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D Marr

Publications and source records attributed to D Marr.

18 recordsLinked to original sources
PubMed1982

Representation and recognition of the movements of shapes.

The problems posed by the representation and recognition of the movements of 3-D shapes are analysed. A representation is proposed for the movements of shapes that lie within the scope of the Marr & Nishihara (1978) 3-D model representation of static shapes. The basic problem is how to segment a stream of movement into pieces, each of which can be described separately. The representation proposed here is based upon segmenting a movement at moments when a component axis, e.g. an arm, starts to move relative to its local coordinate frame (here the torso). For example, walking is divided into a segment of the stationary states between each swing of the arms and legs, and the actual motions between the stationary points (relative to the torso, not the ground). This representation is called the state-motion-state (SMS) moving shape representation, and several examples of its application are given.

Form Perception↗
PubMed1981

Directional selectivity and its use in early visual processing.

The construction of directionally selective units, and their use in the processing of visual motion, are considered. The zero crossings of delta 2G (x,y) * I(x,y) are located, as in Marr & Hildreth (1980). That is, the image is filtered through centre-surround receptive fields, and the zero values in the output are found. In addition, the time derivative delta[delta 2G(x,y) * I(x,y)]/delta t is measured at the zero crossings, and serves to constrain the local direction of motion to within 180 degrees. The direction of motion can be determined in a second stage, for example by combining the local constraints. The second part of the paper suggests a specific model of the information processing by the X and Y cells of the retina and lateral geniculate nucleus, and certain classes of cortical simple cells. A number of psychophysical and neurophysiological predictions are derived from the theory.

Animals↗
PubMed1980

Visual information processing: the structure and creation of visual representations.

For human vision to be explained by a computational theory, the first question is plain: What are the problems that the brain solves when we see? It is argued that vision is the construction of efficient symbolic descriptions from images of the world. An important aspect of vision is therefore the choice of representations for the different kinds of information in a visual scene. An overall framework is suggested for extracting shape information from images, in which the analysis proceeds through three representations: (1) the primal sketch, which makes explicit the intensity changes and local two-dimensional geometry of an image; (2) 2 1/2-D sketch, which is a viewer-centred representation of the deplth, orientation and discontinuities of the visible surfaces; and (3) the 3-D model representation, which allows an object-centred description of the three-dimensional structure and organization of a viewed shape. The critical act in formulating computational theories for process capable of constructing these representations is the discovery of valid constraints on the way the world behaves, that provide sufficient additional information to allow recovery of the desired characteristic. Finally, once a computational theory for a process has been formulated, algorithms for implementing it may be designed, and their performance compared with that of the human visual processor.

Depth Perception↗
PubMed1980

Theory of edge detection.

A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes at a given scale are best detected by finding the zero values of delta 2G(x,y)*I(x,y) for image I, where G(x,y) is a two-dimensional Gaussian distribution and delta 2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination boundaries, and these all have the property that they are spatially. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround delta 2G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).

Animals↗
PubMed1980

Smallest channel in early human vision.

We suggest from the psychophysical data on two-point and line acuity that the smallest foveal channel in human vision must have an excitatory center with a diameter of around 1' 20". Taking into account the optics of the eye and the finite size of the receptors, we show that this would correspond well to the properties of a retinal ganglion cell receiving excitatory input from a single cone.

Humans↗
PubMed1979

A computational theory of human stereo vision.

An algorithm is proposed for solving the stereoscopic matching problem. The algorithm consists of five steps: (1) Each image is filtered at different orientations with bar masks of four sizes that increase with eccentricity; the equivalent filters are one or two octaves wide. (2) Zero-crossings in the filtered images, which roughly correspond to edges, are localized. Positions of the ends of lines and edges are also found. (3) For each mask orientation and size, matching takes place between pairs of zero-crossings or terminationss of the same sign in the two images, for a range of disparities up to about the width of the mask's central region. (4) Wide masks can control vergence movements, thus causing small masks to come into correspondence. (5) When a correspondence is achieved, it is stored in a dynamic buffer, called the 2 1/2-D sketch. It is shown that this proposal provides a theoretical framework for most existing psychophysical and neurophysiological data about stereopsis. Several critical experimental predictions are also made, for instance about the size of Panum's area under various conditions. The results of such experiments would tell us whether, for example, cooperativity is necessary for the matching process.

Humans↗
PubMed1979

Bandpass channels, zero-crossings, and early visual information processing.

Under appropriate conditions zero-crossings of a bandpass signal are very rich in information. The authors examine here the relevance of this result to the early stages of visual information processing, where zero-crossings in the output of independent spatial-frequency-tuned channels may contain sufficient information for much of the subsequent processing.

Humans↗
PubMed1978

Analysis of a cooperative stereo algorithm.

Marr and Poggio (1976) recently described a cooperative algorithm that solves the correspondence problem for stereopsis. This article uses a probabilistic technique to analyze the convergence of that algorithm, and derives the conditions governing the stability of the solution state. The actual results of applying the algorithm to random-dot stereograms are compared with the probabilistic analysis. A satisfactory mathematical analysis of the asymptotic behaviour of the algorithm is possible for a suitable choice of the parameter values and loading rules, and again the actual performance of the algorithm under these conditions is compared with the theoretical predictions. Finally, some problems raised by the analysis of this type of "cooperative" algorithm are briefly discussed.

