Skip to main content

Advertisement

Springer Nature Link
Log in

Visual complexity of shapes: a hierarchical perceptual learning model

  • Original article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Understanding how people perceive the visual complexity of shapes has important theoretical as well as practical implications. One school of thought, driven by information theory, focuses on studying the local features that contribute to the perception of visual complexity. Another school, in contrast, emphasizes the impact of global characteristics of shapes on perceived complexity. Inspired by recent discoveries in neuroscience, our model considers both local features of shapes: edge lengths and vertex angles, and global features: concaveness, and is in 92% agreement with human subjective ratings of shape complexity. The model is also consistent with the hierarchical perceptual learning theory, which explains how different layers of neurons in the visual system act together to yield a perception of visual shape complexity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Ahissar, M.: Perceptual learning. Curr. Dir. Psychol. Sci. 8, 124–128 (1999)

    Article  Google Scholar 

  2. Attneave, F.: Some informational aspects of visual perception. Psychol. Rev. 61(3), 183–193 (1954)

    Article  Google Scholar 

  3. Attneave, F.: Physical determinants of the judged complexity of shapes. J. Exp. Psychol. 53(4), 221–227 (1957)

    Article  Google Scholar 

  4. Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002)

    Article  Google Scholar 

  5. Birkhoff, G.D.: Aesthetic Measure. Harvard University Press, Cambridge (1933)

    Book  MATH  Google Scholar 

  6. Brehar, R., Mitrea, D.A., Vancea, F., Marita, T., Nedevschi, S., Lupsor-Platon, M., Rotaru, M., Badea, R.I.: Comparison of deep-learning and conventional machine-learning methods for the automatic recognition of the hepatocellular carcinoma areas from ultrasound images. Sensors 20(11), 3085 (2020)

    Article  Google Scholar 

  7. Brinkhoff, T., Kriegel, H.P., Schneider, R., Braun, A.: Measuring the complexity of polygonal objects. In: Proceedings of 3rd ACM International Workshop on Advances in Geographical Information Systems, pp. 109–117. Citeseer (1995)

  8. Brown, D.R., Owen, D.H.: The metrics of visual form: methodological dyspepsia. Psychol. Bull. 68(4), 243–259 (1967)

    Article  Google Scholar 

  9. Carballal, A., Fernandez-Lozano, C., Rodriguez-Fernandez, N., Santos, I., Romero, J.: Comparison of outlier-tolerant models for measuring visual complexity. Entropy 22(4), 488 (2020)

    Article  Google Scholar 

  10. Chen, Y., Sundaram, H.: Estimating complexity of 2D shapes. In: Proceedings of 7th Workshop on Multimedia Signal Processing, pp. 1–4 (2005)

  11. Der Helm, P.A.V.: Simplicity versus likelihood in visual perception: from surprisals to precisals. Psychol. Bull. 126(5), 770–800 (2000)

    Article  Google Scholar 

  12. Der Helm, P.A.V., Leeuwenberg, E.: Goodness of visual regularities: a nontransformational approach. Psychol. Rev. 103(3), 429–456 (1996)

    Article  Google Scholar 

  13. Diaconescu, A.O., Litvak, V., Mathys, C., Kasper, L., Friston, K.J., Stephan, K.E.: A computational hierarchy in human cortex. arXiv preprint arXiv:1709.02323 (2017)

  14. Donderi, D.C.: Visual complexity: a review. Psychol. Bull. 132(1), 73–97 (2006)

    Article  Google Scholar 

  15. Dou, Q., Zheng, X.S., Sun, T., Heng, P.A.: Webthetics: quantifying webpage aesthetics with deep learning. Int. J. Hum. Comput Stud. 124, 56–66 (2019)

    Article  Google Scholar 

  16. Dubitzky, W., Granzow, M., Berrar, D.P.: Fundamentals of Data Mining in Genomics and Proteomics. Springer, New York (2007)

    Book  MATH  Google Scholar 

  17. Dutt M.B.A.: Boundary and Shape Complexity of a Digital Object. Lecture Notes in Computer Science Book Series 10149, pp. 105–117 (2017)

  18. Everitt, B., Skrondal, A.: The Cambridge Dictionary of Statistics, vol. 106. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  19. Feldman, J.: Bayesian contour integration. Attent. Percept. Psychophys. 63(7), 1171–1182 (2001)

