David Marr

This article deals with the English neuro-computer scientist. For other people of the same name, see David Marr (disambiguation) .

David Marr (born January 19, 1945 in Essex , † November 17, 1980 in Cambridge (Massachusetts) ) was an English psychologist , computer scientist and mathematician . He is considered to be one of the founders of neuroinformatics and developed a model of vision as information processing in the brain , which works according to the principles of electronic data processing in a computer .

The Marr Prize is named after him and is awarded every two years at the International Conference on Computer Vision (ICCV).

Life

Educated at Rugby School, Marr studied mathematics and neuroinformatics at Cambridge University , where he received his doctorate in 1971 under Giles Brindley (A general theory for cerebral cortex). He later was a professor at the Massachusetts Institute of Technology . Incurably ill with leukemia , at the end of his life he wrote with great effort on his main work Vision , which appeared only two years after his death with the help of many colleagues.

In 1979 he received the IJCAI Computers and Thought Award .

plant

Marr combined the results of psychology , artificial intelligence and neurophysiology to create a new model of how vision works . For him, seeing is an information processing of the brain that does not operate with images at all, the light of which is already stopped on the 2-dimensional retina and converted by it into neural activity. These electrical activity patterns represent the outside world and are only combined in the brain into what we call seeing. In order to understand this process, according to Marr, questions have to be answered on three levels:

• the computational level : What is the purpose of seeing? What should it do?
• the algorithmic level (level algorithmic) : How can the goal of computing level are achieved, d. H. how can input and output data be represented exactly, and what is the algorithm that transforms the input data into the output data?
• the technical level (implementational level) : How is the algorithm physiologically or physically as neuronal activity implemented ?

Marr's distinctions subsequently gained importance in other disciplines, such as the design and analysis of artificial neural networks .

According to Marr, seeing as the processing of two-dimensional data from the retina into a three-dimensional description of the world is a process that takes place in four stages:

• The basis is the retinal image , a projection of the outside world that contains brightness or color information in the form of an intensity image ;
• the first draft ("sketch"), in which edges , contiguous areas and surface textures are recognized in the manner of a line drawing by analyzing the changes in brightness ;
• the 2½-D design , which is created by combining the two retinal information and determines the spatial orientation and rough depth of surfaces, so that a first rough picture of the three-dimensional world is created.
• the 3-D model , which with the transverse disparity of the two retinal images provides precise information about the depth, so that the perception remains stable despite all eye and body movements.

The Marr wavelet

Schematic representation of a brightness curve at an edge (blue curve), its first derivative (red) and its second derivative (black). According to Marr, the zero of the second derivative localizes the edge.

Although Marr's model of vision is controversial, as a by-product it made an important contribution to the theory of wavelets, which only emerged in the late 1980s . According to Marr, the zeros of the second derivative of the brightness function, i.e. their turning points , are decisive for the detection of edges , see the figure on the right. Since the retina provides a two-dimensional image, this approach leads mathematically to the second derivative of the two-dimensional Gaussian normal distribution as a filter function,

${\displaystyle \psi (x,y)=-{\frac {1}{\pi \sigma ^{4}}}\left(1-{\frac {x^{2}+y^{2}}{2\sigma ^{2}}}\right)\mathrm {e} ^{-(x^{2}+y^{2})/2\sigma ^{2}}.}$

Today this function is often called the Marr wavelet , it is the Mexican hat multiplied by (−1) and, because of its shape, so-called Mexican hat :

The two-dimensional Marr wavelet

See also

• Marr-Hildreth operator

literature

• Rainer Guski (1996): Perceiving - a textbook , Kohlhammer Stuttgart Berlin Cologne, ISBN 3-17-011845-5 , §2.8.1
• Stéphane Jaffard, Yves Meyer and Robert R. Ryan (2001): Wavelets. Tools for Science and Technology , SIAM Philadelphia, ISBN 0-89871-448-6 , §8
• David Marr (1982): Vision. A Computational Investigation into the Human Representation and Processing of Visual Information , WH Freeman and Company, ISBN 0-7167-1284-9 .

Web links

• Online biography (English)

Individual evidence

1. ↑ David Marr in the Mathematics Genealogy Project (English)