Mechanisms of Aesthetics: On the Perception of Materials and Their Properties.

The visual perception of material surface qualities holds immense importance in our daily lives, serving as the foundation for various environmental interpretations and behavioural adaptations. These encompass critical safety aspects, like assessing floor safety or food freshness, to appreciating intricate sculptural illusions, such as delicately draped fabric in marble statues. Particularly for products with high aesthetic value, perceived properties play a significant role in subjectively attributing material worth. Given the vast array of material surfaces and the pivotal role of lighting in the overall visual perception process, this presents a major challenge for lighting planners and designers. Currently, the achievement of aesthetic effects in architectural spaces heavily relies on the opinions and experiences of professionals, as there are no specific guidelines for combining materials with different lighting concepts. Hence, decoding the connection between physical properties and their subjective interpretations becomes crucial in facilitating the objective planning of materials. In this study, more than 600 materials were systematically examined to explore the interaction between perceived material properties and the resulting aesthetic effects. The resulting perception model establishes a direct link between objectively assigned and subjectively perceived material properties. These findings hold promise in contributing to both a more accurate evaluation and prediction of material appearances in the long term.


Introduction
Visual perception of material properties plays a fundamental role in how we perceive and interact with the world around us [1].From the comfort of a soft fabric to the coolness of smooth marble, our subjective experiences are heavily influenced by visual appearances.As materials are essential components of both the physical environment and products, understanding the relationship between their inherent features and the perceived aesthetic effects is critical to design, architecture, and product development.Moreover, given the increasing availability of computer vision technologies, subjective experiences are currently gaining importance in other application fields, such as process automation [2] and quality control [3], e.g., food inspection [4], which are mostly defined by the same basic problem of a perceptual characterization the visual appearance of materials.
This problem applies in particular to products with high aesthetic value [5,6], since in these cases the qualitatively perceived properties largely determine the subjectively attributed material value and thus also the price that can be obtained with the materials.Accordingly, objective quantification of material properties requires modeling of subjective human perception.Traditionally, the necessary analyses of visual appearance are performed by trained personnel.However, since this approach provides mainly subjective results and is thus hardly reproducible [7], standardized evaluation methods would have the potential to achieve more reliable quality standards.
In recent years, significant progress has been made in unraveling the intricate connections between material attributes and human perception [8,9,10,11].Researchers have explored various aspects, including texture [12], roughness [13], color [14], and glossiness [15], as potential predictors of the perceived aesthetic appeal of different materials.However, while numerous studies have focused on individual material types, e.g., stone [16], ceramics [17], parquet [18], and fabric [19], the need for a generalized model that can transcend material boundaries and predict aesthetic effects for various materials remains ever-present.
In addition, lighting situations are largely ignored in current modelling approaches.However, the basic perceptibility of material-specific features [20] is shown to be largely dependent on (a) an intrinsic property of the material (reflectance spectrum), (b) a random condition (illumination), and (c) the response of the sensor (human eye).Therefore, intensities [11], color temperatures [21] and light directions [22] have a potential impact on material perception, which is why lighting-related factors should be given increased importance.From this point of view, it is also surprising that there are currently no concrete guidelines for the use of materials in combination with different lighting concepts and that currently the use still depends exclusively on the experience of lighting planners and designers.
In response to this challenge, this paper presents a comprehensive investigation of the visual perception of materials and their properties.Our primary focus lies in the development and evaluation of a robust regression model capable of predicting perceived aesthetic effects based on perceived intrinsic material properties.The development of the regression model was grounded in an extensive dataset obtained through rigorous experimentation.We systematically collected and analyzed perceptual responses from a diverse group of participants who were presented with various materials representing different levels of homogeneity, roughness, and other essential material attributes.By capturing a broad spectrum of material stimuli, we aimed to enhance the model's versatility and ensure its adaptability to real-world scenarios.
In the following work, we outline the methodology employed to build the regression model, including data collection, feature extraction, and model training.We discuss the experimental design and analysis procedures used to validate the model's accuracy and robustness across different material types.Additionally, we present the results and offer insights into the key material attributes that significantly influence perceived aesthetic effects.The results represent a first step towards the objective predictability of the subjective impression of material surfaces and can serve as a basis to improve future decisions by architects, designers and manufacturers in the material selection and design process.Moreover, this research contributes to the broader field of human perception and cognition, bridging the gap between material science and human psychology.

