Abstract
In light of the growing interest in studying the affective and aesthetic attributes of curvature, the present paper describes four digital image processing techniques that can be used to objectively discriminate between angular and curvilinear stimuli. MATLAB scripts for each of the techniques accompany the paper. Three studies are then reported that evaluate the efficacy of five metrics, derived from the four techniques, at quantifying the degree of angularity depicted in an image. Images of simple polygons (Study 1), artistic drawings of everyday objects (Study 2), and real-world objects, typefaces, and abstract patterns (Study 3) were analyzed. Logistic regression models were used to determine the relative importance of the metrics at distinguishing between angular and curvilinear items. With one exception, all of the metrics were capable of distinguishing between angular and curvilinear items at a level above chance, but some metrics were better at doing so than others, and their discriminative capacity was influenced by the characteristics of the image. The strengths and limitations of the metrics are discussed, as well as some practical recommendations.
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Adapted from do Carmo (1976). Bottom left: Changes in the direction of a unit normal vector N(s) are also systematically related to curvature. Bottom right: Change in the direction of the unit tangent can be expressed as a vector (dashed arrow) that points in the direction of the unit normal
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Data availability
The datasets for the studies reported in the manuscript can be found here: https://osf.io/zj92g/
Code availability
The MATLAB scripts for the techniques described in the manuscript can be found here: https://osf.io/zj92g/
References
Armbruster, D., Suchert, V., Gärtner, A., & Strobel, A. (2014). Threatening shapes: The impact of simple geometric configurations on peripheral physiological markers. Physiology & Behavior, 135, 215–221. https://doi.org/10.1016/j.physbeh.2014.06.020
Aronoff, J. (2006). How we recognize angry and happy emotion in people, places, and things. Cross-Cultural Research, 40, 83–105. https://doi.org/10.1177/1069397105282597
Attneave, F. (1954). Some informational aspects of visual perception. Psychological Review, 61(3), 183–193. https://doi.org/10.1037/h0054663
Baker, N., Garrigan, P., & Kellman, P. J. (2021). Constant curvature segments as building blocks of 2D shape representation. Journal of Experimental Psychology: General, 150(8), 1556–1580. https://doi.org/10.1037/xge0001007
Balakrishnan, H. (2015). Chord_point distance accumulation for curvature (Version 1.1) [Computer Software]. MATLAB Central File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/51111-chord_point-distance-accumulation-for-curvature. Accessed 24 Mar 2022.
Bar, M., & Neta, M. (2006). Humans prefer curved visual objects. Psychological Science, 17, 645–648. https://doi.org/10.1111/j.1467-9280.2006.01759.x
Bar, M., & Neta, M. (2007). Visual elements of subjective preference modulate amygdala activation. Neuropsychologia, 45, 2191–2200. https://doi.org/10.1016/j.neuropsychologia.2007.03.008
Bar, M., Neta, M., & Linz, H. (2006). Very first impressions. Emotion, 6(2), 269–278. https://doi.org/10.1037/1528-3542.6.2.269
Bertamini, M., Palumbo, L., Gheorghes, T. N., & Galatsidas, M. (2016). Do observers like curvature or do they dislike angularity? British Journal of Psychology, 107(1), 154–178. https://doi.org/10.1111/bjop.12132
Bertamini, M., Palumbo, L., & Redies, C. (2019). An advantage for smooth compared with angular contours in the speed of processing shape. Journal of Experimental Psychology: Human Perception and Performance, 45(10), 1304–1318. https://doi.org/10.1037/xhp0000669
Bertamini, M., & Sinico, M. (2021). A Study of Objects With Smooth or Sharp Features Created as Line Drawings by Individuals Trained in Design. Empirical Studies of the Arts, 39(1), 61–77. https://doi.org/10.1177/0276237419897048
Sinico, M., Bertamini, M., & Soranzo, A. (2021). Perceiving Intersensory and Emotional Qualities of Everyday Objects: A Study on Smoothness or Sharpness Features with Line Drawings by Designers. Art & Perception, 9(3), 220–240. https://doi.org/10.1163/22134913-bja10026
Bertamini, M., & Wagemans, J. (2013). Processing convexity and concavity along a 2-D contour: Figure–ground, structural shape, and attention. Psychonomic Bulletin & Review, 20(2), 191–207. https://doi.org/10.3758/s13423-012-0347-2
Blazhenkova, O., & Kumar, M. M. (2018). Angular versus curved shapes: Correspondences and emotional processing. Perception, 47(1), 67–89. https://doi.org/10.1177/0301006617731048
Braun, J., Amirshahi, S. A., Denzler, J., & Redies, C. (2013). Statistical image properties of print advertisements, visual artworks and images of architecture. Frontiers in Psychology, 4. https://doi.org/10.3389/fpsyg.2013.00808
do Carmo, M. (1976). Differential geometry of curves and surfaces. Prentice-Hall.
