ABSTRACT. 1 Introduction

Transcription

1 Parallel volume projection in 3D medical images G. Larrazabal,* P. Escalona,* G. Montilla,* V. Torrealba,* M. Acuna,^ V. Barrios** "Departamento de Computation, Facultad Experimental de Cienciasy Tecnologia, Universidad de Carabobo, Apdo. 3155, El Trigal, Valencia 02002, Venezuela ^Grupo de Procesamiento de Imdgenes, Centra de Investigaciones Medicas y Biotecnologicas, Facultad de Ingenieria, Facultad de Ciencias de lasalud, Universidad de Carabobo, Apdo. 3155, El Trigal, Valencia 02002, Venezuela ABSTRACT This paper presents a Parallel Volume Rendering algorithm which was applied in 3D Ecocardiographic and TAG images. This algorithm used a Heuristic partitioning method which distributes both the data and computations to processing units to achieved fast, high quality rendering. The processing nodes perform local Ray Casting of their subvolume simultaneously. No communication between processing units is needed during this local Ray Casting process. A subimages is generated by each processing unit and the final image is obtained by volumetric composition in the proper order, which can be previously determined. This composition is centrally control. Test results over a PowerXplorer Parallel machine reveals a satisfying acceleration of the process. 1 Introduction 3D visualization has become a valuable tool in the diagnostic, surgery, therapy and better understanding of medical images. A classic approach to generate 3D images begins with the acquisition of data in a parallel spatial sequence of slices which are grouped in a stack. This stack is process by different visualization techniques, developed to project the volume on the display. Ray Casting-illumination models combination, allows among other techniques used, the achievement of very realistic images. These techniques are described later in this paper[l]. Visualization involve the management and processing of high volume data. This implies the need of new techniques to lower the time processing to functional levels. Exist a growing amount of reported works on Parallel Volume Rendering on different architectures [2,3,4]. The algorithm once developed for a sequential machine is adapte to run in a parallel PowerXplorer machine with 16 nodes. This algorithm used a Heuristic partitioning method which distributes both the data and computations

2 210 Simulation Modelling in Bioengineering to individual processing units to achieved fast, high quality rendering of the data. The processing nodes perform local Volume Rendering based on computer graphics technique: Ray Casting, Phong Illumination model and Fuzzy Classification, of their subvolume simultaneously. Communication between processor is not required during the local volume rendering process. The final image results from the composition of partial images generated from processors which are control by a centralized process. This composing process is made with a predetermined order. The experimental results shows a lineal acceleration in relation with the number of processors used in every trial. High efficiency and quality images was achieved on this trials. 2 Methodology The algorithm developed in the Image Processing Group involved different visualization techniques that render a sequence of slices from a CT of a skull as shown in figure 1. The machine used was a Parsytec PowerXplorer with a Sparcstation 5 as its front end. The programming language was C under Parix. The algorithm is divided in three stages: ### Volume Partitioning. ### Parallel Volume Rendering. ### Composition. Figure 1. Fraction (3 slices) of a CT sequence. 2.1 Volume Partitioning Each processor received a fraction of the volume, which is render using a local volume rendering algorithm. This data assignment is partition over the XZ plane, the method used establish a compromise between horizontal and cross partitioning [5]. After each processor identify his corresponding initial and final coordinates of the subvolume of interest, data is loaded in memory before the following processing. Figure 2.a and 2.c shows the symmetric partition obtained for a number of nodes with an integer squareroot result.

3 Simulation Modelling in Bioengineering 211 Figure 2.b shows the results for a different case. This distribution allows the prediction of the position of the subvolumes. (a) (b) (c) Figure 2. Heuristic partitioning (a) 4 processors (b) 8 processors (c) 16 processors. 2.2 Parallel Volume Rendering There are a diversity of methods to implement volume rendering which common objective is to project 3D data over a plane. Every subvolume is treated independently by the same graphics method for volume rendering. For the data from the volume to be evaluated and analyze based on their intensity and illumination properties, Ray Casting was the selected method [6]. The purpose of ray casting is to trace imaginary rays over the data and evaluate every intersected voxel. A ray is throw from every pixel on the screen in the same angle and direction. Each voxel is evaluated based on his illumination and opacity components, these component as will explain later depends on the material classification and on the properties specified by the user. The resulting value is accumulated through the ray until the final voxel is intersected and the total calculated value is assign to the pixel of the screen from where the ray started. The result is a 2D representation of the volume. One of the factors that influence the Ray Casting is the selected illumination model. The illumination model selected is the Phong model Phong Illumination Model The illumination of an object depends on several parameters (light position, distance, orientation, surface texture) that defines the resulting color and intensity perceive by the observer. The basic Phong model involves three basic terms: Ka, Kd and Ks which represents color, diffuse and specular properties of the material. The illumination components of the voxel is modeled through the Phong equation (Fig. 3): / = (K-tfy (1) Iff a ambient light component, /^ represents the object color.. Kfl (N-L) : diffuse reflection component, the brightness depends on the angle between the light source and the surface normal.