Study population
A total of 50 people participated in the study, 33 women and 17 men.The average age of the participants was 30.12 ± 12.50 years, with women (31.66 ± 13.13) being slightly older than men (27.24 ± 11.01).Most of the participants (78.00 %) had a secondary school degree, 28.00 % of them had a university degree (bachelor, master, or doctorate).40.00 % of the participants stated that they work with different materials in their professional or private lives.
A large proportion of the participants (58.00 %) used visual aids (e.g., glasses, varifocals, contact lenses) at the time of the test.All participants were screened for color vision deficiencies prior to participation in the study using Ishihara color charts.Beyond that, there were no exclusion criteria.All participants gave a written informed consent prior to study participation and received a financial compensation of 250 €.

Material selection
A total of 612 materials of various types were included in the study (Figure 1).With 313 materials (51.14 %), woods represented the largest group of materials studied.Furthermore, the material selection included 154 solid-colored materials (25.16 %), 54 stones (8.82 %), 28 metals (4.58 %), and 18 textiles (2.94 %).The remaining group included a total of 45 materials (7.35 %) with types that could not be clearly assigned to one of the previously listed (e.g., concrete, tiles, or wallpaper).
93 of the investigated materials (15.20 %) were natural materials.The rest were artificially produced materials, which either aimed at a lifelike imitation of real materials (replica) or at a clearly artificial surface design (e.g., solid-colored surfaces).All the materials were standardized to a size of 50 x 50 cm.The thickness of the material samples varied depending on the material type and resistance-related requirements (e.g., fracture strength).

Description of the laboratory setting
The study was conducted in a controlled laboratory environment in two identical rooms.Both rooms measured 3.65 x 3.90 m and had a ceiling height of 2.80 m.The influence of daylight through a northfacing window opening of 1.5 m² each was reduced to a minimum by a shading system (controllable blinds in the space between the double glazing; light transmission < 5 %).The floors were covered with light gray carpet tiles (ρ = 0.35).Both the walls, which were draped with white curtains, and the suspended ceiling of the rooms were kept in neutral white (ρ = 0.85).
Both rooms were equipped with two evaluation stations in the central area of each room, which consisted of two light gray, height-adjustable desks at a height of 1.00 m (Figure 2).The stations were equipped with lighting prototypes for direct illumination of the material samples, which were mounted diagonally across both tables at a height of 82 cm above the desk surface and prevented a view into the  The material samples were positioned horizontally on the table surface at approx. 10 cm distance normally on the privacy screens in both free table corners.To prevent the possibility of inferring material-specific properties from different thicknesses of the materials, the materials were placed in an approx.5 cm wide passe-partout frame made of powder-coated aluminum.The coating was in a neutral light gray color.

Characterization of the light condition
The light condition used in the study was defined visually using various materials and under consideration of both the assessability of material surface properties and the occurrence of gloss effects.After the visual adjustment, the light condition was characterized photometrically.All material samples were illuminated at 5,000 K with a horizontal illuminance of 2,800 lx and CRI 93.
The direct lighting component (Luxeon Z-ES, 2,200-5,700 K) was zoned to the material position and amounted to 2,470 lx.The remaining 330 lx were diffusely generated via the general room illumination (Bridgelux Vesta Series Tunable White 2,700-5,000 K Gen2 29 mm Array).Overall, a min/max luminance ratio of 1/1.8 was achieved on the material samples (Figure 3).The luminance ratio of the material sample to the spatial environment was approx.1/10.The luminance of the back walls was adapted to the environment and made a negligible contribution to the illuminance on the material sample (< 0.5%).