Chuquichambi, E. G., Corradi, G. B., Munar, E., & Rosselló-Mir, J. (2021). When symmetric and curved visual contour meet intentional instructions: Hedonic value and preference. The Quarterly Journal of Experimental Psychology, 74(9), 1525–1541. https://doi.org/10.1177/17470218211021593
Chuquichambi, E. G., Palumbo, L., Rey, C., & Munar, E. (2021). Shape familiarity modulates preference for curvature in drawings of common-use objects. PeerJ, 9, e11772. https://doi.org/10.7717/peerj.11772
Chuquichambi, E. G., Sarria, D., Corradi, G. B., & Munar, E. (2023). Humans Prefer to See and Imagine Drawing Curved Objects. Empirical Studies of the Arts, 41(1), 135–156. https://doi.org/10.1177/02762374221084212
Chuquichambi, E. G., Vartanian, O., Skov, M., Corradi, G. B., Nadal, M., Silvia, P. J., & Munar, E. (2022). How universal is preference for visual curvature? A systematic review and meta-analysis. Annals of the New York Academy of Sciences, 1518(1), 151–165. https://doi.org/10.1111/nyas.14919
Cormen, T.H., Leiserson, C.E., Rivest, R.L., & Stein, C. (2009). Introduction to Algorithms, Third Edition. The MIT Press.
Corradi, G., Belman, M., Currò, T., Chuquichambi, E. G., Rey, C., & Nadal, M. (2019). Aesthetic sensitivity to curvature in real objects and abstract designs. Acta Psychologica, 197, 124–130. https://doi.org/10.1016/j.actpsy.2019.05.012
Corradi, G., Chuquichambi, E. G., Barrada, J. R., Clemente, A., & Nadal, M. (2020). A new conception of visual aesthetic sensitivity. British Journal of Psychology, 111(4), 630–658. https://doi.org/10.1111/bjop.12427
Corradi, G., & Munar, E. (2020). The Curvature Effect. In M. Nadal & O. Vartanian (Eds.), The Oxford Handbook of Empirical Aesthetics (pp. 35–52). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780198824350.013.24
Corradi, G., Rosselló, M. J., Vañó, J., Chuquichambi, E., Bertamini, M., & Munar, E. (2019). The effects of presentation time on preference for curvature of real objects and meaningless novel patterns. British Journal of Psychology, 110(4), 670–685. https://doi.org/10.1111/bjop.12367
Damiano, C., Walther, D. B., & Cunningham, W. A. (2021). Contour features predict valence and threat judgements in scenes. Scientific reports, 11(19405). https://doi.org/10.1038/s41598-021-99044-y
De Winter, J., & Wagemans, J. (2006). Segmentation of object outlines into parts: A large-scale integrative study. Cognition, 99(3), 275–325. https://doi.org/10.1016/j.cognition.2005.03.004
De Winter, J., & Wagemans, J. (2008). Perceptual saliency of points along the contour of everyday objects: A large-scale study. Perception & Psychophysics, 70(1), 50–64. https://doi.org/10.3758/PP.70.1.50
Feldman, J., & Singh, M. (2005). Information Along Contours and Object Boundaries. Psychological Review, 112(1), 243–252. https://doi.org/10.1037/0033-295X.112.1.243
Fischer, P., & Brox, T. (2014). Image Descriptors based on Curvature Histograms. In Jiang, X., Hornegger, J., & Reinhard, K. (Eds.), Lecture Notes in Computer Science, Vol: 8753. German Conference on Pattern Recognition (pp. 239–249). Springer. https://doi.org/10.1007/978-3-319-11752-2_19
Grebenkina, M., Brachmann, A., Bertamini, M., Kaduhm, A., & Redies, C. (2018). Edge-Orientation Entropy Predicts Preference for Diverse Types of Man-Made Images. Frontiers in Neuroscience, 12, 678–678. https://doi.org/10.3389/fnins.2018.00678
Gómez-Puerto, G., Munar, E., & Nadal, M. (2016). Preference for curvature: A historical and conceptual framework. Frontiers in Human Neuroscience, 9. https://doi.org/10.3389/fnhum.2015.00712
Gómez-Puerto, G., Rosselló, J., Corradi, G., Acedo-Carmona, C., Munar, E., & Nadal, M. (2018). Preference for curved contours across cultures. Psychology of Aesthetics, Creativity, and the Arts, 12(4), 432–439. https://doi.org/10.1037/aca0000135
Gonzalez, R. C., Woods, R. E., & Eddins, S. L. (2020). Digital image processing using MATLAB, Third Edition. Gatesmark Publishing.