Depth Perception↗
PubMed1976

Early processing of visual information.

An introduction is given to a theory of early visual information processing. The theory has been implemented, and examples are given of images at various stages of analysis. It is argued that the first step of consequence is to compute a primitive but rich description of the grey-level changes present in an image. The description is expressed in a vocabulary of kinds of intensity change (EDGE, SHADING-EDGE, EXTENDED-EDGE, LINE, BLOB etc.). Modifying parameters are bound to the elements in the description, specifying their POSITION, ORIENTATION, TERMINATION points, CONTRAST, SIZE and FUZZINESS. This description is obtained from the intensity array by fixed techniques, and it is called the primal sketch. For most images, the primal sketch is large and unwieldy. The second important step in visual information processing is to group its contents in a way that is appropriate for later recognition. From our ability to interpret drawings with little semantic content, one may infer the presence in our perceptual equipment of symbolic processes that can define "place-tokens" in an image in various ways, and can group them according to certain rules. Homomorphic techniques fail to account for many of these grouping phenomena, whose explanations require mechanisms of construction rather than mechanisms of detection. The necessary grouping of elements in the primal sketch may be achieved by a mechanism that has available the processes inferred from above, together with the ability to select items by first order discriminations acting on the elements' parameters. Only occasionally do these mechanisms use downward-flowing information about the contents of the particular image being processed. It is argued that "non-attentive" vision is in practice implemented by these grouping operations and first order discriminations acting on the primal sketch. The class of computations so obtained differs slightly from the class of second order operations on the intensity array. The extraction of a form from the primal sketch using these techniques amounts to the separation of figure from ground. It is concluded that most of the separation can be carried out by using techniques that do not depend upon the particular image in question. Therefore, figure-ground separation can normally precede the description of the shape of the extracted form. Up to this point, higher-level knowledge and purpose are brought to bear on only a few of the decisions taken during the processing. This relegates the widespread use of downward-flowing information to a later stage than is found in current machine-vision programs, and implies that such knowledge should influence the control of, rather than interfering with, the actual data-processing that is taking place lower down.

Computers↗
PubMed1976

Cooperative computation of stereo disparity.

The extraction of stereo-disparity information from two images depends upon establishing a correspondence between them. In this article we analyze the nature of the correspondence computation and derive a cooperative algorithm that implements it. We show that this algorithm successfully extracts information from random-dot stereograms, and its implications for the psychophysics and neurophysiology of the visual system are briefly discussed.

Depth Perception↗
PubMed1969

A theory of cerebellar cortex.

1. A detailed theory of cerebellar cortex is proposed whose consequence is that the cerebellum learns to perform motor skills. Two forms of input-output relation are described, both consistent with the cortical theory. One is suitable for learning movements (actions), and the other for learning to maintain posture and balance (maintenance reflexes).2. It is known that the cells of the inferior olive and the cerebellar Purkinje cells have a special one-to-one relationship induced by the climbing fibre input. For learning actions, it is assumed that:(a) each olivary cell responds to a cerebral instruction for an elemental movement. Any action has a defining representation in terms of elemental movements, and this representation has a neural expression as a sequence of firing patterns in the inferior olive; and(b) in the correct state of the nervous system, a Purkinje cell can initiate the elemental movement to which its corresponding olivary cell responds.3. Whenever an olivary cell fires, it sends an impulse (via the climbing fibre input) to its corresponding Purkinje cell. This Purkinje cell is also exposed (via the mossy fibre input) to information about the context in which its olivary cell fired; and it is shown how, during rehearsal of an action, each Purkinje cell can learn to recognize such contexts. Later, when the action has been learnt, occurrence of the context alone is enough to fire the Purkinje cell, which then causes the next elemental movement. The action thus progresses as it did during rehearsal.4. It is shown that an interpretation of cerebellar cortex as a structure which allows each Purkinje cell to learn a number of contexts is consistent both with the distributions of the various types of cell, and with their known excitatory or inhibitory natures. It is demonstrated that the mossy fibre-granule cell arrangement provides the required pattern discrimination capability.5. The following predictions are made.(a) The synapses from parallel fibres to Purkinje cells are facilitated by the conjunction of presynaptic and climbing fibre (or post-synaptic) activity.(b) No other cerebellar synapses are modifiable.(c) Golgi cells are driven by the greater of the inputs from their upper and lower dendritic fields.6. For learning maintenance reflexes, 2(a) and 2(b) are replaced by2'. Each olivary cell is stimulated by one or more receptors, all of whose activities are usually reduced by the results of stimulating the corresponding Purkinje cell.7. It is shown that if (2') is satisfied, the circuit receptor --> olivary cell --> Purkinje cell --> effector may be regarded as a stabilizing reflex circuit which is activated by learned mossy fibre inputs. This type of reflex has been called a learned conditional reflex, and it is shown how such reflexes can solve problems of maintaining posture and balance.8. 5(a), and either (2) or (2') are essential to the theory: 5(b) and 5(c) are not absolutely essential, and parts of the theory could survive the disproof of either.

Animals↗