    Article  Google Scholar 

  20. Feldman, J., Singh, M.: Information along contours and object boundaries. Psychol. Rev. 112(1), 243–252 (2005)

    Article  Google Scholar 

  21. Gartus, A., Leder, H.: Predicting perceived visual complexity of abstract patterns using computational measures: the influence of mirror symmetry on complexity perception. PLoS ONE 12(11), e0185276 (2017)

    Article  Google Scholar 

  22. Gellmann, M., Lloyd, S.: Information measures, effective complexity, and total information. Complexity 2(1), 44–52 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  23. Graham, L.: Gestalt theory in interactive media design. J. Hum. Soc. Sci. 2(1), 571 (2008)

    Google Scholar 

  24. Haddad, K., Rahman, A., Zaman, M.A., Shrestha, S.: Applicability of monte carlo cross validation technique for model development and validation using generalised least squares regression. J. Hydrol. 482, 119–128 (2013)

    Article  Google Scholar 

  25. Harper, S., Jay, C., Michailidou, E., Quan, H.: Analysing the visual complexity of web pages using document structure. Behav. Inf. Technol. 32(5), 491–502 (2013)

    Article  Google Scholar 

  26. Hawkins, D.M., Lombard, F.: Cusum control for data following the von mises distribution. J. Appl. Stat. 44(8), 1319–1332 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hubel, D.H., Wiesel, T.N.: Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195(1), 215–243 (1968)

    Article  Google Scholar 

  28. Kanwisher, N.: Functional specificity in the human brain: A window into the functional architecture of the mind. Proc. Nat. Acad. Sci. USA 107, 11163–11170 (2010)

    Article  Google Scholar 

  29. Kayaert, G., Wagemans, J.: Delayed shape matching benefits from simplicity and symmetry. Vis. Res. 49(7), 708–717 (2009)

    Article  Google Scholar 

  30. Kim, S., Lyu, I., Fonov, V., Vachet, C., Hazlett, H., Smith, R., Piven, J., Dager, S., Mckinstry, R., Pruett, J., Evans, A., Collins, D., Botteron, K., Schultz, R., Gerig, G., Styner, M.: Development of cortical shape in the human brain from 6 to 24 months of age via a novel measure of shape complexity. NeuroImage 35, 163–176 (2016)

    Article  Google Scholar 

  31. Koffka, K.: Principles of Gestalt Psychology, vol. 44. Routledge, Abingdon (2013)

    Book  Google Scholar 

  32. Konovalov, D.A., Sim, N., Deconinck, E., Heyden, Y.V., Coomans, D.: Statistical confidence for variable selection in qsar models via monte carlo cross-validation. J. Chem. Inf. Model. 48(2), 370–383 (2008)

    Article  Google Scholar 

  33. Kwon, S.: Mun DKBHS: feature shape complexity: a new criterion for the simplification of feature-based 3d cad models. Int. J. Adv. Manuf. Technol. 88(5–8), 1–13 (2017)

    Google Scholar 

  34. Matsumoto, T., Sato, K., Matsuoka, Y., Kato, T.: Quantification of “complexity” in curved surface shape using total absolute curvature. Comput. Graph. 78(10), 108–115 (2019)

    Article  Google Scholar 

  35. Maunsell, J.H.R., Newsome, W.T.: Visual processing in monkey extrastriate cortex. Annu. Rev. Neurosci. 10(1), 363–401 (1987)

    Article  Google Scholar 

  36. Mavrides, C.M., Brown, D.R.: Discrimination and reproduction of patterns: feature measures and constraint redundancy as predictors. Attent. Percept. Psychophys. 6(5), 276–280 (1969)

    Article  Google Scholar 

  37. McCormack, J., Lomas, A.: Understanding aesthetic evaluation using deep learning. In: International Conference on Computational Intelligence in Music, Sound, Art and Design (Part of EvoStar), pp. 118–133. Springer (2020)

  38. Mcdougall, S., De Bruijn, O., Curry, M.B.: Exploring the effects of icon characteristics on user performance: the role of icon concreteness, complexity and distinctiveness. J. Exp. Psychol. Appl. 6(4), 291–306 (2000)

    Article  Google Scholar 

  39. Murray, S.O., Kersten, D., Olshausen, B.A., Schrater, P., Woods, D.L.: Shape perception reduces activity in human primary visual cortex. Proc. Nat. Acad. Sci. USA 99, 15164–15169 (2002)