Hess, U., Gryc, O., & Hareli, S. (2013). How shapes influence social judgments. Social Cognition, 31(1), 72–80. https://doi.org/10.1521/soco.2013.31.1.72
Han, J. H., & Poston, T. (2001). Chord-to-point distance accumulation and planar curvature: A new approach to discrete curvature. Pattern Recognition Letters, 22(10), 1133–1144. https://doi.org/10.1016/S0167-8655(01)00063-0
Hevner, K. (1935). Experimental studies of the affective value of colors and lines. Journal of Applied Psychology, 19(4), 385–398.
Hoffman, D. D., & Richards, W. A. (1984). Parts of recognition. Cognition, 18(1–3), 65–96. https://doi.org/10.1016/0010-0277(84)90022-2
Jadva, V., Hines, M., & Golombok, S. (2010). Infants’ preferences for toys, colors, and shapes: Sex differences and similarities. Archives of Sexual Behavior, 39(6), 1261–1273. https://doi.org/10.1007/s10508-010-9618-z
Kruizinga, P., & Petkov, N. (1999). Nonlinear operator for oriented texture. IEEE Transactions on Image Processing, 8(10), 1395–1407. https://doi.org/10.1109/83.791965
Kurosu, A., & Todorov, A. (2017). The shape of novel objects contributes to shared impressions. Journal of Vision, 17(13). https://doi.org/10.1167/17.13.14
Larson, C. L., Aronoff, J., Sarinopoulos, I. C., & Zhu, D. C. (2009). Recognizing threat: A simple geometric shape activates neural circuitry for threat detection. Journal of Cognitive Neuroscience, 21(8), 1523–1535. https://doi.org/10.1162/jocn.2009.21111
Larson, C. L., Aronoff, J., & Stearns, J. J. (2007). The shape of threat: Simple geometric forms evoke rapid and sustained capture of attention. Emotion, 7(3), 526–534. https://doi.org/10.1037/1528-3542.7.3.526
Larson, C. L., Aronoff, J., & Steuer, E. L. (2012). Simple geometric shapes are implicitly associated with affective value. Motivation and Emotion, 36, 404–413. https://doi.org/10.1007/s11031-011-9249-2
Levin, D. T., Takarae, Y., Miner, A. G., & Keil, F. (2001). Efficient visual search by category: Specifying the features that mark the difference between artifacts and animals in preattentive vision. Perception & Psychophysics, 63(4), 676–697. https://doi.org/10.3758/BF03194429
Loffler, G. (2008). Perception of contours and shapes: Low and intermediate stage mechanisms. Vision Research, 48(20), 2106–2127. https://doi.org/10.1016/j.visres.2008.03.006
Mermillod, M., Droit-Volet, S., Devaux, D., Schaefer, A., & Vermeulen, N. (2010). Are coarse scales sufficient for fast detection of visual threat? Psychological Science, 21, 1429–1437. https://doi.org/10.1177/0956797610381503
Meyers, L.S., Gamst, G., & Guarino, A.J. (2017). Applied Multivariate Research: Design and Interpretation, Third Edition. Sage Publications.
Monroy, A., Eigenstetter, A., & Ommer, B. (2011). Beyond straight lines — Object detection using curvature. Proceedings of the 18th IEEE International Conference on Image Processing, Belgium (pp. 3561–3564). IEEE. https://doi.org/10.1109/ICIP.2011.6116485
Munar, E., Gómez-Puerto, G., Call, J., & Nadal, M. (2015). Common Visual Preference for Curved Contours in Humans and Great Apes. PloS one, 10(11), e0141106. https://doi.org/10.1371/journal.pone.0141106
Norman, J. F., Phillips, F., & Ross, H. E. (2001). Information concentration along the boundary contours of naturally shaped solid objects. Perception, 30(11), 1285–1294. https://doi.org/10.1068/p3272
Palumbo, L., Ruta, N., & Bertamini, M. (2015). Comparing angular and curved shapes in terms of implicit associations and approach/avoidance responses. PLoS ONE, 10(10). https://doi.org/10.1371/journal.pone.0140043
Pasupathy, A. (2006). Neural basis of shape representation in the primate brain. Progress in brain research, 154, 293–313. https://doi.org/10.1016/S0079-6123(06)54016-6
Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996). A simulation study of the number of events per variable in logistic regression analysis. Journal of clinical epidemiology, 49(12), 1373–1379. https://doi.org/10.1016/s0895-4356(96)00236-3
Poffenberger, A. T., & Barrows, B. E. (1924). The feeling value of lines. Journal of Applied Psychology, 8(2), 187–205. https://doi.org/10.1037/h0073513
Redies, C., Brachmann, A., & Wagemans, J. (2017). High entropy of edge orientations characterizes visual artworks from diverse cultural backgrounds. Vision Research, 133, 130–144. https://doi.org/10.1016/j.visres.2017.02.004
Richards, W., & Hoffman, D. D. (1985). Codon constraints on closed 2D shapes. In A. Rosenfeld (Ed.), Human and machine vision II (pp. 207–223). Academic Press.
