Building a 21st Century Organization

The spot and versatility of the gentle opthalmic administration derive in en whoppingd character reference from its remarkable ability to finger organise and brass in the forecasts encoded by the retinas. To disc over and describe structure, the opthalmic establishment uses a wide lay out of perceptual organization mechanisms ranging from the comparatively low-level mechanisms that belowlie the simplest article of beliefs of classify and segregation, to relatively high-level mechanisms in which analyzable learned associations guide the discovery of structure.The Gestalt psychologists were the early to fully appreciate the fundamental importance of perceptual organization (e. g. , mark Kohler, 1947 Pomerantz & Kubovy, 1986). Objects ofttimes appear in different contexts and atomic number 18 al al close never encounterd from the kindred stand thus, the retinene characters associated with physical objects argon generally complex and varied. To guide whatever hope of obtaining a useful interpretation of the retinal proposes, such as recognizing objects that bugger off been encountered previously, on that point must be sign executees that organize the witness info into those groups most presumable to form meaning(prenominal) objects.Perceptual organization is as well as important because it generally results in highly thick-skulled images of the simulacrums, facilitating later processing, storage, and retrieval. (See Witkin & Tenenbaum, 1983, for a tidings of the importance of perceptual organization from the picturepoint of computational vision. ) Although much has been learned about the mechanisms of perceptual organization (see, e. g. , Beck, 1982 Bergen, 1991 Palmer & Rock, 1994 Pomerantz & Kubovy, 1986), progression in growing testable denary theories has been slow. atomic number 53 atomic number 18a w present substantial progress has been ease up is in stumpers of metric grain group and segregation. These st icks accommodate begun to put the study of perceptual organization on a firm theoretical footing that is lucid with the psychophysics and physiology of low-level vision. Two general parts of sham for texture segregation hire been proposed. In the feature-based models, retinal externalizes atomic number 18 initially processed by mechanisms that find specific features, such as edge segments, run along segments, blobs, and terminators. chemical group and segregation are whitherfore polite by finding the image regions that contain the same feature or cluster of features (see, e. g. , Julesz, 1984, 1986 Marr, 1982 Treisman, 1985). These models are relatively simple, are legitimate with most aspects of low-level vision, and clear been able to account for a float of experimental results. In the filter-based models, retinal images are initially processed by tuned enthralls, for example, contrast-energy channels selective for size and orientation. assort and segregation are because accomplished by finding those image regions with approximately constant output from hotshot or more(prenominal) channels (Beck, Sutter, & Ivry, 1987 Bergen & Landy, 1991 Bovik, Clark, & Geisler, 1990 Caelli, 1988 Chubb & Sperling, 1988 Clark, Bovik, & Geisler, 1987 Fogel & Sagi, 1989 Graham, Sutter, & Venkatesan, 1993 Victor, 1988 Victor & Conte, 1991 Wilson & Ric lumberings, 1992).These models puzzle some advantages over the existing feature-based models They deal be applied to arbitrary images, they are generally more consistent with have sexn low-level mechanisms in the opthalmic system, and they have proven capable of accounting for a wider cat of experimental results. However, the flowing models do non make accurate predictions for certain important crystalizees of stimuli. One class of stimuli are those that contain regions of texture that evoke be nonintegrated only on the basis of local anesthetic structure (i. e. , shape).An some other broad class of st imuli for which most current perceptual organization models do not make adequate predictions are those containing nonstationary structures specifically, structures that change swimmingly and doctrinalally across office. Nonstationary structures are the general rule in raw(a) images because of perspective projection, and because some(prenominal) natural objects are the result of some irregular growth or corrosion process. A simple example of a nonstationary structure would be a contour formed by a sequence of line segments (a bucket along contour) embedded in a background of randomly oriented line segments.Such contours are usually easily picked out by human observers. However, the elements of the contours cannot be grouped by the mechanisms contained in current filter-based or feature-based models, because no unity orientation channel or feature is activated across the tout ensemble contour. Grouping the elements of such contours requires some kind of contour integration proc ess that binds the successive contour elements together on the basis of local likeness. A more complex example of a nonstationary structure would be an image of wood grain.Such a texture contains many contours whose spacing, orientation, and curvature vary smoothly across the image. Again, such textures are easily grouped by human observers but cannot be grouped by the mechanisms contained in the current models. Grouping the contour elements of such textures requires some form of texture integration (the planar analogue of contour integration). The heart of the problem for existing quantitative models of chemical group and segregation is that they do not represent the structure of the image data with the importance achieved by the human ocular system.The human visual system apparently represents image reading in an blow up hierarchical mode that captures many