Shape Perception in 3-D Scatterplots Using Constant Visual Angle GlyphsRasmus Stenholt∗ Claus B. Madsen †

Aalborg University, Dept. of Architecture, Design, and Media Technology

ABSTRACT

When viewing 3-D scatterplots in immersive virtual environments,one commonly encountered problem is the presence of clutter,which obscures the view of any structures of interest in the visu-alization. In order to solve this problem, we propose to render the3-D glyphs such that they always cover the the same amount ofscreen space. For perceptual reasons, we call this approach con-stant visual angle glyphs, or CVA glyphs. The use of CVA glyphsimplies some desirable perceptual consequences, which have notbeen previously described or discussed in existing literature: CVAglyphs not only have the prospect of dealing with clutter, but alsothe prospect of allowing for a better perception of the continuousshapes of structures in 3-D scatterplots. In a formal user evalua-tion of CVA glyphs, the results indicate that such glyphs do allowfor better perception of shapes in 3-D scatterplots compared to reg-ular perspective glyphs, especially when a large amount of clutteris present. Furthermore, our evaluation revealed that perception ofstructures in 3-D scatterplots is significantly affected by the volu-metric density of the glyphs in the plot.

Keywords: Virtual Reality, 3-D Interaction, User Testing andEvaluation

Index Terms: H.5.1 [Information Systems]: Information Inter-faces and Presentation—Multimedia Information Systems H.5.2[Information Systems]: Information Interfaces and Presentation—User Interfaces; I.3.6 [Computing Methodologies]: ComputerGraphics—Methodology and Techniques

1 INTRODUCTION

3-D scatterplots is a very commonly used way of visualizing highdimensionality data. In such a plot, each data sample is often visu-alized as a small 3-D object, called a glyph, whose visual propertiesdepend on the data. These visual properties can e.g. include posi-tion, size, shape, colour, etc. 3-D scatterplots and glyphs are e.g.presented and discussed in [2]. The goal of viewing such plots isoften to identify structures or patterns of interest in the data. Onecommon problem arising in this context is the presence of clutter,represented by glyphs which are not currently of interest. Suchclutter often obscures the view of relevant structures, reducing theviewer’s abilities to discover and correctly assess the nature of thesestructures. This problem is one of the key issues, which we seek toaddress in this work. Furthermore, we hypothesize that the volu-metric density of the rendered glyphs is highly influential in user’sability to correctly assess the shape of structures in a 3-D scatter-plot. I.e. that the internal, spatial proximity of glyphs in a structureinfluences the ability to correctly perceive the overall shape of thatstructure.

As a possible solution to the problem of clutter, we propose torender the glyphs such that they are of constant size measured bythe amount of pixels that they cover. We have chosen to name this

∗e-mail: rs@create.aau.dk†e-mail: cbm@create.aau.dk

approach constant visual angle (CVA) glyphs. This choice of visu-alization method has several potentially beneficial properties, whichwe discuss in the next section. Existing approaches to dealingwith clutter include geometrically distorting the space around theglyphs [1], using clipping planes [5], or making the glyphs semi-transparent [4].

2 PERCEPTUAL ANALYSIS OF CVA GLYPHS

In the real world as well as virtual worlds, the most common way ofseeing objects is through the perspective transformation. This trans-formation is performed by the optical system of the eyes in the realworld, and is simulated efficiently through the use of perspectiveprojection matrices in real-time virtual environments. With a per-spective transformation, nearby objects cover a lot of space on thescreen or retina compared to far-away objects. This is one of themain reasons why clutter from perspective glyphs is problematic:As the viewer moves close, the visual angle covered by individ-ual glyphs grows until they eventually cover up the entire field-of-view (FoV). The effect can be somewhat mitigated by decreasingthe physical size of the glyphs, however, it will always be the casethat perspective glyphs will begin to cover the entire FoV at somedistance. In perceptual terms, the increase/decrease in on-screensize is interpreted as if the physical size of the object is constant,while the distance or depth of the object is changing. Thus, relativesize is a powerful real-world depth cue.

With CVA glyphs, the opposite is true. Here the on-screen sizeis fixed, implying that the visual angle covered by the glyphs isapproximately constant, at least at reasonable FoV’s. The percep-tual consequence of this is that such glyphs will be perceived tobe changing their physical size in response to the user’s motions.This implies that the relative size depth cue will no longer work.Figure 1 presents an illustration of the issue.

Figure 1: The consequence of constant visual angle objects. Thetwo objects, A and B, cover the same visual angle of the viewer.However, A and B are placed at different distances from the viewer.If the viewer is able to perceive this depth difference due to otherdepth cues than relative size, the logical consequence must be thatA is smaller than B, as shown in the figure. Furthermore, if the viewermoves closer to A, and the visual angle of A remains constant, thenthe physical size of A must be decreasing. Conversely, A’s physicalsize will be perceived to be increasing, if the viewer moves away fromA, and the visual angle remains constant.

