The types of presentation in use are as diverse as the multitude of fields of application for data exploration and visualization with virtual interactive environments. Adapted from a classification applied by Biocca and Levy [ BL95 ] and based on [ Ber04 ], three basic forms of visual VR presentation exist:

For additional information on VR display technologies see [ Hof05 ].

Three-dimensionally resolved image data, traditionally on a macroscopic scale in medical applications, have become more and more available to life sciences and biology on microscopic or even molecular resolution, often delivering stunning insights into structures and function. The observation of structure and function in its natural spatial or spatio-temporal extension is not only more intuitive to investigators, but often elucidates the underlying principles of dynamics and mechanisms in living matter, e.g. [ JLM08 ] deliver impressive examples of proving assumptions about intra-cellular motor mechanisms by 3-D image analysis and visualization. While in medical applications a standard for imaging devices and acquisition exists, 3-D imaging in biology is highly application-specific. Non-destructive bio-imaging methods such as laser scanning microscopy, X-ray or magnetic resonance imaging have been employed to generate models of insects [ PH04 ], [ KHKB07 ] and plants [ Gli06 ], [ BMH00 ] on microscopic scales, either by direct intensity-based visualizations or further processing such as tissue or organ labeling. Destructive methods overcome limitations in resolution and sample depth by serially sectioning the object allowing analysis of histological structure and functional data, such as gene-specific expression levels [ RBB94 ], [ GDB07 ], with comprehensive demands in image reconstruction on the downside.

While sample preparation and wet-experiments are labor- and resource-intensive, careful analysis and visualization of biological 3-D images has become more and more important in the past. Standard or device-shipped software often seems to provide insufficient functionality for specific tasks, resulting in an increasing number of published software and comprehensive libraries for biomedical image analysis and visualization.

A small number of VR applications are in use in plant and crop research. While they are based on VR technologies, they employ different approaches and have different foci. Based on their applications, VR technologies for plant biological objects can be subdivided into the following categories:

While the field of biomedical data research has a variety of feasible solutions at its disposal, the field of plant biology research unfortunately still does not. Hence, algorithms and VR technologies have to be adapted for specific applications.

Biological material was generated for visual analysis, specifically microtome serial section data of different stages of barley seed development (days after flowering or DAF) for high resolution histological images similar to the method described in [ GDB07 ]. Each dataset consists of approximately 2.000 slice images of a developing barley caryopsis, which were obtained from a microtome at 3μm slice thickness. Digitized with a color CCD camera, images originally measured 1600 x 1200 pixels at a spatial resolution of 1.83 μm x 1.83μm per pixel. Since color-space analysis revealed an almost linear correlation and a limited range, it was possible to reduce the optical resolution of 12 bits for each RGB channel to 8 bit grayscale images without significant loss, reducing the data volume for each dataset to approximately 5 GB. Depending on the developmental stage of the specimen, sections can be too large to be captured in a single frame with the given spatial resolution and imaging setup. As a result, the mosaic images are composed from several sub-image scans. Since sub-image acquisition is not performed in a fixed arrangement, the restored image is computed based on image contents using a phase-correlation-based algorithm (see [ Bra65 ]) and multi-resolution blending of image intensities proposed in [ SHC04 ].

Available data include gene expression assay data utilizing mRNA in-situ hybridization (ISH) probing of histological cross-sections. Whereas in-situ data allows visualizing spatial gene expression patterns, staining with gene-specific samples requires complex chemical protocols so that the ISH image data originates from different individual grains.

Magnetic resonance spectroscopy measurements (¹H-NMR) of caryopses at different points in time were sampled in a specific device. While being non-destructive,the detected proton distribution has a lower spatial resolution of approximately 10μm (isotropic) per voxel, and does not resolve histology or structural features (see Figure 5).

Figure 5. NMR imaging data of a developing barley grain, specifically two volume renderings of intensity voxel data from different angles and cutting planes. While NMR is a noninvasive imaging, it has a smaller (10μm/voxel) spatial resolution than light microscopy.

