We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

A popular technique for rendition of isosurfaces in sampled data is to consider cells with sample points as corners and approximate the isosurface in each cell by one or more polygons whose vertices are obtained by interpolation of the sample data. That is, each polygon vertex is a point on a cell edge, between two adjacent sample points, where the function is estimated to equal the desired threshold value. The two sample points have values on opposite sides of the threshold, and the interpolated point is called an intersection point. When one cell face has an intersection point ineach of its four edges, then the correct connection among intersection points becomes ambiguous. An incorrect connection can lead to erroneous topology in the rendered surface, and possible discontinuities. We show that disambiguation methods, to be at all accurate, need to consider sample values in the neighborhood outside the cell. This paper studies the problems of disambiguation, reports on some solutions, and presents some statistics on the occurrence of such ambiguities. A natural way to incorporate neighborhood information is through the use of calculated gradients at cell corners. They provide insight into the behavior of a function in well-understood ways. We introduce two gradient-consistency heuristics that use calculated gradients at the corners of ambiguous faces, as well as the function values at those corners, to disambiguate at a reasonable computational cost. These methods give the correct topology on several examples that caused problems for other methods we examined.

. In this paper a new gradient estimation method is presented which is based on linear regression. Previous contextual shading techniques try to fit an approximate function to a set of surface points in the neighborhood of a given voxel. Therefore, a system of linear equations has to be solved using the computationally expensive Gaussian elimination. In contrast, our method approximates the density function itself in a local neighborhood with a 3D regression hyperplane. This approach also leads to a system of linear equations but we will show that it can be solved with an efficient convolution. Our method provides at each voxel location the normal vector and the translation of the regression hyperplane which are considered as a gradient and a filtered density value respectively. Therefore, this technique can be used for surface smoothing and gradient estimation at the same time. 1 Introduction In direct volume rendering the quality of the generated image is strongly influ...

Maximum projection is a volume rendering technique that, for each pixel, finds the maximum intensity along a projector. For certain important classes of data, this is an approximation to summation rendering which produces superior visualizations. In this paper we will show how maximum projection rendering with additional depth cues can be implemented using simple affine transformations in object space. This technique can be used together with 3D graphics libraries and standard graphics hardware,thus allowing interactive manipulations of the volume data. The algorithm presented in this paper allows for a wide range of tradeoffs between interactivity and image quality. 1 Introduction The existing approaches to volume visualization can be classified into two categories: direct volume rendering and model based techniques. While these two techniques have often been portrayed as competitors, we think they should actually be seen as being complementary. The method described in this paper us...

294,018 vertices, compressed to 0.7437 bits per face. C: UNC CThead data set, level 1160, 312,488 faces, 312,287 vertices, compressed to 0.8081 bits per face. In this paper we introduce a new and simple algorithm to compress isosurface data. This is the data extracted by isosurface algorithms from scalar functions defined on volume grids, and used to generate polygon meshes or alternative representations. In this algorithm the mesh connectivity and a substantial proportion of the geometric information are encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder closely related to the JBIG binary image compression standard. The remaining optional geometric information that specifies the location of each Marching Cubes vertex more precisely along its supporting intersecting grid edge, is efficiently encoded in scan-order with the same mechanism. Vertex normals can optionally be computed as normalized gradient vectors by the encoder and included in the bitstream after quantization and entropy encoding, or computed by the decoder in a postprocessing smoothing step. These choices are determined by trade-offs associated with an in-core vs. out-of-core decoder structure. The main features of our algorithm are its extreme simplicity and high compression rates.

Abstract—Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue is often addressed through postprocessing operations such as smoothing. As we demonstrate in experiments with several data sets, while these improve the mesh, they do not remove all degeneracies and incur an increased and unbounded error between the resulting mesh and the original isosurface. Rather than modifying the resulting mesh, we propose a method to modify the grid on which Marching Cubes operates. This modification greatly increases the quality of the extracted mesh. In our experiments, our method did not create a single degenerate triangle, unlike any other method we experimented with. Our method incurs minimal computational overhead, requiring at most twice the execution time of the original Marching Cubes algorithm in our experiments. Most importantly, it can be readily integrated in existing Marching Cubes implementations and is orthogonal to many Marching Cubes enhancements (particularly, performance enhancements such as out-of-core and acceleration structures). Index Terms—Meshing, marching cubes. Ç 1

The display of iso-surfaces in medical data sets is an important visualization technique used by radiologists for the diagnosis of volumetric density data sets. The demands put by radiologists on such a display technique are interactivity, multiple stacked transparent surfaces and cutting planes that allow an interactive clipping of the surfaces. This paper presents a Java based, platform independent implementation of a very fast surface rendering algorithm which combines the advantages of explicit surface representation, splatting, and shear-warp projection to fulfill all these requirements. The algorithm is implemented within the context of J-Vision, an application for viewing and diagnosing medical images which is currently in use at various hospitals. CR Categories: I.3.3 [Computer Graphics]: Picture / Image generation---display algorithms; J.3 [Life and Medical Sciences]: Medical information systems Keywords: volume visualization, surface rendering, medical applications. tomogra...

This dissertation gives accurate and efficient methods for the object-order rendering of discrete objects. Discrete objects are typically represented with a volume raster and rendered with a volume rendering algorithm. However, current object-order volume rendering algorithms suffer from several problems. First, they require that the volume raster be traversed in a strict visibility order, but existing visibility ordering methods do not always correctly order perspective projections of volume rasters. Second, both perspective and orthographic renderings of volume rasters can contain aliasing artifacts, but current object-order techniques have no method for addressing these artifacts. Third, computergenerated animations suffer from temporal aliasing artifacts, which can be addressed by adding motion blur. But currently the only motion-blur method for object-order techniques is super-sampling, which is very expensive. This

The main contributions of this work are summarised as follows: A flexible and low-cost object modelling framework, with rendering methods, for intermixing discrete and continuous volume data. Image-swept volumes: A new modelling paradigm in which attribute fields of volume objects are defined by sweeping discrete image or volume templates along arbitrary trajectories. A projection-based texture mapping method for volume objects. A method for rendering Bezier volumes and free-form deformations of volume objects. vlib: A volume graphics API, including detailed design and implementation details. The field-based modelling framework addresses the limitations of using discrete data for representing volume objects. It not only results in very high quality images (with shadows, reflection and refraction) while supporting "traditional" volume graphics, which we demonstrate using several examples, but also it frequently reduces the significant memory overhead that is normally associated

Volume rendering is a title often ambiguously used in science. One meaning often quoted is: `to render any three volume dimensional data set'; however, within this categorisation "surface rendering" is contained. Surface rendering is a technique for visualising a geometric representation of a surface from a three dimensional volume data set. A more correct definition of Volume Rendering would only incorporate the direct visualisation of volumes, without the use of intermediate surface geometry representations. Hence we state: `Volume Rendering is the Direct Visualisation of any three dimensional Volume data set; without the use of an intermediate geometric representation for isosurfaces'; `Surface Rendering is the Visualisation of a surface, from a geometric approximation of an isosurface, within a Volume data set'; where an isosurface is a surface formed from a cross connection of data points, within a volume, of equal value or density. This paper is an overview of both Surface Render...