, completness, it is homotopic with the object characteristics and it is continuous if the object is path-connected. In many applications of 2D digital image processing, discrete approximations of the MAT, such as skeletal representations, thinning, morphological and Distance Map based methods. The main drawback of these methods is that they do not keep up all properties of the continuous $MAT$ simultaneously. In this report, a Discrete Medial Axis definition is proposed as a direct extension of Blum's definition in order to achieve a complete and compressed model representation of discrete objects which retains the significant features of the object and preserves the axis connectivity based on local properties of the Distance Map. This enables to construct it with a seed algorithm whose cost is linear with the size of the object.

Report Number: LSI-99-55-R
Title: Discrete Medial Axis Transform for Discrete Thin and Elongated Objects
Author(s): Puig, A., Tost, D., Navazo, I.
Date: Dec 21, 1999
Nr. of pages: 20
Source file: Postscript/gzip, 234K

Abstract:
Skeletons are compact shape descriptions of discrete images. They have been extensively studied because of their utility in various applications such as data compression, shape abstraction, navigation and features detection. In this article, a new Euclidean skeletal definition for 2D discrete objects based on the Distance Map (DMAT) is being proposed. As a novel feature, it is shown that this skeleton is a connected subset of the discretization of the continuous medial axis of the object. Because of this property, the DMAT is 8-connected, it reflects all the features of the object and it preserves its topological characteristics. In addition, it provides dimensionality reduction, symmetry detection and invertibility. Moreover, it has a reasonable size and it guarantees low thickness.
An efficient seed algorithm for the extraction of the DMAT is also proposed. The usage of a seed strategy is made possible by the connectivity of the DMAT. This algorithm requires a number of passes proportional to the dimensions of the object. Thus, it is especially suitable for thinned objects or for objects whose radius is low in relation to the size of the image. The simulations have shown that this method is useful in several applications, such as the extraction of blood vessels from medical images.

Report Number: LSI-99-56-R
Title: Hybrid Model for Vascular Tree Structures
Author(s): Puig, A., Tost, D., Navazo, I.
Date: Dec 21, 1999
Nr. of pages: 23
Source file: Postscript/gzip, 420K

Abstract:
This paper proposes a new representation scheme of the cerebral blood vessels. This model provides information on the semantics of the vascular structure: the topological relationships between vessels and the labeling of vascular accidents such as aneurysms and stenoses. In addition, the model keeps information of the inner surface geometry as well as of the vascular map volume properties, i.e. the tissue density, the blood flow velocity and the vessel wall elasticity.
The model can be constructed automatically in a pre-process from a set of segmented MRA images. Its memory requirements are optimized on the basis of the sparseness of the vascular structure. It allows fast queries and efficient traversals and navigations. The visualizations of the vessel surface can be performed at different levels of detail. The direct rendering of the volume is fast because the model provides a natural way to skip over empty data.
The paper analyzes the memory requirements of the model along with the costs of the most important operations on it.

Report Number: LSI-00-69-R
Title: Visualization of labeled segments cross-contour surfaces
Author(s): Tost , D,, Puig, A.
Date: Des 28, 2000
Nr. of pages: 20
Source file: Postscript/gzip , 584K

Abstract:
Cross contour surfaces are composed of sets of planar contours. They are the natural output of surface extraction algorithms based on contouring features in parallel image slices of volume models. They are also suitable for the representation of CAD objects with tubular elongated shapes such as pipes and tools. Rendering these surfaces consists of tiling between successive contours, which is mainly a problem of establishing correspondences: between successive contours (branching) and also between vertices of consecutive contours (triangles definition). Most of the existing algorithms solve these problems by minimizing a distance function between vertices. However, contours are generally composed of segments belonging to different semantic regions that should not be mixed during tiling, as for instance, functional regions of the brain and types of terrain in elevation maps. A drawback of the existing distance based approaches is that they may establish correspondences between points of different segments. This paper proposes a representation model for surfaces from cross contours composed of labeled segments. In addition, a rendering algorithm of this model is described, that removes undesirable tiles between segments of different labels. The proposed method allows the tiling to be done on the fly, avoiding thus a double representation of the surface (contours plus triangle mesh). It also allows adaptive levels of resolution in the rendering.

Report Number: LSI-01-46-R
Title: Funciones en el modelado de solidos y paradigmas de diseño
Author(s): Solano, L., Vigo, M., Puig, A.
Date: Oct 26, 2001
Nr. of pages: 11
Source file: PDF/gzip , 131K

(written in spanish)

Abstract:
En este artículo se describen y analizan las diferentes funciones de modelado de sólidos más comunes que ofrecen los actuales sistemas de CAD. Se explican también las limitaciones e inconsistencias a qué pueden dar lugar el uso de dichas funciones. Por otro lado, también se analizan y comparan los diferentes paradigmas de diseño con los que trabajan los actuales sistemas. Se describe, evalúa y compara el paradigma clásico basado en operaciones booleanas, con los paradigmas basados en el diseño paramétrico y el diseño basado en características. También se describe cual es la interrelación a través de la interfaz de usuario entre los paradigmas de diseño y las funciones de modelado.

Report Number: LSI-02-13-R
Title: Rendering techniques for multimodal data
Author(s): Ferre, M., Puig, A., Tost, D.
Date: Feb 6, 2002
Nr. of pages: 16
Source file: PDF/gzip , 449K

Abstract:
Many different direct volume rendering methods have been developed to visualize 3D scalar fields on uniform rectilinear grids. However, little work has been done on rendering simultaneously various properties of the same 3D re-gion measured with different registration devices or at different instants of time. The demand for this type of visualization is rapidly increasing in scientific appli-cations such as medicine in which the visual integration of multiple modalities allows a better comprehension of the anatomy and a perception of its relation-ships with activity. This paper presents different strategies of Direct Multimodal Volume Rendering (DMVR). It is restricted to voxel models with a known 3D rigid alignment transformation. The paper evaluates at which steps of the render-ing pipeline must the data fusion be realized in order to accomplish the desired visual integration and to provide fast re-renders when some fusion parameters are modified. In addition, it analyzes how existing monomodal visualization al-gorithms can be extended to multiple datasets and it compares their efficiency and their computational cost.

Report Number: LSI-02-37-R
Title: Design of a Multimodal Rendering System
Author(s): Puig, A., Tost, D., Ferre, M.
Date: May 22, 2002
Nr. of pages: 7
Source file: Postscript/gzip , 632K

Abstract:
This paper addresses the rendering of aligned regular multimodal datasets. It presents a general framework of multimodal data fusion that includes several data merging methods. We also analyze the requirements of a rendering system able to provide these different fusion methods. On the basis of these requirements, we propose a novel design for a multimodal rendering system. The design has been implemented and proved showing to be efficient and flexible.

Report Number: LSI-02-38-R
Title: Visual Clues in Multimodal Rendering
Author(s): Tost, D., Puig, A., Ferre, M.
Date: May 22, 2002
Nr. of pages: 32
Source file: Postscript/gzip , 3894K

Abstract:
This report presents a comparative analysis of different multimodal rendering methods proposed in [FPT02]. It shows how relevant features of a property as well as relationships between data can be outlined by choosing an appropriate fusion modality. In addition, it analyses the visual clues that can be provided by using different shading models and by enabling rendering parameters such as depth cueing and light source attenuation. The simulations are performed on the software Hipo whose design is described in [PTF02].

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