Other potential datasets, such as macroarray gene expression data or metabolomic assays by laser microdissection (LMD), could be integrated into the database to enhance synergy and facilitate the inference of analysis results. Figure 6 presents the database with different data domains and an example image. Figure 7 shows a pie chart breaking down data distribution per model. The organization is derived from the entity-attribute-value (EAV) design as in [ Anh03 ]. This approach has the advantage of high flexibility when extending the database with other data domains.

Figure 6. Schematic view: Integration of different data domains by using an EAV model for the visualization database.

Figure 7. Data distribution for one model, the absolute data totaling around 9 GB.

In general, data sampled from real world objects exhibits an inevitable level of noise and limited spatial and temporal resolution. Therefore, image processing and image analysis is necessary to enhance relevant information. Applications have many diverse requirements, and solutions for end users are often devoted to specific questions with little transparency on algorithms and parameters. While users with biological backgrounds frequently lack detailed knowledge of image processing algorithms and theory, consistent and comprehensible approaches are necessary for reproducible and exact results.

Eliminating artifacts, distortions and signal noise in sampled images, e.g. caused by preparation and handling during digitization, is not only beneficial in terms of generating'good' data for subsequent processing and visualization, but is often a preliminary for measurements of biological quantities in image data.

While the following categories are somewhat arbitrary, they nevertheless can be considered as prominent problems occurring in 3-D biomedical imaging.

The processing workflow for high-resolution 3-D models generation from digitized raw data follows the flowchart in Figure 4: While the principles behind the three main tasks preprocessing, segmentation and surface reconstruction are relevant for subsequent visualization and navigation, a detailed description of the process would go beyond the scope of this paper.

Since the full spatial resolution is conserved to the final surface-modeling, data amounts to be processed are large. The preprocessing of raw images includes image intensity normalization and noise removal. While adequate mapping of intensity values is computationally cheap, the exact delineation and masking of the object of interest (see Figure 9) is performed using geodesic active contours [ CKS97 ] in hierarchical image representation for faster convergence.

Image registration is the process of transforming two or more n-D images so that corresponding structures match, i.e. registering images onto a reference is a prerequisite to collecting and comparing structural features, and therefore a problem most frequently arising in biomedical image processing prior to any further analysis and visualization, as surveyed in [ MV98 ] and [ GB92 ].

Image registration is generally formulated as an optimization problem regarding an image metric, maximizing the correspondence of images based on image grid point intensities or extracted features such as edge information, employed in quadratic or correlation-based distance formulations. Desired properties, such as smoothness of the transformation etc. can be enforced by regularizing the objective function with additional terms evaluating the actual transformation (see [ Mod04 ] for an overview).

Registration based on the correspondence of unique points, i.e. landmarks is difficult since such landmarks are often ambiguous and hard to detect in biomedical images.

The choice of transformations is driven by the application, i.e. by the physical process underlying the distortion of images, necessitating different numerical schemes. This study employs registration techniques to reconstruct distorted serial section 2-D images to compose an intact 3-D intensity dataset and integrate image data from different imaging modalities in a 3-D model. Modersitzki [ Mod04 ] extensively discusses numerical schemes and applications.

The 2-D / 3-D reassembly of a serial section dataset requires registration of the whole image stack. Since in-core processing of arrays of several gigabytes in size is unfeasible, transformations are optimized within a local range of consecutive stack images as described in [ Mod04 ]. Resolution hierarchies allow fast and robust optimization schemes that combine exhaustive and gradient-descent searches, (see [ ISNC03 ] for details). The intact 3-D object is thereby restored composing a large voxel dataset showing internal histological structures (Figure 8).

Figure 8. Serial section data: The three-dimensional coherence of histological structures is reconstructed by registering the stack of section images. The figure depicts a volume rendering of the histological voxel data and virtual cutting planes.

Segmenting images into homogeneous regions on the basis of application-specific criteria is a crucial step of image analysis.

Figure 9. Using automated segmentation algorithms a complete labeling of multiple biologically relevant tissues in images is obtained.

All image segmentation algorithms are intended to decompose an image into segments with specific meaning for a given application [ HS85 ] or, expressed more technically, to identify regions that uniformly relate to a specific criterion such as texture or image intensity [ Hah05 ]. The literature, specifically [ LM01 ], [ Hah05 ] and [ Kan05 ], presents a variety of approaches to classification. As it relates to user interaction, here, image segmentation methodology is classified according to the following techniques: manual segmentation, semiautomatic segmentation, and automatic segmentation. Figure 9 shows an example of a complete segmentation of a barley grain slice with its tissue legend.