Salgado-Montejo, A., Alvarado, J. A., Velasco, C., Salgado, C. J., Hasse, K., & Spence, C. (2015). The sweetest thing: The influence of angularity, symmetry, and the number of elements on shape-valence and shape-taste matches. Frontiers in Psychology, 6. https://doi.org/10.3389/fpsyg.2015.01382
Sapiro, G. (2001). Geometric Partial Differential Equations and Image Analysis. Cambridge University Press.
Silvia, P. J., & Barona, C. M. (2009). Do people prefer curved objects? Angularity, expertise, and aesthetic preference. Empirical Studies of the Arts, 27(1), 25–42. https://doi.org/10.2190/EM.27.1.b
Sochi, T. (2017). Introduction to Differential Geometry of Space Curves and Surfaces. CreateSpace Independent Publishing Platform.
Soranzo, A., Petrelli, D., Ciolfi, L., & Reidy, J. (2018). On the perceptual aesthetics of interactive objects. The Quarterly Journal of Experimental Psychology, 71(12), 2586–2602. https://doi.org/10.1177/1747021817749228
Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Allyn & Bacon/Pearson Education.
Toet, A., & Tak, S. (2013). Look out, there is a triangle behind you! The effect of primitive geometric shapes on perceived facial dominance. I-Perception, 4(1). https://doi.org/10.1068/i0568sas
Üher, J. (1991). On Zigzag Designs: Three Levels of Meaning. Current Anthropology, 32(4), 437–439. https://doi.org/10.1086/203979
Vartanian, O., Navarrete, G., Chatterjee, A., Fich, L. B., Leder, H., Modroño, C., ..., & Skov, M. (2013). Impact of contour on aesthetic judgments and approach-avoidance decisions in architecture. Proceedings of the National Academy of Sciences of the United States of America, 110(Suppl. 2), 10446–10453. https://doi.org/10.1073/pnas.1301227110
Vartanian, O., Navarrete, G., Chatterjee, A., Fich, L. B., Leder, H., Modroño, C., ..., & Nadal, M. (2019). Preference for curvilinear contour in interior architectural spaces: Evidence from experts and nonexperts. Psychology of Aesthetics, Creativity, and the Arts, 13(1), 110–116. https://doi.org/10.1037/aca0000150
Walther, D. B., Farzanfar, D., Han, S., & Rezanejad, M. (2023). The mid-level vision toolbox for computing structural properties of real-world images. Frontiers in Computer Science, 5. https://doi.org/10.3389/fcomp.2023.1140723
Walther, D. B., & Shen, D. (2014). Nonaccidental properties underlie human categorization of complex natural scenes. Psychological Science, 25(4), 851–860. https://doi.org/10.1177/0956797613512662
Watier, N. (2018). The Saliency of Angular Shapes in Threatening and Nonthreatening Faces. Perception, 47(3), 306–329. https://doi.org/10.1177/0301006617750980
Watier, N. (2023). Subtle threat cues in marketing horror and children’s entertainment. Psychology of Popular Media, 12(2), 231–241. https://doi.org/10.1037/ppm0000401
Westerman, S. J., Gardner, P. H., Sutherland, E. J., White, T., Jordan, K., Watts, D., & Wells, S. (2012). Product design: Preference for rounded versus angular design elements. Psychology & Marketing, 29(8), 595–605. https://doi.org/10.1002/mar.20546
Worring, M., & Smeulders, W. M. (1992). The accuracy and precision of curvature estimation methods. Proceedings of the 11th IAPR International Conference on Pattern Recognition, Vol. III, Conference C: Image, Speech and Signal Analysis, Netherlands (pp. 139–142). IEE Computer Society Press. https://doi.org/10.1109/ICPR.1992.201946
Yue, X., Robert, S., & Ungerleider, L. G. (2020). Curvature processing in human visual cortical areas. NeuroImage, 222, 117295. https://doi.org/10.1016/j.neuroimage.2020.117295
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Watier, N. Measures of angularity in digital images. Behav Res (2024). https://doi.org/10.3758/s13428-024-02412-5
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DOI: https://doi.org/10.3758/s13428-024-02412-5