“Invariants” in Koffka’s Theory of Constancies in Vision: Highlighting Their Logical Structure and Lasting Value

Open access


By introducing the concept of “invariants”, Koffka (1935) endowed perceptual psychology with a flexible theoretical tool, which is suitable for representing vision situations in which a definite part of the stimulus pattern is relevant but not sufficient to determine a corresponding part of the perceived scene. He characterised his “invariance principle” as a principle conclusively breaking free from the “old constancy hypothesis”, which rigidly surmised point-to-point relations between stimulus and perceptual properties. In this paper, we explain the basic terms and assumptions implicit in Koffka’s concept, by representing them in a set-theoretic framework. Then, we highlight various aspects and implications of the concept in terms of answers to six separate questions: forms of invariants, heuristic paths to them, what is invariant in an invariant, roots of conditional indeterminacy, variability vs. indeterminacy, and overcoming of the indeterminacy. Lastly, we illustrate the lasting value and theoretical power of the concept, by showing that Koffka’s insights relating to it do occur in modern perceptual psychology and by highlighting its role in a model of perceptual transparency.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Beck J. Prazdny K. & Ivry R. (1984). The perception of transparency with achromatic colors. Perception & Psychophysics 35(5) 407–422.

  • Bergström S. S. (1977). Common and relative components of reflected light as information about the illumination colour and three-dimensional form of objects. Scandinavian Journal of Psychology 18(3) 180–186.

  • Bloj M. G. & Hurlbert A. C. (2002). An empirical study of the traditional Mach card effect. Perception 31(2) 233–246.

  • Chen L. (2005). The topological approach to perceptual organization. Visual Cognition 12(4) 553–637.

  • Cutting J. E. (1986). Perception with an eye for motion. Cambridge MA: MIT Press.

  • Cutting J. E. & Vishton P. M. (1995). Perceiving layout and knowing distances: The integration relative potency and contextual use of different information about depth. In W. Epstein & S. Rogers (Eds.) Perception of space and motion (pp. 69–117). New York NY: Academic Press.

  • Da Pos O. & Burigana L. (2013). Qualitative inference rules for perceptual transparency. In L. Albertazzi (Ed.) Handbook of experimental phenomenology: Visual perception of shape space and appearance (pp. 343–367). New York NY: Wiley.

  • Dechter R. (2003). Constraint processing. San Mateo CA: Morgan Kaufmann.

  • Epstein W. (1982). Percept-percept couplings. Perception 11(1) 75–83.

  • Gibson J. J. (1979). The ecological approach to visual perception. Boston MA: Houghton Mifflin.

  • Gilchrist A. L. (2006). Seeing black and white. Oxford UK: Oxford University Press.

  • Gilchrist A. L. Kossyfidis C. Bonato F. Agostini T. Cataliotti J. Li X. Spehar B. Annan V. & Economou E. (1999). An anchoring theory of lightness perception. Psychological Review 106(4) 795–834.

  • Gogel W. C. (1973). The organization of perceived space. I. Perceptual interactions. Psychologische Forschung 36(3) 195–221.

  • Gogel W. C. (1976). An indirect method of measuring perceived distance from familiar size. Perception & Psychophysics 20(6) 419–429.

  • Hatfield G. C. (2003). Representation and constraints: The inverse problem and the structure of visual space. Acta Psychologica 114(3) 355–378.

  • Heidelberger M. (2010). Functional relations and causality in Fechner and Mach. Philosophical Psychology 23(2) 163–172.

  • Hochberg J. E. (1957). Effects of the Gestalt revolution: The Cornell symposium on perception. Psychological Review 64(2) 73–84.

  • Jäkel F. Singh M. Wichmann F. A. & Herzog M. H. (2016). An overview of quantitative approaches in Gestalt perception. Vision Research 126 3–8.

  • Johansson G. (1970). On theories for visual space perception. A letter to Gibson. Scandinavian Journal of Psychology 11(2) 67–74.

  • Kersten D. Mamassian P. & Yuille A. L. (2004). Object perception as Bayesian inference. Annual Review of Psychology 55 271–304.

  • Koenderink J. J. van Doorn A. J. Pont S. & Richards W. (2008). Gestalt and phenomenal transparency. Journal of the Optical Society of America Series A 25(1) 190–202.

  • Koffka K. (1935). Principles of Gestalt psychology. New York NY: Harcourt Brace and Company.

  • Kogo N. Strecha C. van Gool L. & Wagemans J. (2010). Surface construction by a 2-D differentiation-integration process: A neurocomputational model for perceived border ownership depth and lightness in Kanizsa figures. Psychological Review 117(2) 406–439.

  • Köhler W. (1913). Über unbemerkte Empfindungen und Urteilstäuschungen. Zeitschrift für Psychologie 66(Hefte 1 und 2) 51–80.

  • Marr D. (1982). Vision. A computational investigation into the human representation and processing of visual information. San Francisco CA: Freeman.

  • Metelli F. (1970). An algebraic development of the theory of perceptual transparency. Ergonomics 13(1) 59–66.

  • Neapolitan R. E. (2004). Learning Bayesian networks. Upper Saddle River NJ: Pearson Prentice Hall.

  • Oyama T. (1969). S-S relations in psychophysics and R-R correlations in phenomenology. Psychologia 12(1) 17–23.

  • Poggio T. Torre V. & Koch C. (1985). Computational vision and regularization theory. Nature 317(No. 6035) 314–319.

  • Rock I. (1983). The logic of perception. Cambridge MA: MIT Press.

  • Rock I. (1997). Indirect perception. Cambridge MA: MIT Press.

  • Sarris V. (2006). Relational psychophysics in humans and animals: A comparative developmental approach. London UK: Psychology Press.

  • Sarris V. (2012). Epilogue: Max Wertheimer in Frankfurt and thereafter. In L. Spillmann (Ed.) On perceived motion and figural organization (pp. 253–265). Cambridge MA: MIT Press.

  • Savardi U. & Bianchi I. (2012). Coupling Epstein’s and Bozzi’s “percept-percept coupling”. Gestalt Theory 34(2) 191–200.

  • Sinico M. (2013). Epistemic line of explanation for experimental phenomenology. Gestalt Theory 35(4) 365–376.

  • Spillmann L. (2012). The current status of Gestalt rules in perceptual research: Psychophysics and neurophysiology. In L. Spillmann (Ed.) On perceived motion and figural organization (pp. 191–251). Cambridge MA: MIT Press.

  • Todd J. T. Chen L. & Norman J. F. (1998). On the relative salience of Euclidean affine and topological structure for 3-D form discrimination. Perception 27(3) 273–282.

  • Trommershäuser J. Körding K. P. & Landy M. S. (Eds.). (2011). Sensory cue integration. Oxford UK: Oxford University Press.

  • Wagemans J. Elder J. H. Kubovy M. Palmer S. E. Peterson M. A. Singh M. & von der Heydt R. (2012a). A century of Gestalt psychology in visual perception: I. Perceptual grouping and figure-ground organization. Psychological Bulletin 138(6) 1172–1217.

  • Wagemans J. Feldman J. Gepshtein S. Kimchi R. Pomerantz J. R. van der Helm P. A. & van Leeuwen C. (2012b). A century of Gestalt psychology in visual perception: II. Conceptual and theoretical foundations. Psychological Bulletin 138(6) 1218–1252.

Journal information
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 234 133 4
PDF Downloads 112 79 1