4 212 Simulation Modelling in Bioengineering Kg (R'V)**\ specular reflection, property of some objects to unequally reflect lights in different directions. Luz 0!> J L ' R L*7 \ "" ^ Figure 3. Details of the Phong equation. A more complete Phong illumination model includes reflections terms. Multiples reflections are not consider in medical images. However transparency from some structures is important to observed sometimes hidden surfaces. The Fuzzy classification includes this properties for a better visualization of different materials (blood,flesh,bones) [7] Fuzzy Classification Fuzzy classification is related to the degree of pertenence of the voxel to a region of interest, object, material or a class. The material has his proper opacity coefficient. Based in the range of gray level values, the object may be present, partially present or not present at all. Figures 4 shows the diffuse classification function assign to two materials based on the intensity of the voxel. Degree of ^ pertenence Class 1 Class 2 X X1cla X2cla Intensity Figure 4. Fuzzy coefficient for two materials. For a voxel composed of two materials A y B, Poster propose the following composition formula: (2) A, B, C are the colors; p,%, jlly are the voxel degree of pertenence, a^, a*,, are the individual opacity and the combine opacity.

5 Simulation Modelling in Bioengineering 213 From figure 5 /(/-i) and IQ^\ are the foreground and background colors (two media) with opacity GL^(i-l) and a(i) repectivelly. /(i-i) and OC0(f-7) are the accumulated valued. IQ is the value related to the result of formula (1) apply to an individual voxel, a is the opacity coefficient of the evaluating voxel, with a range indicating the opacity propertie of the material. Figure 5. Recursive Volumetric Composition is formulate to consecutive voxels. The interpolated transparency definition is given by the formulas (3) and (4); If ct=l, the foreground object is totally opaque and the background object is totally hidden. If a=0 the foreground object is totally transparent. The value of a varies with the definition of Xlcla and X2cla for every object. As shown in figure 5 the calculation is made from "Front to Back". I ft) =( 1 -< (3) 2.3 Centralized Composition (4) Each processor generates a partial image that result from the applied volume rendering algorithm describe earlier in this work. This images are send to a control processor with the objective to combine them, with a particular order base in the observer perspective, to display the final image. This order is determined by the sign of the coordinates (X, Y) obtained from the geometric distribution of the data and the angle of projection. A 2D grid is generated in the control processor where each cell represent a partial image as shown in figure 6. The sign of the coordinates represents the direction of the composition and the order of the combination process which allows the visualization of the subvolume that are closer to the observer and hidding of those that are farther to him. The combination of the partial images are made through a simpler transparency definition.

6 214 Simulation Modelling in Bioengineering I (0,1) (1,0) (-1,0) f (0.-1) Figure 6. Direction of the composition in the 2D grid of partial images. 3 Results Figure 7 shows the result of the partial images obtain from an execution of the algorithm over 4 processor. The images show the results of the volume rendering algorithm apply to each subvolume. Figure 7.a. Partial images Figure 7.b. Partial images Processing time using four nodes was approximately of 18 seconds, this times includes the communication required to centralized partial images and composing the result. This reveals an advanced over the sequential time of 65 seconds for the an images of the same characteristic ( angle of visualization, illumination constants, distance from the observer), indicating that the parallel algorithm is approximately four time faster than the sequential. Figure 8 shows

7 Simulation Modelling in Bioengineering 215 the final composition, the brighter lines helps in visualizing the boundaries integration between every sub volume. 4 Conclusion Figure 8. Final result We have present a parallel algorithm for volume rendering that guarantee a fast execution without loosing the quality of the image resolution. This directly implies the processing of large volumes of data since every processor can handle a independent fraction of image. The experimental results reveals a high efficiency in the implementation, given a linear acceleration. Acknowledgment This work is part of the "Miranda" supported by CONICIT (project SI ), CONICIT-BID (project SIC-E08), CODECIH and The European Economic Community (project ITDC-230). Reference [1] Foley J.D., Van Dam A., Feiner S. K., Hughes J. F., "Computers Graphics Principle and Practice", Addison-Wesley, , [2] Law A., Yagel R., Jayasimha D. N., "Voxel Flow: A Parallel Volume Rendering Method for Scientific Visualization.", Proceedings of ISCA International Conference. March 15-17,1995. PP [3] Law A., Yagel R. "Cell Flow: A Parallel Rendering Scheme for Distributed Memory Architecture". International Symposium on Parallel and Distributed Processing Techniques and Applications. Athens, Georgia, November 3-4,1995. [1] Watt A., "Fundamentals of Three Dimensional Computer Graphics", Addison-Wesley, , [4] Badouel D., Bouatouch K., Priol T., "Ray TRacing on Distributed Memory Parallel Computers: Strategies for Distributing Computations and Data.", Rapports de Recherche No IRIS A. Feb

8 216 Simulation Modelling in Bioengineering [5] Dirgan Y. Larrazabal G. " Implementation de un Particionamiento Heuristico". Reporte Tecnico #Tl Departamento de Computation. FACYT. [6] Barillot C., "Surface and Volume Rendering Techniques to Display Data", IEEE Engineering in Medicine and Biology. Vol 12, , Marzo [7] Passariello G., Mora F.(Eds.), "Imagenes Medicas: Adquisicion, Analisis, Procesamiento e Interpretation", Chapter 8 "Avances en Imagenologia Medica 3D". Equinocio (USB), , 1995.