    Article  Google Scholar 

  40. Page, D.L., Koschan, A., Sukumar, S.R., Rouiabidi, B., Abidi, M.A.: Shape analysis algorithm based on information theory. In: Proceedings of International Conference on Image, vol. 1, pp. 229–232 (2003)

  41. Perkio, J., Hyvarinen, A.: Modelling image complexity by independent component analysis, with application to content-based image retrieval. In: Proceedings of 19th International Conference Artificial Neural Networks, pp. 704–714 (2009)

  42. Psarra, S., Grajewski, T.: Describing shape and shape complexity using local properties. In: Proceedings of 3rd International Space Syntax Symposium, pp. 28.1–28.16. Citeseer (2001)

  43. Rashid, M., Khan, M.A., Alhaisoni, M., Wang, S.H., Naqvi, S.R., Rehman, A., Saba, T.: A sustainable deep learning framework for object recognition using multi-layers deep features fusion and selection. Sustainability 12(12), 5037 (2020)

    Article  Google Scholar 

  44. Rigau, J., Feixas, M., Sbert, M.: An information-theoretic framework for image complexity. In: Computational Aesthetics in Graphics, Visualization and Imaging, pp. 177–184 (2005)

  45. Rossignac, J.: Shape complexity. Vis. Comput. 21(12), 985–996 (2005)

    Article  Google Scholar 

  46. Serre, T., Wolf, L., Poggio, T.: Object recognition with features inspired by visual cortex. Comput. Vis. Pattern Recognit. 2, 994–1000 (2005)

    Google Scholar 

  47. Severeyn, E., Velásquez, J., Herrera, H., Perpiñan, G., Wong, S., Altuve, M.: Estimation of invasive physiological parameters from non invasive parameters using dimensionless numbers and Monte Carlo cross-validation. In: 2019 XXII Symposium on Image, Signal Processing and Artificial Vision (STSIVA), pp. 1–5. IEEE (2019)

  48. Sieu, B., Gavrilova, M.: Biometric identification from human aesthetic preferences. Sensors 20(4), 1133 (2020)

    Article  Google Scholar 

  49. Su, H., Bouridane, A., Crookes, D.: Scale adaptive complexity measure of 2D shapes. In: Proceedings of 18th International Conference of Pattern Recognition, vol. 2, pp. 134–137 (2006)

  50. Swindale, N.V.: Orientation tuning curves: empirical description and estimation of parameters. Biol. Cybern. 78(1), 45–56 (1998)

    Article  MATH  Google Scholar 

  51. Treisman, A.: Perceptual grouping and attention in visual search for features and for objects. J. Exp. Psychol. Hum. Percept. Perform. 8(2), 194 (1982)

    Article  Google Scholar 

  52. Tuch, A.N., Bargas-Avila, J.A., Opwis, K., Wilhelm, F.H.: Visual complexity of websites: effects on users’ experience, physiology, performance, and memory. Int. J. Hum Comput Stud. 67(9), 703–715 (2009)

    Article  Google Scholar 

  53. Ullman, S., Vidalnaquet, M., Sali, E.: Visual features of intermediate complexity and their use in classification. Nat. Neurosci. 5(7), 682–687 (2002)

    Article  Google Scholar 

  54. Xu, Q., Liang, Y., Du, Y.: Monte carlo cross-validation for selecting a model and estimating the prediction error in multivariate calibration. J. Chemom. 18(2), 112–120 (2004)

    Article  Google Scholar 

  55. Zheng, X.S., Chakraborty, I., Lin, J.J., Rauschenberger, R.: Correlating low-level image statistics with users—rapid aesthetic and affective judgments of web pages. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 1–10 (2009)

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou, Zhejiang, China

    Lingchen Dai & Jinhui Yu

  2. Department of Computer Science, University of Texas at Dallas, Dallas, TX, USA

    Kang Zhang

  3. Department of Psychology, Tsinghua University, Beijing, China

    Xianjun Sam Zheng

  4. School of Computer Science and Informatics, Cardiff University, Cardiff, UK

    Ralph R. Martin

  5. School of Management, University of Science and Technology of China, Hefei, China

    Yina Li

Authors
  1. Lingchen Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xianjun Sam Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ralph R. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yina Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jinhui Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinhui Yu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, L., Zhang, K., Zheng, X.S. et al. Visual complexity of shapes: a hierarchical perceptual learning model. Vis Comput 38, 419–432 (2022). https://doi.org/10.1007/s00371-020-02023-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-020-02023-z

Keywords

Search

Navigation