Manual segmentation: This is the easiest image segmentation technique and commonly applied to structures with widely varying morphologies. The user specifies a set of points that will be connected afterwards. The contour can additionally be smoothed by familiar interpolation methods [ Far88 ].

Since numerous segmentation points have to be specified manually, the main disadvantage of this technique is the necessary time and mental effort, and accordingly, these segmentation results are less reproducible in terms of inter-rater variability. An example of manual segmentation in the context of the authors work regarding spatial plant models is discussed in [ GDB07 ].

Voxel data is decomposed into subvolumes of specific tissues. The method described in [ BS08 ] enables automatically segmenting the full stack of approximately 2.000 images with a small set of reference images that a biologist has labeled manually or semiautomatically.

Automatic segmentation: Algorithmically addressing segmentation is generally superior over manual or semiautomatic segmentation for time-saving and non-subjectiveness. Although a large number of methods, e.g. graph-based [ BSC06 ] or variational formulations of the segmentation problem [ CKS97 ], [ TYJW03 ] have been proposed, biomedical image segmentation remains difficult. The non-uniqueness of features and structures often necessitates expert knowledge for correct identification and labeling. This particularly holds for histological image data in plant sciences, since here tissues in images discriminate on small-scale structures in their structural context due to cell walls (see Figure 8) rather than global properties, such as intensity. The authors have demonstrated in previous studies that incorporating expert knowledge is inevitable to achieve exact segmentation results (see [ BSS06 ], [ BS08 ]).

Segmentation algorithms incorporating expert-generated reference data as described in [ BS08, BWSS09 ] have proven to deliver high segmentation accuracy, especially in non-binary segmentation scenarios. In [ BS08 ] a registration-based segmentation algorithm is described that performs equally well with supervised classification schemes as support vector machines and neural approaches to segment serial section data into multiple classes based on a small set of user-generated references.

Semiautomatic segmentation: These approaches are helpful since automatic segmentation results may contain inaccuracies or applied algorithms may require a small set of reference images to solve a given problem. In some cases, it may be impossible to use automatic segmentation at all. User-steered semiautomatic segmentation algorithms can help to eliminate these drawbacks. Although a multitude of other semiautomatic segmentation algorithms exist, the LiveWire method [ MB98 ] and [ FUS98 ] provides the best method to postprocess only a few misclassifications and prepare a few reference segmentations. A modified LiveWire technique for fast and accurate segmentation of independent serial sections is presented in [ SBH08 ].

Semiautomatic segmentation algorithms ideally supplement automatic segmentation. The solution presented here is a hybrid approach consisting of automatic offline segmentation and the option for users to intervene with semiautomatic segmentation.

For a level of abstraction higher than intensity stacks of images, boundaries of the labeled voxel data are converted into an explicit, geometric representation. The algorithm applied in Section 3.4 - Triangulation - generates triangle-mesh approximations of isosurfaces in one pass, but has the disadvantage of generating a large number of faces without adapting the geometry to the true isosurface. This makes a subsequent surface simplification necessary to reduce the number of faces (see Section 3.4 - Surface reduction and remeshing).

The literature supplies a variety of reconstruction methods, each with different drawbacks. Methods operating at the voxel level execute subvoxel resampling, use non-binary segmentation masks or apply segmentation with subvoxel accuracy.

Other data sources for surface reconstruction include point clouds resulting from the intersection of different models or contour lines as output from the semiautomatic segmentation. A number of existing solutions have already been implemented including the adaption of the parameters to the specific data characteristic. Commercial applications are also used to reconstruct the 3-D surface. The necessary or optional steps for surface reconstruction are described below.

