Understanding Perception of Simulated Elastic Deformations CS838 Project Report

Transcription

1 Understanding Perception of Simulated Elastic Deformations CS838 Project Report Tomislav Pejsa December 17, 2012 In this project, my goal was to enhance the understanding of human perception of computationally simulated elastically deforming objects. Control parameters for existing computational models of elastic materials do not map intuitively to visually salient properties of elastic objects and phenomena, which makes their use by non-experts difficult. I conduct a set of two exploratory perceptual studies revolving around simple deformations of cubeshaped objects in order to understand which properties of deforming objects people perceive, and which vocabulary terms they use to describe these properties. Results of my studies are presented in this report. 1 Introduction Computational simulation of elastic deformations is supported through a wide range of parametrically controllable elastic material models. Models of elasticity such as linear, corotated linear and Neohookean can differ in a number of traits, from rotational invariance and volume preservation, to isotropy. Some of these properties are perceptually salient in deformations themselves; for example, people can perceive when an elastic object changes shape, compresses, or stretches non-uniformly. Yet control parameters of material models do not have a direct, one-on-one mapping to perceivable properties of elastic objects instead, these properties result from a combination of different model parameters. For example, Figure 1 illustrates how two materials (simulated using Neohookean elasticity) with the same value of the stiffness parameter (known as Young s modulus) can have very different behaviors even when subjected to identical external forces. These issues make the use of physics-based simulations by non-experts such as modelers and animators problematic. It can be difficult to explain to people without a background in physics-based modeling how different parameters work, and how desired deformation behavior can be achieved. In order to help non-experts take advantage of physics-based simulation methods, we need to offer them a more intuitive set of control 1

2 parameters, with a basis in human perception of physical phenomena. However, before we can develop such a set of parameters, we need to improve our understanding of how humans perceive and reason about those phenomena. As part of this project, I set out to achieve the following goals: 1. Establish a vocabulary of terms which people use to describe observed elastic deformations. 2. Determine which properties of deforming objects and materials people perceive. 3. Establish hypotheses on the relationship between these perceptual properties and physics-based model parameters. To achieve these goals, I conducted two exploratory studies with human participants. In both studies, the participants were shown a set of prerendered simulations of elastically deforming objects and asked to give their observations. In the remainder of the report, I give a more detailed overview of the studies, and present their results and implications. 2 Stimuli In both studies, the same set of stimuli were used: a simple cubic object being dropped onto a flat surface below. The object is a tetrahedralized volume simulated using the Neohookian model and backward Euler time integration scheme. I created 9 simulations with different sets of material parameter values, yielding 9 prerendered videos which were shown to participants. Each simulation had the length of 200 frames, and was Figure 1: Though Young s modulus parameter k controls stiffness, the perceptual property of stiffness is actually a result of a combination of parameters, including density ρ. Top: Deformation with k = 10 5, ρ = Bottom: Same value of k, but low density (ρ = 10) yields a drastically stiffer material. 2

3 Table 1: Videos and accompanying material parameter presets used as stimuli in my studies. Video k v ξ ρ Jell-O Wet Sponge Accordion Dry Sponge Water Balloon Baking Dough Sandbag Bouncy Ball Crazy rendered at 30 frames per second. Two examples of the generated simulations are shown in Figure 1. The parameter presets were selected because I believed them to be representative of the kinds of deformations possible with the Neohookian model and the available conjugate gradient solver. The parameters I manipulated were the following: 1. Young s modulus k Stiffness/stretch resistance. 2. Poisson s ratio v Compressibility/volume preservation. 3. Rayleigh s coefficient ξ Damping amount. 4. Density ρ Effectively mass, because we hold the volume constant across all conditions. For example, the top simulation shown in Figure 1 used the following parameter values: k = 10 5, v = 0.4, ξ = 10 3, ρ = This yielded a material that behaved like soft gelatin, so we labeled it Jell-O. Complete overview of different parameter presets and video labels is given in Table 1. In addition, for materials such as Bouncy Ball I also decrease the value of the time step parameter t in order to support their low damping coefficients. 3 Study 1: TAP The first study I conducted took the form of a think-aloud protocol (TAP). I recruited 6 participants (3 male, 3 female) and showed each participant the 9 stimulus videos in random order. The participant was then asked to describe the behavior of the object in each video. As the participant discussed their observations, I took notes of the terms they used, and asked for clarifications when necessary. Analysis of the notes yielded the following findings: Participants tended to describe the project behavior by using a lot of adjectives (e.g. elastic, wiggly, compressible ), idioms ( has a lot of give, can t support its own weight ) and similes ( like Jell-O, like baking dough ). 3