Study protocol
The study was conducted as a block randomized trial with repeated measures in the period from 13.12.2021 to 30.05.2022.For this purpose, the 612 materials were divided into 20 blocks of approx.30 materials each, which were then presented to the participants for evaluation in a randomized order during five participation days (four blocks per day, one day per week for five weeks).Randomization was done with respect to both the order of the blocks and the materials within each block.Daily assessment time averaged approximately 3.5 hours and two individuals could participate simultaneously.Since two time slots were available each day (morning 07:00 -12:00, afternoon 13:00 -18:00), 4 participants could be included per day.
During the material evaluation, both participants were always in the same room and occupied different evaluation stations at which two different materials of the same block were presented.Before the evaluation of the material, the participants had about one minute in which they could move freely to look at the materials from different angles to experience any glossy behavior of the surfaces.The participants were not allowed to touch the materials.The subsequent evaluation of the material sample was then carried out from a defined observer position (Figure 3), which was designated by means of a standing stool and was located outside the reflected glare area of the direct lighting.After the evaluation was completed by both participants, they changed the evaluation stations first within the room and repeated the procedure.After both material samples were evaluated, the participants changed to the second laboratory room, which was equipped with two new material samples by the supervising personnel during the preceding evaluation process.The procedure was then repeated until all materials in the daily assigned blocks were evaluated.Both breaks and the consumption of beverages were always permitted.
All participants rated all materials first in terms of their inherent material properties (13 items) and then according to their aesthetic effect (15 items) using bipolar pairs of adjectives (Table 1).All items were presented in German.The scale for each of the 28 items ranged from -100 to +100 with a step size of 1.The survey was conducted using software (LimeSurvey, version 3.24.0+201013[23]) on two identical tablets and the scales were presented by means of a horizontal slider in a neutral central starting position and without numerical indication of the currently set value.The order of the items was randomized for each material evaluation.The assignment of the submitted ratings to the respective materials was done by means of QR codes, which were attached to the materials, contained referencing identification codes, and had to be scanned by the participants to call up the rating questionnaire.All QR codes were checked for accuracy several times before the start of the study.

Data Analysis
As part of the data analysis, the raw data collected was first adjusted for outliers.Outliers were identified separately for each material and each evaluated item using the 1.5*IQR method.Detected outliers were removed without substitution.Subsequently, material-related characteristic values were derived from the individual scores by calculating the mean, standard deviation, median and inter-quartile range (IQR) for each item.The pre-processed data were used for material classification as well as for the modelbased prediction of the aesthetic material effect.To exclude a dependence of the results on the calculated measure of central tendency, all following analyses were carried out for both variants and the results were checked for consistency.

Material classification.
The classification of the materials pursued the goal of identifying material groups with similarly rated material-inherent properties.Accordingly, the data analysis focused on the use of the 13 items evaluated in this respect.To reduce the data complexity, the data were normalized in a first step by means of a standard scaling procedure, and then reduced in their dimensionality by using a principal component analysis (PCA) [24].With an assumed cut-off value of variance to be retained of 80%, a reduction from 26 (13 items for each of two positional measures) to 10 dimensions was achieved.Subsequently, the classification of the materials was performed in the calculated principal component space by means of a k-means clustering [25].Since the number of clusters to be created must be specified within the scope of the application of the method, an estimation of the results and the associated derivation of the optimal number of clusters was carried out by means of the elbow method, a graphical representation of the search for the optimal number of clusters using the WCSS (Within-Cluster Sum of Squares), i.e. the sum of the squared distances between points in a cluster and the associated cluster centroid.The cluster assignment resulting from the k-means procedure was finally mapped to the original dataset and the clusters in all items were examined for their distinguishing features and visually verified for coherence.

Aesthetic Predictive Modelling.
To build the prediction models of aesthetic material effects, the pre-processed data set was divided into a training and test data set on an 80-20 basis.The data division was randomized.Since cluster-specific correlations between the material-inherent properties and the aesthetic effects could be assumed, the data division was stratified based on the calculated cluster memberships to ensure an equal percentage distribution of clusters in the training and test data set.Modelling was performed separately for each aesthetic item using a linear regression procedure [26].The generalized applicability of the derived models was determined by means of the determination coefficient R², which denotes the proportion of variation in the test data that can be explained by the derived regression model.

Relationship between material-inherent and aesthetic properties.
In addition to calculating the determination coefficient R² to check the accuracy of the model on the test data, the regression coefficients of the material-inherent input features were calculated to obtain a statement about their impact on the aesthetic material effects.To ensure comparability of the feature-related impact between regression models, individual regression coefficients were normalized with respect to both their percentage contribution to and the explanatory power achieved by each model.
For statistical testing, a one-factor ANOVA was performed with the factor input feature.Because the data violated the equal variance requirement (Levene's test), a Welch correction was applied to the calculation.All post-hoc comparisons to determine pairwise differences between models were performed with Bonferroni-corrected significance levels.