Triangulation: Cell-based simple triangulation similar to the marching cubes algorithm proposed by Lorensen [ LC87 ] and variants [ LLVT03 ] have been implemented. The main drawbacks experienced so far are the immense number of triangles generated and problems with sampling in areas where sharp edges are expected. The power crust algorithm (see [ ACK01 ]) calculates a triangulated boundary representation of the input dataset, which is a structured or unstructured point cloud. The premises for good results are a dense point cloud (this criterion is generally fulfilled) and a smooth object surface (due to the origin of the data, a weak criterion which is not fulfilled every time). Moreover, the standard power crust algorithm is unable to handle large quantities of input data. Triangulation may also be based on proximate or quite proximate contour lines in an image stack, e.g. [ MBMB06 ] with an implicit curve fitting approach, or [ Kep75 ] who applies a 2-D directed graph search problem as isomorphic problem statement to solve the problem of 3-D triangulation of subsequent contour lines.

Surface reduction and remeshing: The 3-D surface data of plant biological models may consist of a very large number of small triangles (80 million triangles or more per model). The surface reconstruction algorithms (e.g., marching cubes) tend to result in oversampled representations in most regions of the triangulated structure. Eliminating extraneous data necessitates a surface reduction as in [ SZL92 ] and [ GH97 ]. Figure 10 presents a grain model with different mesh resolutions. Figure 10(b) contains 16% of the number of triangles in Figure 10(a). A remeshing step can be advantageous for a well distributed surface representation especially if the surface data is used for simulation purposes (see Section 4.2).

Figure 10. Surface models of one grain at different resolutions (a) left, a grain with a mesh size of 250,000 triangles, and right, detail with highlighted faces (b) left, reduced mesh with approximately 40,000 highlighted faces, and right, detail with highlighted faces.

Surface smoothing: In [ BHP06 ] a survey of mesh smoothing algorithms applied to data for medical applications, concerning efficiency, accuracy, and appropriateness of different smoothing strategies for surface models was presented. No such work has been done on plant biological data, which has its own idiosyncrasies from imaging, segmentation and surface extraction. At the moment, research is being done on handling staircases, i.e., small shifts caused by the rigid registration process, and oversegmented areas. Comparable surveys of surface smoothing can be found in [ BO03 ] and [ YOB02 ]. Figure 11 reproduces an automatically segmented grain model with triangulation, triangle reduction and remeshing shown from different perspectives.

Figure 11. A surface representation of multiple label isovalues is obtained by automatically segmenting histological section datasets into biologically relevant tissues. The extracted isosurfaces are smoothed and remeshed.

The main purpose of the visualization is to represent the acquired data in a way that a user understands intuitively [ MJM06 ]. The following two examples are representative for the multitude of visualizations of plant biological models. With the aid of VR technologies, these concrete examples produce an obvious value added for biologists.

Visualization of different data domains: One of the most import tasks for biologists is the comparison of data from different data domains. An applicable visualization can in this case provide added value, as shown in the following example. Using 4-D warping algorithms, as described in [ PSM08 ], virtual intermediate developmental stages can be generated to achieve a better congruence of data resulting from different individual grains. Figure 13 combines an NMR volume representation and a surface model representation of histological data.

Figure 13. Visualization of different data modalities: NMR-based voxel intensities are displayed by volume rendering and combined with a surface view of labeled histological data.

Visualization of model differences: Since grain growth and size are subjects to inherent biological diversity, models representing morphological variances at a specific developmental stage are highly feasible, especially to integrate heterogeneous data sampled from different individual grains. [ BWSS09 ] analyzes variances and features common among individual grains at a specific point in time and quantifies them by compiling inter-individual stochastic atlases of grains, thus enabling the quantification and visualization of biodiversity in a specimen.

Once the user has visualized the desired dataset, an appropriate interface must be provided to define the volume of interest (VOI). This can be achieved by initially choosing a prototype from a model catalog or selecting the structure to be modified. The user can then interact with the 3-D model. An efficient and more intuitive way of doing this is in 3-D space with a 3-D interface (for example with the SpaceNavigator www.3dconnexion.de). Figure 14 presents the 2-D standard case of deformation feature use. Even with new innovative metaphors (see [ SSB08 ]), a 2-D view of the model modified by 3-D widgets with a 2-D mouse interface is in general not as intuitive and accurate as a direct 3-D modification, especially for beginners. The current deformation area is chosen through freehand region selection (OpenGL picking, see the red points in Figure 14). Mass-spring models, as described in [ Wit97 ] and [ BC00 ], are used for deformation purposes. Well distributed intraconnectivity and uniformly distributed triangles on the surface (see the wireframe model in Figure 14) ensure that the mass-spring model's behavior is stable and visually plausible [ LSH07 ]. Good intraconnectivity can, for example, be achieved by tetrahedization, as described in [ AMSW08 ]. Given the extremely high complexity of these 3-D plant models the deformation model was also realized based on extensive GPU support.