Even with the CVA property, the positions of the CVA glyphscan still be subjected to the usual linear perspective transforma-tion. This means that the perception of the spatial relationship ofthe glyphs can remain unchanged with CVA glyphs. The combina-tion of the linear perspective transformation for the glyph positions

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Figure 2: A CVA glyph cloud with the noise-spreading and pattern-solidification properties illustrated. Yellow glyphs are noise, blue ones arepattern. Note that all glyphs are the same size in pixels across all 4 images. (A) The cloud is viewed at such a large distance that none of theblue pattern is revealed. Instead, the noise is solid. (B) Moving closer to the cloud reveals the blue pattern, relatively unobscured by the noise.This situation also represents a sweet spot, where noise-spreading and pattern-solidification are both helping. (C) Standing inside a patterncauses it to spread out and become imperceptible. (D) Moving away from the pattern causes it to solidify into a recognizable shape.

and the CVA property gives two useful properties, which are also il-lustrated in Figure 2. It is often possible to find a sweet-spot, whereboth these properties are in effect, giving a clear view of a solidifiedstructure:

1. Noise-spreading: As the viewer moves close to a cloud ofCVA glyphs, linear perspective ensures that the glyphs spreadout. However, the CVA property ensures that the glyphs donot increase their on-screen size at the same time. This meansthat clutter, or noise, can be effectively spread out and thinnedsuch that any structure behind the clutter becomes visible.

2. Pattern-solidification: If a viewer moves away from a pat-tern of interest, linear perspective causes the on-screen dis-tances between the glyphs to decrease. At the same time, theCVA property ensures that the on-screen size of the glyphsdoes not decrease. This means that glyphs in the pattern willeventually overlap and solidify into a continuous shape.

3 EXPERIMENT

In the performed experiment, 17 unpaid participants were presentedwith a randomized series of trials which featured a box-shapedpattern cloud completely embedded in a spherical cloud of noiseglyphs. The user task of each trial was to create the smallest pos-sible bounding box around the pattern cloud. This was done in or-der to evaluate how well the participant’s perception of the patternshape matched the ground truth bounding box from which the pat-tern glyphs were sampled. The size of the CVA glyphs was chosenat a 25 pixel diameter, and perspective glyphs at a physical radius of1 cm. This implies that the on-screen size of the CVA glyphs wasequal to the perspective glyphs at a viewing distance of approxi-mately 69 cm. At closer distances, CVA glyphs would cover lessscreen space than perspective glyphs, and vice versa further away.The volumetric density of the pattern cloud in each trial was oneof 5 pre-chosen density levels: 1000, 5000, 10000, 50000, 100000glyphs/m3. All density levels were tested with and without noise,and with and without the use of CVA glyphs. Thus, the experimentwas a 3-factor design with 2×2×5= 20 unique test conditions. Allsubjects were exposed to all conditions twice, which was achievableapproximately within an hour. The user task of shaping a box wasperformed using the 3+3+3 DoF 3C box shaping technique intro-duced in [3]. The difference between the ground truth bounding boxand the user-created box was measured quantitatively using the boxdifference metric also introduced in [3]. The completion times anda 1-10 scale subjective assessment of the task difficulty was alsomeasured. During the experiment, the participants wore a motion-tracked nVisor SX111 HMD with a 102◦ horizontal FoV. The user’shands were controlling the interactions through two motion-trackedwireless mice.

4 RESULTS

The statistical analysis of the results used a significance level ofα = 0.05 in all cases. The results of the experiment show thatthe participants found it subjectively easier to perceive the correctbounding box when using CVA glyphs than without (p = 0.026).In terms of the quantitative error between the ground truth boxand the user-created box, CVA glyphs are only significantly bet-ter than perspective glyphs in the most dense and cluttered cases(p < 0.001). Investigating the data wrt. density levels shows thatonly having 1000 glyphs/m3 makes accurate shape recognition sig-nificantly harder than any other tested condition (p < 0.005). Sim-ilarly, having more than 10000 glyphs/m3 makes perception of thecorrect bounding box significantly easier (p < 0.044). This impliesthat at least two perceptual thresholds exist with respect to densityin a 3-D scatterplot. Visualizing data with a lower density thanthe lower threshold is undesirable, because structures and patternsare likely to be missed by the viewer. Having more than the upperthreshold, on the other hand, significantly improves the ability toperceive patterns. A significant interaction between the use of CVAglyphs and the density thresholds was also found. The use of CVAglyphs, makes the lower perceptual threshold between 1000 and5000 glyphs/m3 vanish. However, not using CVA glyphs, makesthe upper threshold disappear. Our interpretation of this is that therelative size depth cue becomes increasingly important as the den-sity is lowered, whereas the beneficial properties of CVA glyphs aremore important in dense cases.

REFERENCES

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