4 Participants referred to a set of 6 distinct perceptual properties of deforming objects portrayed. The perceptual properties referred to by the participants, as well terms they used, are as follows: 1. Deformability elastic, springy, fluid, floppy, melty, oozy 2. Oscillatory characteristics - wiggly, bouncy, shaky, vibrating, jiggly 3. Compressibility compressible, squishy, shape-retaining 4. Internal structure uniform, balanced, porous, hollow, something loose inside 5. Mass and density dense, heavy, saggy, cannot support its own weight 6. Naturalness natural, unexpected behavior, unlike anything in the real world, slow-motion 4 Study 2: Controlled Experiment The results of the previous study allowed me to hypothesize on a possible vocabulary of terms for elastic deformations, as well as perceptual properties these terms refer to. To confirm and expand these findings, I conducted another study, with the following objectives: 1. Confirm experimentally the existence of perceptual properties indicated by the previous study. 2. Find a minimum set of vocabulary terms with accepted meanings that express these properties. 3. Investigate relationships between these properties, as well as possible connections with parameters of the material model. 4.1 Design and Procedure Study 2 took the form of a web-based controlled experiment. The study followed a within participants design with subsampling. For each video from Study 1, I created another version with a different camera viewpoint. Each participant saw a randomly chosen subset of the total number of conditions (5 out of 9), meaning they were shown a total of 10 videos (since each condition had two trials, with different camera viewpoints). After watching a video, each participant was asked to rate it on a series of 27 7-point scale items. The items were directly derived from vocabulary terms obtained in Study 1. I recruited 21 native English-speaking participants on Amazon Mechanical Turk. To ensure quality of collected data, participants were shown two training and acclimation videos at the start of the task (not included in data analysis), while two-trial design allowed easy verification of response consistency. 4

5 4.2 Data Analysis Having collected the experimental data, I set out to conduct a series of statistical analyses. These analyses included: 1. Factor analysis to derive a set of factors corresponding to perceptual properties of elastically deforming objects. 2. Construction of highly consistent perceptual scales for numerically describing deformations, using a minimal set of items (vocabulary terms). 3. Analysis of correlations between perceptual scales using Pearson s r statistic. 4. Use of ANOVAs to examine the effects of different material parameter settings on perceptual scale ratings Deriving Perceptual Properties To extract perceptual properties from the obtained data, I conducted factor analysis using PCA. Given a set of 27 observed variables (my scale items), I expected to discover a smaller set of unobserved or latent variables corresponding to the perceptual properties indicated by the previous study. Of the factors obtained from PCA, only the first five had eigenvalues higher than 1.0. Following the application of the Kaiser criterion, these factors were retained and rotated, yielding the following results. On factor 1, the following items had high loadings: wiggly, springy, shaky, vibrating, floppy, jiggly, elastic, bouncy, heavy*. This factor clearly describes oscillatory characteristics of the deformation, so we label it oscillatoriness. Negative correlation with the item heavy indicates highly oscillatory objects are likely to be seen as lightweight. On factor 2 there were high loadings for items: uniform*, melty, compressible, fluid, elastic, squishy, saggy, oozy, slowmotion, looseinside*. This factor corresponds to the preceptual property of deformability, and we label it as such. The following items had high loadings on factor 3: heavy, hollow, dense. We label this factor density. On factor 4, the items with high loadings were natural, retainshape*, realworld. We label it naturalness. Negative correlation with retainshape item indicates that items that do not retain their original shape are seen as more natural. However, the interpretation of the shape retention is ambiguous it could refer either to stiffness (the item never changes shape at all) or tendency to revert to the original shape following a deformation. Factor 5 had only a single item: unexpectedbehavior ( This cube behaves in an unexpected way ). I had expected this item to correlate with naturalness, but that was not the case. Since this factor has only a single item, its interpretation is unclear and I discard it from further analyses. Unexpectedly, I found no factors corresponding to properties of either compressibility or internal structure. Either the scale items were inadequate to capture these concepts, or the participants lacked the ability to perceive them consistently. 5

6 Table 2: Numeric scales for measuring perceptual properties of elastic deformations. Property Scale Items Cronbach s α Oscillatoriness wiggly, springy, shaky, jiggly, bouncy.954 Deformability melty, fluid, elastic, squishy, saggy, oozy.926 Density heavy, dense.797 Naturalness natural, realworld, shaperetaining* Constructing Perceptual Scales I use the results of factor analysis to construct perceptual scales, giving a numerical expression of the four perceptual elastic deformation properties. The scales are constructed by iteratively discarding items until I maximize the item reliability metric Cronbach s α, which serves as a measure of internal consistency. To compute participants scores on each scale, the items of that scale are averaged, with their factor loadings used as weights. Overview of the constructed scales is given in Table 2. Scales for oscillatoriness and deformability have high reliability, while density and naturalness scales have acceptable to good reliability. It is interesting to note that the constructed scales are very robust to removal of items. For example, if I remove all items but wiggly and shaky from the oscillatoriness scale, it still has high reliability (Cronbach s α =.913). This indicates that perceptual properties of deformations can be described using a very small number of vocabulary terms with universally accepted meanings Effects of Material Model Parameters Figure 2 shows how different material parameter presets were rated by the participants on perceptual scales constructed in the previous step. By examining these results we can get some indication about the effects of different material parameters on perceptual Figure 2: Scores of different material parameter settings on perceptual deformation property scales. 6