Figure 14. Modification of model data to determine the VOI.

The VOI can be saved later (e.g. as a VRML-file) and used for the dissection.

The VOI is extracted from physical objects with a technique patented by an industrial machinery manufacturer named Molecular Machines & Industries www.molecular-machines.com. This application will not be discussed further here.

Microdissection experiments allow quasi spatially localized assays based on small sample volumes dissected from a specimen, thus providing a 'snapshot' of the differently expressed genes and their regulation during development. The authors of [ TWS08 ] present a study of gene expression patterns in tissue-specific assays of developing barley caryopses utilizing 2-D-LMD preparation of fixated serial sections. Being tissue-specific, the results of the LMD assays can be reintegrated into the visualization process (see Figure 12) and integrated into other data modalities.

Hardware Setup: The new SpacePilot Pro from 3Dconnexion was employed in the experiments to perform 6 DOF interactions (see Figure 18). A standard laser mouse from Microsoft served as 2-D input device (see Figure 18). A low-cost tracking system with an IR sensor (see www.nintendo.com) and IR LEDs (reflection angle larger than 70 degrees) was used for head tracking. The LEDs are mounted on (stereo) glasses. Figure 18 presents the setup with standard glasses and IR LEDs.

Figure 18. The different interaction devices: (left) SpacePilot Pro, (middle) standard mouse, and (right) head tracking.

Software Setup: In order to obtain results that lend themselves to comparison, a virtual trackball navigation metaphor (see [ Hul90 ]) was applied to the head tracking navigation as well as the 2-D and the 3-D mouse navigation. Table 1 provides a brief overview of the implemented navigation.

Subjects: The experiments were conducted with two groups. The first group consisted of ten subjects (two female, eight male, researchers and university students) without any special background in biology. They all had moderate or substantial experience with 3-D techniques. The second group consisted of five subjects (two female, three male, all researchers) with backgrounds in biology. They all had little or moderate experiences with 3-D techniques. technique was chosen randomly.

In the experimental tasks the users employ the different techniques / controllers to approximately adjust their position, orientation and direction (equivalent to a virtual camera) to a set of specified positions (within a predefined radius) and / -or orientations (scalar product above a predefined threshold). A common navigation metaphor is applied for this task (see Table 1). The Navigation Task represents a typical and important function in the application.

Initial Conditions: Before a complex navigation test could start, the spin, zoom, and roll had to be evaluated separately to verify the subjects would obtain comparable results with the different controllers for each navigation metaphor subset (e.g., spin). For instance the zoom and roll was disabled for the spin evaluation. The sensitivity of the controlling devices was adjusted once before the start of testing. To ensure conditions were equal, no acceleration parameters were used (e.g. for the 3-D mouse). Ten users from both groups participated in the initial testing. Since the differences remained within an expected range (see Figure 25 in the Appendix), the subsequent navigation and exploration tests delivered results that are conducive to sound.

Procedure: Each subject was required to solve a set of eight subtasks twice by employing each of the three techniques (3-D mouse, mouse and head tracking). The sequence of controlling devices employed was altered randomly and every task had to be finished before the next controller was used. Before the start of a test, each controller's mode of action was explained and the subjects were given a brief preparation time (approximately two minutes) to familiarize themselves with it. Completion times and accuracy values, i.e. the average between the position accuracy (spin and zoom) and the roll accuracy, were measured for each subtask.

Experimental Results from the First Group: The first group's results of the complex navigation task (combination of spin, zoom, and roll) confirm the experimental results yielded by the initial navigation experiment. Subjects performed the complex task best with the mouse. The subjects' mean completion time using the mouse technique (derived from the averaged times of the subtasks) is half the mean completion time using the 3-D mouse (SpacePilot Pro) or the head tracking system. The standard deviation of the mean completion time for a subtask (2-D mouse) was far smaller than the standard deviation from the 3-D mouse but comparable to the standard deviation of head tracking. The accuracy of the tasks performed was best with the head tracking system but did not differ very much from the accuracy with the 3-D mouse. The accuracy with the 2-D mouse was worst (approximately 8-10% less accurate than 3-D mouse and head tracking). The results with the different techniques were as good as the results of the separate navigation analysis.

