David Marr (neuroscientist)

David Courtenay Marr (19 January 1945 – 17 November 1980)

Born in Woodford, Essex, and educated at Rugby School; he was admitted at Trinity College, Cambridge on 1 October 1963 (having been awarded an Open Scholarship and the Lees Knowles Rugby Exhibition).

He was awarded the Coutts Trotter Scholarship in 1966 and obtained his BA in mathematics the same year. He was elected a Research Fellow of Trinity College, Cambridge in 1968. His doctoral dissertation, supervised by Giles Brindley, was submitted in 1969 and described his model of the function of the cerebellum based mainly on anatomical and physiological data garnered from a book by J.C. Eccles. His interest turned from general brain theory to visual processing. Subsequently, he worked at the Massachusetts Institute of Technology, where he took on a faculty appointment in the Department of Psychology in 1977 and was subsequently made a tenured full professor in 1980. Marr proposed that understanding the brain requires an understanding of the problems it faces and the solutions it finds. He emphasised the need to avoid general theoretical debates and instead focus on understanding specific problems.

Marr died of leukemia in Cambridge, Massachusetts, at the age of 35. His findings are collected in the book Vision: A computational investigation into the human representation and processing of visual information, which was finished mainly in the summer of 1979, was published in 1982 after his death and re-issued in 2010 by The MIT Press. This book had a key role in the beginning and rapid growth of computational neuroscience field.^[2] He was married to Lucia M. Vaina of Boston University's Department of Biomedical Engineering and Neurology.

There are various academic awards and prizes named in his honour. The

The theory of neocortex^[5] was primarily motivated by the discoveries of David Hubel and Torsten Wiesel, who found several types of "feature detectors" in the primary visual area of the cortex. Marr proposed, generalising on that observation, that cells in the neocortex are flexible categorizers—that is, they learn the statistical structure of their input patterns and become sensitive to combinations that are frequently repeated.

The theory of

Marr treated vision as an information processing system. He put forth (in concert with Tomaso Poggio) the idea that one must understand information processing systems at three distinct, complementary levels of analysis.^[10] This idea is known in cognitive science as Marr's Tri-Level Hypothesis:^[11]

• computational level: what does the system do (e.g.: what problems does it solve or overcome) and similarly, why does it do these things
• algorithmic level (sometimes representational level): how does the system do what it does, specifically, what representations does it use and what processes does it employ to build and manipulate the representations
• implementational/physical level: how is the system physically realised (in the case of biological vision, what neural structures and neuronal activities implement the visual system)

Marr illustrates his tripartite analysis recurring to the example of a device whose functioning is well understood: a cash register.^[12]

At the computational level, the functioning of the register can be accounted for in terms of arithmetic and, in particular, in terms of the theory of addition: at this level are relevant the computed function (addition), and such abstract properties of it, as commutativity or associativity. The level of representation and algorithm specify the form of the representations and the processes elaborating them: "we might choose Arabic numerals for the representations, and for the algorithm we could follow the usual rules about adding the least significant digits first and `carrying' if the sum exceeds 9".^[12] Finally, the level of implementation has to do with how such representations and processes are physically realized; for example, the digits could be represented as positions on a metal wheel, or, alternatively, as binary numbers coded by the electrical states of digital circuitry. Notably, Marr pointed out that the most important level for the design of effective systems is the computational one.^[12]

Stages of vision

Marr described vision as proceeding from a two-dimensional visual array (on the retina) to a three-dimensional description of the world as output. His stages of vision include:^[10]

• a primal sketch of the scene, based on feature extraction of fundamental components of the scene, including edges, regions, etc. Note the similarity in concept to a pencil sketch drawn quickly by an artist as an impression.
• a 2.5D sketch of the scene, where textures are acknowledged, etc. Note the similarity in concept to the stage in drawing where an artist highlights or shades areas of a scene, to provide depth.
• a 3D model, where the scene is visualised in a continuous, 3-dimensional map.

2.5D sketch is related to

Marr's three-stage framework does not capture well a central stage of visual processing: visual attention. A more recent, alternative, framework proposed that vision is composed instead of the following three stages: encoding, selection, and decoding.^[14] Encoding is to sample and represent visual inputs (e.g., to represent visual inputs as neural activities in the retina).^[15] Selection, or attentional selection, is to select a tiny fraction of input information for further processing, e.g., by shifting gaze to an object or visual location to better process the visual signals at that location. Decoding is to infer or recognize the selected input signals, e.g., to recognize the object at the center of gaze as somebody's face.

See also

• High and low level (description)
• Marr Prize
• Level of analysis

Publications

• (1969) "A theory of cerebellar cortex." J. Physiol., 202:437–470.
• (1970) "A theory for cerebral neocortex." Proceedings of the Royal Society of London B, 176:161–234.
• (1971) "Simple memory: a theory for archicortex." Phil. Trans. Royal Soc. London, 262:23–81.
• (1974) "The computation of lightness by the primate retina." Vision Research, 14:1377–1388.
• (1975) "Approaches to biological information processing." Science, 190:875–876.
• (1976) "Early processing of visual information." Phil. Trans. R. Soc. Lond. B, 275:483–524.
• (1976) "Cooperative computation of stereo disparity." Science, 194:283–287. (with Tomaso Poggio)
• (March 1976) "Artificial intelligence: A personal view." Technical Report AIM 355, MIT AI Laboratory, Cambridge, MA.
• (1977) "Artificial intelligence: A personal view." Artificial Intelligence 9(1), 37–48.
• (1977) "From understanding computation to understanding neural circuitry." Neurosciences Res. Prog. Bull., 15:470–488. (with Tomaso Poggio)
• (1978) "Representation and recognition of the spatial organization of three dimensional shapes." Proceedings of the Royal Society of London B, 200:269–294. (with H. K. Nishihara)
• (1979) "A computational theory of human stereo vision." Proceedings of the Royal Society of London B, 204:301–328. (with Tomaso Poggio)
• (1980) "Theory of edge detection." Proc. R. Soc. Lond. B, 207:187–217. (with E. Hildreth)
• (1981) "Artificial intelligence: a personal view." In Haugeland, J., ed., Mind Design, chapter 4, pages 129–142. MIT Press, Cambridge, MA.
• (1982) "Representation and recognition of the movements of shapes." Proceedings of the Royal Society of London B, 214:501–524. (with L. M. Vaina)
• (1982) Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. San Francisco: W. H. Freeman and Company.
  ISBN 9780262514620
  .)

Further reading

• Vaina, L. M., ed. (1990). From the retina to the neocortex: selected papers of David Marr. Boston, MA: Birkhauser.
• Vaina, Lucia M.; Passingham, Richard E., eds. (2016). Computational Theories and their Implementation in the Brain: The legacy of David Marr. Oxford University Press.
  ISBN 978-0-19-874978-3
  .

External links

Scholia has a profile for David Marr (Q92844).

• Extensive online biography