Visualization

VISUALIZATION AND RECONSTRUCTION

Slice videos

Computer video files can be assembled directly from the datasets resulting from grinding (see Appendix 1, section 2), providing a simple way of leafing backwards and forwards through the slice images (Figure 3). These files form an invaluable tool for the exploration of datasets and, although less striking than full three-dimensional reconstructions, are often more useful for tracing the origins and termination of small or obscure structures. Nonetheless, they do not constitute a three-dimensional reconstruction in the accepted sense and are best used to complement rather than substitute for such reconstructions.

Construction of three-dimensional models

The ‘surfaces’ method. Two methodologies exist for the construction of three-dimensional models from data based on slices (Brown and Herbert 1996; Herbert 1999). The first, the ‘surfaces’ approach (Herbert 1999; see also Chapman 1989), begins with a manual interpretation step, tracing all structures of interest from each slice image (Figure 4.1-4.3). Traced outlines are digitized into line segments forming closed loops (Figure 4.4). The reconstruction algorithm assembles these stacked two-dimensional loops into a three-dimensional geometry, typically a mesh of triangular facets (Figure 4.5), which can be rendered into a two-dimensional view by a number of standard computer graphics techniques. The two key advantages of this method are that it, (1) does not require photographic images of the slices and, (2) is capable of working with low-quality, sparsely-spaced data. Neither of these is relevant to the present study. This method also has several disadvantages, especially in the context of the Herefordshire fauna. The initial interpretation stage is extremely time-consuming when a large number of slice images are involved, and also threatens the objectivity of the reconstruction as structures must be delineated before the three-dimensional form becomes apparent. When the margins of the fossil structures are unclear (as is often the case with the Herefordshire fossils), there is a danger that subjective interpretations will influence the reconstructed morphology. In addition, the algorithmic reconstruction of stacked two-dimensional loops into three-dimensional surfaces is subject to the ‘correspondence problem’–that is, the difficulty of determining the manner in which loops in subsequent slices connect to each other. Herbert (1999) approached this problem with algorithms that made a priori assumptions about the morphology of the object to be reconstructed, an approach that is clearly not viable for the reconstruction of poorly understood morphologies such as those of many Herefordshire fossils. Other available approaches require the user to determine correspondence, a procedure that is both time consuming and represents another potential source of subjectivity.

Volume-based methods. The second reconstruction methodology, that of volume-based reconstruction, is preferred in the present study. Volume representation is a three-dimensional extension of ‘raster’ or ‘bitmap’ representations of two-dimensional images, in which an image is modelled as a rectangular array of regularly spaced pixels. A volume dataset thus consists of a three-dimensional array of regularly spaced volume elements or ‘voxels’, each stored as a number representing the value of some property of the object at that point. The sequential slice images generated by the grinding technique (after minor post-processing — see Appendix 1, section 3), represent a volume of this sort in which the values of the voxels represent the reflectivity of the surface as captured by the digital camera. Volume-based three-dimensional reconstructions, largely utilizing datasets from MR or CT scanners, are routinely used in medical applications and have been used to produce volume-based reconstructions of fossils (e.g., Hamada et al. 1991; Torres 1999). These methods have also been applied to optically captured volumes. Brown and Herbert (1996) attempted to produce volume-based models from serial section data, although the low resolution of the graptolite sections on which that work was based precluded a successful reconstruction. More successfully, Hammer (1999) reconstructed a halysitid coral colony from volume data obtained by serial grinding and captured with a flatbed scanner.

Volume rendering. There are various techniques, collectively known as volume rendering, for the direct visualization of volume data . Although they vary in detail, all involve forms of ‘ray casting’, where the computer calculates an array of virtual light rays ‘shone’ into the volume from a specified angle, determines their fate according to mathematical rules based on the values of voxels in the volume, and builds a two-dimensional image from the results of these calculations. We have used mean-intensity volume rendering, where the final intensity of the virtual ray is determined by the mean values of the voxels it encounters. This algorithm produces a virtual ‘X-ray’ image of the volume from any angle the user chooses (Figure 5). Like true X-radiographs, the images are a relatively poor aid to visualizing the outer surface of objects, but are effective for imaging of large or strongly absorbent (=dark) structures that otherwise may be obscured by less substantial features.

Isosurfaces. While volume data can thus be rendered directly, the preferred approach for medical visualization from CT or MR data is usually to generate polygon mesh surfaces known as isosurfaces. These are generated by algorithms that connect points of a constant (user-determined) intensity within the volume. If the threshold level is chosen correctly, an isosurface generated from a dataset such as shown in Figure 3 should correspond to the original external surface of the organism. Isosurfaces can be rendered with any of several computer graphics techniques available for the visualization of geometrically defined surfaces. Ray-tracing, though the most computationally expensive of these techniques, provides the clearest and most natural visualizations (Figure 6). Although volume-rendered ‘X-ray’ reconstructions have some application to the Herefordshire fossils, ray-traced isosurfaces are our preferred means of three-dimensional visualization. Reconstructions produced in this way retain the objectivity of volume data without compromising the clarity and sharpness of the rendered images.

Animation. Isosurfaces have been used previously to produce static images of fossils (e.g., Torres 1999; Hammer 1999; Brown and Herbert 1996). While such images have some illustrative value, a true appreciation of three-dimensional morphology is best achieved with an interactive model. We produce these (for both isosurface and volume rendering techniques) from a batch of images rendered from sequential angles and assembled into a computer video file that can be presented as a reconstruction of the specimen (Figure 7, Figure 8, Figure 9, Figure 10, and Figure 11). As with video files assembled directly from slice images, these files can be played backwards or forwards and provide a simple but effective means of viewing the reconstruction from a variety of angles. They also enable the reconstruction to be distributed easily for viewing on any modern computer without the need for dedicated software.