Figure 19. Results of the complex Navigation Task from the first group, which included subjects without any background in biology.

The 2-D mouse is the input device for nearly every 2-D and 3-D task. Given their familiarity with this device, the subjects were able to complete the task more quickly as the results in Figure 19 indicate. The simple virtual trackball metaphor supports this and allows fast and accurate navigation. On the other hand, fine tuning appeared to be more difficult (in relation to accuracy). Alternatively, the subjects may have achieved faster completion times at the expense of the accuracy. Since not all subjects changed their strategy at once to be faster or more accurate this may not be true. The standard deviation of the completion times was significantly smaller with head tracking than with the 3-D mouse. Obviously, head tracking is easy (or difficult) to use without prior experience. The simple head tracking concept is conducive to intuitive use head tracking. This hypothesis was corroborated by subjects' responses to an informal questionnaire.

Experimental Results from the Second Group: The results from the second group are correspond with those from the first group. The subjects were also able to complete the task fastest with the mouse (twice as fast as with the reference technique) but at the expense of accuracy. The standard deviations of all techniques were far higher than in the reference group.

Figure 20. Results of the complex Navigation Task from the second group, which included subjects with backgrounds in biology.

The results presented in Figure 20 point to the same conclusion as the results from group one, taking into account that the pool of subjects is too small for statistical conclusions. The nearly constant navigation times with good accuracy values for head tracking in this group too reinforces the preceding assumption.

In a second evaluation scenario, concealed areas of interest in a typical 3-D plant biology were analyzed. Since the regions are represented by glyphs, subjects without a biology background are also able to localize them. The glyphs are only visible when the subject's position is located within a predefined range to the glyph, which is similar to a small detail of a model that is only recognizable up close. The alpha values decreases when the subjects' virtual position converges on the glyph. The roll is not relevant for this task.

Procedure: Each subject was required to solve an exploration task consisting of a set of twelve subtasks by employing each of the three techniques (3-D mouse, mouse and head tracking). The sequence of control devices was altered randomly just as the positions of the glyphs in the model. Every task had to be completed before the next controller was used. This experimental task built upon the Navigation Task. Before the start of a test, each controller's mode of action was explained and the subjects were given a brief preparation time (approximately one minute) to familiarize themselves with it. The completion times of each subtask were measured for this task.

Experimental Results from the First Group: 2-D mouse interaction was the fastest technique to complete the exploration tasks. Nine out of ten subjects performed bestwith the 2-D mouse, and the final subject (see Figure 21, user #4) was nearly just as fast with the 2-D mouse as with the other techniques. On average, users performed 50% faster with 2-D mouse interaction than with the 3-D mouse and head tracking. On average, subjects performed similarly with head tracking and the 3-D mouse. The head tracking results were only a little faster. Seven out of ten participants were faster or nearly as fast with head tracking interaction than with the 3-D mouse. The standard deviations of the averaged completion times of the subtasks were very high for the 3-D mouse as well as for the head tracking approach. Furthermore, timing differed among different users greatly.

Figure 21. Experimental results of the first group for the Exploration Task.

Again, subjects displayed good results with the 2-D mouse for this task. The relative time differences of the tested devices do not vary as greatly as the average time differences of the subtasks obtained during the Navigation Task. The variations in the standard deviation were large because not all glyphs can be found with the same speed.

Experimental Results from the Second Group: The subjects achieved the best results with the 2-D mouse interaction technique (see Figure 22). On average, users performed approximately 66% faster with 2-D mouse interaction than with the 3-D mouse, and only 15% faster than with head tracking. Four out of five subjects were faster or nearly as fast with head tracking interaction than with the 3-D mouse. The standard deviations of the averaged completion times of the subtasks were higher than in the reference group. Furthermore, the timing differed among different users greatly.

Figure 22. Results of the Exploration Task from the second group.

The second group also displayed good results using the 2-D mouse for this task. The difference was not much greater than the timing differences of the averaged subtasks performed during the Navigation Task and the first group's timing. The timing for head tracking differed only marginally from the head tracking timing of the group with more 3-D skills.