Identified Material Classes
The applied clustering procedure resulted in the identification of six distinct material classes.Statistical testing showed significant agreement between the results of the median and mean-based classification (Fisher's exact test, p < .001),thus ruling out any dependence of the resulting classification on the applied measure of central tendency.Clusters 4 to 6 (see Figure 4) proved to be defined by individual material classes, since the position in the principal component space of solid-colored materials (high chromaticity and low naturalness) and metals (low naturalness and high gloss) differed significantly from the rest of the samples examined.Furthermore, there was a clear separation between highly saturated (colored) and neutral (muted) solidcolored materials (clusters 4 and 5).The three remaining subdivisions (clusters 1 to 3, see Figure 4), on the other hand, proved to be dependent on structural distinguishing characteristics regarding the materials included, which led to a stronger type-related mixing of the derived material classes.Specifically, the ratings of the items in terms of warmth (mainly warm materials in cluster 1), contrast (neutral light and dark stones and woods in cluster 2), and regularity and depth of structure (strongly patterned materials in cluster 3) proved to be decisive for the resulting classification.

Prediction accuracy
The 15 specifically derived models for the prediction of the individual aesthetic effects of the materials basically showed a very high quality with 79.86 ± 12.41 % (prediction of the mean values) and 76.49 ± 12.99 % (prediction of the medians).Mean values were predicted significantly better than medians (Ttest, paired samples, p = .001).

Impact of material-inherent characteristics on aesthetic ratings
The pairwise comparisons were able to identify three distinct groups of input features (Figure 6) with varying influence on aesthetic ratings.Both the group with low (1.91 ± 2.06 %) and high influence (10.91 ± 8.77 %) had 5 items each.The group with medium influence (5.25 ± 3.84%) accounted for the remaining 3 items.While all groups differed significantly among themselves (all p > .001), the items included within the groups showed no significant differences (all p > .05).

Discussion
Both the clustering procedure applied in the study and the item selection used proved to be useful for deriving distinct material classes.However, the resulting material groupings only proved to be unambiguously type-related if the underlying material types clearly exhibited strongly pronounced inherent properties that set them apart from other materials (such as the colorfulness of solid-colored materials or the reflective behavior of metallic surfaces).In contrast, for material types, where a clear lack of such properties comes to the fore due to an increased possible variation, superordinate property conglomerates proved to be decisive for class formation, resulting in a clearly type-related mixing of the classes.Therefore, it can be assumed that generally intuitive classifications (e.g., wood or stone) for the classification of materials prove to be insufficiently meaningful and that a perceptually accurate subdivision is far more differentiated.To the best of the authors' knowledge, these results are also largely consistent with existing research [11].
Secondly, the models calculated on the basis of the clustering results for the prediction of the aesthetic material effect by means of perceived material-inherent properties basically showed a very high level of accuracy.The resulting confirmation of a simple and direct connection between the objectively assigned and subjectively perceived qualities of a material surface accordingly suggests the existence of an intrinsic perception model.This would mean that subjectively perceived material qualities are not subject to stochastically intersubjective characteristics but are systematically formed from underlying visually extracted characteristics.However, to complete this model assumption, it is Finally, it should be mentioned that the accuracies achieved by the simple regression models are limited to the impact of a few material-inherent properties on closer inspection for all aesthetic items.Interestingly, the items with a strong impact on the predicted values are properties that are generally more difficult to define.Concepts such as complexity, restlessness or harmony are explicit material properties, but at the same time require a conceptual interpretation by the viewer, which in turn can be assigned a socio-cultural code.On the other hand, simpler and more direct material properties, such as warmth or brightness, which would also have physically measurable definitions, had only a moderate or low impact on the formation of aesthetic sensations.Although a comprehensive depiction of the material-related perception can be considered necessary to predict all aesthetic effects, the possibility of a greatly simplified consideration of materials opens based on the five decisive influencing factors, which prove to be responsible for almost 68.32 % of the prediction accuracy.Especially when a precise prediction of a specific aesthetic parameter (e.g., attractiveness) is desired.In the long term, this can simplify the applicability of the prediction models and potentially make them easier to put into practice.

