Volume rendering on the MasPar MP-1

This work presents the implementation of data-parallel perspective volume rendering on a massively parallel SIMD computer, the MasPar MP-1, and shows the benefits of e$icient indirect addressing (an MP-1 feature) which allows individual processing elements to address their local memory independently. Emphasis is put on the geometric transformations required for volume rendering algorithms. TJte data-parallel algorithm separates multi-dimensional spatial transformations into a series of one-dimensional operations that can be performed in parallel on regular data domains, providing performance linear with data size. The rotation andperspective transformation is reduced to four shearlscale passes. The separable approach allows for predictable and regular data handling, independent of data values, allowing optimization of communication between processing elements. The communications required are data axis transpositions, wJtich can be peflormed using the MP-1 ‘s global router, which delivers scalable peflormance. Wrtualization allows graceful scaling in both problem size and architecture size, and a hierarchical design provides a flexible and portable fiamework suitable for different data-parallel SIMD architectures. 1 IMAGE-BASED VISUALIZATION Massively data-parallel architectures can realise close to peak performance on regularly structured image processing and viewing operations, allowing in some cases for real-time (or near real-time) interaction with modelling and viewing parameters [17]. A number of special architectures have been used for volume rendering [ 111. Polygon-based graphic algorithms pose problems of scalability, discretization independent of problem domain, and dependence on special purpose hardware for high performance [9]. Imageor pixel-based algorithms can be scalable with problem size, need not introduce geometrical artifacts and can be implemented on general purpose data-parallel computers. As a result, increases in model complexity (e.g. molecular modelling), empirical data generated from sensors (e.g. remote sensing and medical imaging) and inter* GPO Box 664, Canberra, ACT 2601, Australia Tel.: +616 275 0911 Fax: +616 257 1052 guy.vezina@csis.dit.csiro.au peter.fletcher@csis.dit.csiro.au phil.robertson@csis.dit.csiro.au Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 1992 Workshop on Volume Visualization/l 0/92/Boston, MA o 1992 ACM 0-89791-5293/92/0010/00003...$1.50 action impose requirements that polygon-based systems often cannot satisfy. Image-based approaches are particularly well-suited to handling large multidimensional empirical data and the integration of computer vision, computer graphics and image processing 131. 2 DATA-PARALLEL VOLUME RENDERING The data-parallel algorithm achieves data access regularization by following the approach taken by Drebin&al.[4], which is a source for better efficiency in data access. Data-parallel geometrical transformations, including rotation and perspective, are applied to the data to localize projection rays within individual processing element memories. Once localization is completed, iso-surface rendering is computed using Levoy’s technique [12]. This consists of computing voxel opacities for iso-surface classification, computing Phong shading, and compositing along the viewing rays for the final view (See also [21] for an extensive discussion on volume rendering issues). The data-parallel geometrical transformation algorithm is based on separating multi-dimensional transformations into a series of one-dimensional operations that can be performed in parallel on regular data domains, providing an adequate level of parallelism for massively parallel architectures. A three-pass rotation algorithm is used, requiring shear/scale operations along orthogonal axes [lo]. Following volume rotation, perspective projection is performed in two passes by applying scaling to the scanlines. The rotation and perspective transformation can be combined and reduced to a four-pass shear/scale algorithm For a generic set of data-parallel geometric transformation tools for visualization applications, several issues must be considered: efficiency, flexibility, resampling artifacts, scalability and portability. 2.1 Requirements For interactive visualization, and for handling large volumetric data sets, efficiency is critical. F.vo classes of operations underlie imagebased transformations: the first is data processing comprising geometric or spatial transformation, resampling and associated filtering; the second is data handling, comprising data formatting and access according to algorithm and data-dependent requirements. Efficiency in handling large data sets on massively data-parallel machines relies heavily on two factors: regularizing data access, and reducing the data-value dependence of access requirements. Achieving the latter substantially eases the requirements for providing the former. Key to the approach is the common localization of domains which can be processed in parallel. The result is that some operations may be less efficient than they might otherwise have been independently, but that effectively the “lowest common denominator” domains guarantee that no operation can introduce severe penalties that dominate the results, either in data-dependent time complexity or in the potential introduction of artifacts