7 properties of deformations. Though experimental conditions do not sufficiently sample the space of model parameters to learn a mapping function between perceptual scales and model parameters, I use significance testing to confirm that different parameter setting produces significantly different perceptual scores, and that there is no one-on-one mapping between perceptual properties and model parameters. I use one-way repeated measures ANOVA for all omnibus and post-hoc tests on all scales. My analysis has shown significant effects of material parameter settings on oscillatoriness, F (8, 206.9) = , p < Effect size is η 2 =.824 (large effect). Results show that oscillatoriness property is definitely not equivalent to damping amount as specified by Rayleigh coefficient ξ. For example, materials 2 and 4 have the same value of ξ, yet their oscillatoriness is significantly different, F (1, 207.3) = , p < Similarly, there are significant effects of material parameter settings on deformability, F (8, 208.5) = , p <.0001, with effect size of η 2 =.731 (large effect). It is again obvious that deformability is not equivalent of physical stiffness as specified by Young s modulus k. For example, materials 0 and 3 have the same value of k, yet their deformability is significantly different, F (1, 209.9) = , p < I found significant effects of material parameter settings on perceived density, F (8, 205.3) = , p <.0001, with effect size of η 2 =.502 (large effect). Interestingly, there is also no equivalence between perceived density and the density parameter ρ, as shown by materials 3 and 4 having the same value of ρ, yet significantly different perceived density, F (1, 205) = , p < Furthermore, if we compare graphs for density, deformability and oscillatoriness, it appears that more elastic and bouncy materials are likely to be seen as less dense. Pearson s r statistic (measure of correlation) between density and deformability is r = 0.438, indicating a moderate inverse correlation. Likewise, there is a strong inverse correlation (r = 0.615) between density and oscillatoriness. Based on these results, it seems probable that people cannot accurately judge density visually, and are likely to confound it with more visually salient properties. There are also significant effects of material parameters on deformation naturalness, F (8, 205.6) = , p < Effect size is again large, η 2 =.466. Comparing the naturalness graph with graphs for deformability and oscillatoriness, it appears that more deformable and oscillatory materials are more likely to be seen as unnatural. Pearson s r confirms moderately negative correlation between naturalness and deformability (r = 0.470), as well as naturalness and oscillatoriness (r = 0.389). Possible explanation of these results is that deformations on impact draw attention to the fact that there is no friction between the deforming object (cube) and the surface. It is also possible that the shape of the object acts as a confounding factor it may be that people do not expect a cube to deform that way. Although I was not able to build a scale for compressibility, I analyzed the individual scale item compressible in hopes of getting a better idea of how people interpret the term. Results seem to indicate that participants partially confound compressibility with deformability and oscillatoriness. Pearson s r seems to confirm that hypothesis there is a strong correlation between compressibility and deformability (r = 0.603). However, there is no equivalence with Poisson s Ratio v, which controls actual physical compressibility for example, materials 3 and 4 have the same v, yet their compressibil- 7

8 ity scores are significantly different, F (1, 205.7) = , p < Implications Results of my studies clearly indicate that there is a consensus between people regarding existence of visually salient perceptual properties of elastically deforming materials, as well as a small and universal vocabulary of terms sufficient to describe them. The properties found in my studies are: deformability, oscillatoriness, density, and naturalness. Some properties such as density (and likely compressibility) are difficult to judge perceptually, as they tend to be conflated with more visually salient properties namely, deformability and oscillatoriness. My analyses have confirmed the obvious fact that perceptual properties of deformations have no one-on-one mappings to physical parameters. Understanding the correlation between the two requires additional research. 4.4 Limitations and Future Work My work presented in this report is limited in two ways. Firstly, the physical model employed limits the kinds of deformations that can be simulated and precludes more extreme deformations. For example, since the Neohookean model strongly resists inversion, it is difficult to simulate deformations that greatly reduce the object s volume. Moreover, the current model does not simulate self-collisions or surface friction, which precludes more extreme deformations and, in the latter case, may be impairing naturalness of even the less extreme ones. Future studies of this sort should employ more complex and varied physical models, incorporating a broader set of elasticity models and supporting even greater parametric control, e.g. by allowing controlled violation of physical laws such as conservation of energy and momentum. Secondly, the task context used in my studies is very limited and may call into question the generalizability of the obtained results. Future studies should consider more varied and realistic contexts. For example, an interesting context might be character animation, in particular animation of cartoon characters with squash-and-stretch deformations. This project has yielded a set of perceptual properties of elastic deformations, which can serve as a basis for construction of perceptually-grounded parameters for controlling elasticity models. Such parameters would have intuitive meanings and could make it easy for non-experts to produce simulations of elastically deforming objects. In order to derive such parameters, it is necessary to learn mappings between perceptual properties and parameters of material models. A possible methodology for achieving this would be to collect a large amount of human participants data, sufficiently sampling the space of physics-based material parameters, and then learn a mapping from perceptual parameters to physics-based parameters by performing some form of multivariate regression. This is certainly one of the more interesting avenues for continued research in this problem space. 8