Limitations of the present study
Despite the comprehensive examination of 612 materials, which aimed to ensure broad applicability of the results, it is essential to acknowledge that the materials selected may not entirely represent the entire spectrum of potentially available materials.Especially the inclusion of a larger number of woods in the investigation might introduce certain biases, possibly affecting the accuracy of the prediction models when the dataset is altered.
Moreover, it is crucial to recognize that aesthetic material effects are not inherently fixed but influenced by contemporary trends and socio-cultural backgrounds.Regrettably, these factors were not addressed in the current study, making it difficult to claim universal validity for the derived prediction models.
Additionally, it is worth noting that the modeling process was limited to a single light condition.Given that lighting significantly impacts the recognizability and interpretability of material surfaces, the predictive accuracy of the models might diminish under unexamined lighting situations.
Finally, the validity of the presented results can only be guaranteed in the context of normal-sighted people since all kinds of visual disturbances were excluded.Color blindness, for example, can have a significant impact on the visual appearance of objects or materials.It is also well documented that agerelated weaknesses in the visual system, such as age-related macular degeneration, also have a significant impact on both visual acuity [27] and color vision [28,29].Appropriate mapping of such groups of people would require an expansion of the existing basic model using experimental investigations.

Conclusion
Aesthetic sensations cannot be understood independently of neural systems or physiological sensors, as they are primarily influenced by perceptual and cognitive processes.They arise from an interaction of recognition and evaluation of emotion and meaning [30], which, due to their subjectivity, make an objective evaluation complex and demanding.Since international research is currently still trying to derive a general mathematical model of human aesthetic appreciation [31,32,33,34,35], the present results offer the potential to make a significant contribution to solving a currently challenging problem.
Due to the complexity of the underlying processing mechanisms and perception processes, the derivation of a generalized model within the framework of a single study proves to be impracticable.The presented models should accordingly be considered as a generalized base model, created under a well-documented lighting situation, making it suitable for multidimensional extension.In the long term, extensions regarding the potential influence of different lighting situations could enable lighting planners and designers to mutually optimize key performance indicators of buildings, such as energy efficiency or melanopic illuminance levels, for the first time, considering the aesthetic effects of the material selection made.
However, this requires further research, which should also take up long-term and intercultural tendencies to rule out a personal exclusion of fringe groups.In general, the presented results confirm the potential that can result from more objective material planning for future-oriented lighting practice.

Figure 1 :
Figure 1: Exemplary presentation of 70 randomly selected materials out of the 612 materials examined.
.1088/1755-1315/1320/1/012023 4 respective opposite evaluation station by means of a neutral white back wall (160 x 80 cm, ρ > 0.80).Additional up-lights were installed on the light prototypes for both general room lighting and the provision of diffuse light components on the material samples.

Figure 2 :
Figure 2: Frontal view of an evaluation station with the diagonally arranged lighting prototypes and the applied material positioning.

Figure 3 :
Figure 3: Luminance image from the position of the viewer defined for material evaluation with clear zoning of the direct portion of the light on the material sample (neutral white).

Figure 4 :
Figure 4: Representation of 8 materials randomly selected from each cluster.The resulting clusters 1 to 3 (top from left to right) are mainly characterized by structural material features, whereas clusters 4 to 6 (bottom from left to right) mainly contain materials of the same type.

Figure 5 :
Figure 5: Exemplary representation of the comparison of the real evaluations to the calculated predictions (R² = 0.95) of the mean values of the aesthetic item diverse (-100) -monotonous (+100) for the test data set of 120 materials.

Figure 6 :
Figure 6: Boxplots of the normalized impacts of the individual material-inherent input features on the aesthetic ratings of the materials, sorted in ascending order based on their respective mean value.The impact groups derived from the analyses are color-coded in the diagram (red: low influence, yellow: medium influence, green: high influence).
.1088/1755-1315/1320/1/012023 10 still necessary to find out to what extent these visually extracted characteristics directly represent the material surfaces under consideration or to what extent the influence of both empirical values and interpretation processes contributes to the formation of the objectively assigned material properties.The determination of these reciprocal mechanisms of action was not part of the present investigation.

Table 1 :
Bipolar pairs of adjectives used for material evaluation separated according to material-inherent properties and aesthetic material effects.All pairs were evaluated on a scale ranging from -100 to +100 with a step size of 1.