The last test scenario is intended to evaluate the influence of the visual representation (monoscopic / stereoscopic / shadow indication / stereoscopic with shadow indication) on the accuracy of a manipulation task being performed. This is an elementary task in the definition process of VOIs. The subjects were required to move a 3-D arrow in a precise direction indicating the main direction of the subsequent deformation (cf. the same principle in Figure 14). The stereo method utilized throughout the experiment was circular polarization (see [ Hof05 ]). Shadow indication was implemented by means of hard shadows (see [ Wil78 ]). The biologists defined an average variation of 5-10 degrees from the optimal orientation as the accuracy requirement for this task. The goal was to identify the forms of representation that meet this requirement.

Procedure: Each subject was required to solve the manipulation task consisting of a set of eight randomized subtasks by employing each of the representations (monoscopic, stereoscopic, shadow, and stereo with shadow). The sequence of forms of representation was altered randomly. Before the start of a test, each subject achieved a short briefing on the task to be performed (approximately one minute). The accuracy was measured for this task (angular deviation between target direction and adjusted direction).

Experimental Results from the First Group: As expected, the accuracy values of the stereoscopic approach were better than the monoscopic approach, but the differences between both approaches are not very significant (two degrees on average). The accuracy results of shadow indication were very good (on average twice as good as the monoscopic and stereoscopic approach). A combination of stereo vision and shadow indication produced better accuracy when the manipulation arrow was adjusted. The different users' accuracy values were virtually identical. The results of the Manipulation Task for the first group are presented in Figure 23 . The difference between the optimal manipulation direction and the adjusted direction is used to determine accuracy. Smaller angle values represent better accuracy. The last column avg stands for the average values of all participants of the group.

Figure 23. Evaluation results of the Manipulation Task for the first group.

Experimental Results from the Second Group: The second group's results are comparable to the first group's. The stereoscopic approach was more important to the second group (difference between stereo and mono 12 degrees) than to the first group (difference between stereo and mono 2 degrees). The use of shadows to adjust the manipulation angle (7 degrees on average) is twice as effective as the stereoscopic approach and four times as effective as the monoscopic approach. The use of stereo techniques in addition to shadow indication produced higher accuracy among all the subjects in the second group. The average difference of one degree between the two approaches was marginal. On the other hand, the standard deviation with stereo and shadow is smaller. The results of the Manipulation Task from the second group are presented in Figure 24 .

Figure 24. Evaluation results of the Manipulation Task for the second group.

After the user experiments, the subjects were asked for their subjective impression. Both groups (biologists and non-biologists) preferred the interaction technique of the standard mouse for the Navigation Task and the Exploration Task. Head tracking was rated far better than the 3-D mouse. All the subjects, including those with slow completion times, saw great potential in this approach. Head tracking was rated as the technique best suited for spin navigation. The mouse was rated best for the navigation components zoom and roll. However, the measured times for a task for one subject (intra-rater) and the average times among the subjects (inter-rater) varied greatly. The mapping of the navigation metaphor demonstrated that a standard device such as the mouse can perform better than the six-degree of freedom approaches evaluated.

Indeed, this is not always possible because of the inherent limitations of two dimensions on the mouse. The influence of stereoscopic viewing on the adjustment of the manipulation angle was more important for the second group (participants with little or no 3-D experience) than for the experienced participants. The first group's average deviation accuracy was 15 degrees with the monoscopic approach. The second group's was on 27 degrees. Almost all subjects in the first group reported that they automatically used the shading and silhouette information (cf. importance of depth cues [ WFG92 ]). This might be an indication that the results of monoscopic and stereoscopic accuracy did not differ very much in this group. A few participants reported that they did not use the arrow's shadow as indirect 3-D information. This might be an explanation for these subjects' comparatively poor accuracy values. The application of stereo techniques and shadow indication was demonstrated to meet biologists' requirements for this task. None of the subjects in the second group was able to fulfill the predefined accuracy requirement by using a stereo representation alone. Finally, while the application of stereo techniques demonstrably improves the adjustment of the manipulation angle, the shadow application with stereoscopic support does so much better and reliably.