of the spatial, temporal, and chromatic relationships among the entities grouped at each level of the hierarchy. Gro uping and segregation based on simple feature distinctions or channel receptions whitethorn well be an important initial component of perceptual organization, but the final organization that emerges must depend on more sophisticated processes.The major(ip) theoretical aim of this study was to develop a framework for constructing and testing models of perceptual organization that capture some of the richness and complexity of the representations conjureed by the human visual system, and yet are computationally well defined and biologically doable. Within this framework, we have developed a model of perceptual organization for cardinal-dimensional (2D) line images and evaluated it on a number of textbook perceptual organization demonstrations.In this article we refer to this model as the extended model when it is necessary to distinguish it from a alter version, the circumscribe model, described later. Perceptual organization must depend in some way on find similarities and dif ferences between image elements. Furthermore, it is straightforward that similarities and differences along many different comment dimensions can contribute to the organization that is perceived. Although there have been many studies of individual stimulus dimensions, there have been few systematic attempts to study how multiple dimensions interact (Beck et al., 1987 Fahle & Abele, 1996 Li & Lennie, 1996). The major experimental aim of this study was to tone how multiple stimulus dimensions are combined to determine class strength between image elements. To this end, we conducted a series of three-pattern group experiments to directly measure the tradeoffs among twain, three, or four stimulus dimensions at a time. Predictions for these experiments were begetd by a dependant version of the model appropriate for the experimental task. The experimental results provided both a test for the restricted model and a means of estimating the models parameters.The estimated parameter v alues were apply to generate the predictions of the extended model for complex patterns. The next four sections describe, respectively, the theoretical framework, the restricted model, the experiments and results, and the extended model and demonstrations. Theoretical Framework for Perceptual Organization In this section we discuss four important components of perceptual organization hierarchical representation, detection of uninitiates, detection of similarities and differences among image parts, and mechanisms for grouping image parts.These components taken together form the theoretical framework on which the restricted and extended quantitative models are based. Hierarchical Representation It is evident that the mechanisms of perceptual organization knuckle under a rich hierarchical representation that describes the relationship of parts to wholes at a number of levels that is, the wholes at one level often require the parts at the next level. However, there is evidence that the process by which the hierarchical representation is constructed does not proceed strictly either from local to global or from global to local.The global structure of a large letter composed of low-down letters can be discovered before the structure of the individual fiddling letters is discovered (Navon, 1977), and there exist ambiguous figures, such as R. C. Jamess classic Dalmatian dog, that can be solved locally only after at least(prenominal) some of the global structure is discovered. On the other hand, the discovery of structure must sometimes proceed from local to global for example, it would be hard to extract the symmetry of a complex object without first extracting some of the structure of its subobjects.Any well-specified theory of perceptual organization must define what is meant by parts, wholes, and relationships between parts and wholes. Given the current state of subsistledge, all definitions, including the ones we have adopted, must be tentative. Nonetheles s, some basic definitions must be do in order to form working models. In our framework, the most primitive objects are defined on the basis of the current understanding of image encoding in the chief(a) visual mantle of the primate visual system.Higher order objects are defined to be collections of cut back order objects (which whitethorn include primitive objects), together with selective information about the relationships between the lower order objects. The range of relationships that the visual system can discover, the order and drive with which they are discovered, and the mechanisms used to find them are un pocktled issues. As a starting point the relationships we contain are quantitative similarities and differences in size, position, orientation, color, and shape.These dimensions were picked for historic and intuitive reasons They are major categories in human language and accordingly are likely to correspond to perceptually important categories. The precise defin itions of these dimensions of comparison between objects are habituated later. Detection of Primitives Receptive-Field Matching One of the simplest mechanisms for signal detection structure within an image is receptive-field unified, in which relatively hard-wired circuits are used to detect the different spatial patterns of interest.For example, simple cells in the immemorial visual cortex of rascals behave approximately like hard-wired scouts A strong response from a simple cell indicates the presence of a local image pattern with a position, orientation, size (spatial frequency), and phase (e. g. , even or unrivalled symmetry) similar to that of the receptive-field profile (Hubel & Wiesel, 1968 for a review, see DeValois & DeValois, 1988). The complex cells in the primary visual cortex are other example.A strong response from a typical complex cell indicates a particular position, orientation, and spatial frequency independent of the spatial phase (Hubel & Wiesel, 1968 D eValois & DeValois, 1988). Receptive field matching may come up in areas other than the primary visual cortex, and may take detection of image structures other than local luminance or chromatic contours, for example, structures such as phase discontinuities (von der Heydt & Peterhans, 1989) and simple radially symmetric patterns (Gallant, Braun, & forefront Essen, 1993).An important aspect of receptive-field matching in the visual cortex is that the information at each spatial location is encoded by a large number of neurons, each selective to a particular size or scale. The population as a whole spans a wide range of scales and hence provides a multiresolution or multiscale representation of the retinal images (see, e. g. , DeValois & DeValois, 1988). This multiresolution representation may play an important role in perceptual organization.For example, grouping of low-resolution information may be used to constrain grouping of high-resolution information, and vice versa. The quan titative models described here assume that receptive-field matching provides the primitives for the incidental perceptual organization mechanisms. However, to hold down the complexity of the models, the receptive-field matching face is restricted to include only units similar to those of cortical simple cells with small receptive fields. These units proved sufficient for the line pattern stimuli used in the experiments and demonstrations.Receptive-field matching is practical only for a few classes of simple image structure, such as contour segments it is unreasonable to suppose that there are hard-wired receptive fields for every image structure that the visual system is able to detect, because of the combinatorial explosion in the number of receptive-field shapes that would be required. Thus, there must be additional, more flexible, mechanisms for detecting similarities and differences among image regions. These are discussed next. simile/Difference Detection MechanismsStructure exists within an image if and only if some systematic similarities and differences exist between regions in the image. Thus, at the heart of any perceptual organization system there must be mechanisms that match or differentiate image regions to detect similarities and differences. (For this discussion, the reader may think of image regions as either parts of an image or as groups of detected primitives. ) Transformational matching A well-known general method of comparing image regions is to find out how well the regions can be mapped onto each other, accustomed certain allowable work shifts (see, e.g. , Neisser, 1967 Pitts & McCulloch, 1947 Rosenfeld & Kak, 1982 Shepard & Cooper, 1982 Ullman, 1996). The idea is, in effect, to use one image region as a transformable template for comparison with another image region. If the regions closely match, following application of one of the allowable transformations, then a certain similarity between the image regions has been detected. Fu rthermore, the specific transformation that produces the closest match provides information about the differences between the image regions.For example, consider an image that contains two groups of small line segment primitives detected by receptive-field matching, such that each group of primitives forms a triangle. If some particular translation, rotation, and leveling of one of the groups brings it into perfect alignment with the other group then we would know that the two groups are same in shape, and from the aligning transformation itself we would know how much the two groups differ in position, orientation, and size. There are many possible versions of transformational matching, and thus it represents a broad class of similarity-detection mechanisms.Transformational matching is overly very powerfulthere is no relationship between two image regions that cannot be described given an appropriately general facility of allowable transformations. Thus, although there are other credible mechanisms for detecting similarities and differences between image regions (see section on attribute matching), transformational matching is general large to serve as a useful starting point for developing and evaluating quantitative models of perceptual organization. Use of both spatial position and colorThe most obvious form of transformational matching is based on standard template matching that is, maximizing the correlation between the two image regions under the family of allowable transformations. However, template matching has a well-known limitation that often produces undesirable results. To understand the problem, note that each point in the two image regions is described by a position and a color. The most general form of matching would consist of comparing both the positions and colour of the points. However, standard template matching compares only the colors (e. g. , gray levels 2 ) at like positions.If the points cannot be lined up in space then large m atch errors may occur even though the positional errors may be small. A more useful and plausible form of matching mechanism would treat spatial and color information more equivalently by comparing both the spatial positions and the colors of the points or parts making up the objects. For such mechanisms, if the colors of the objects are identical then similarity is determined solely by how well the spatial coordinates of the points or parts making up the objects can be line up and on the values of the spatial transformations that bring them into the best possible alignment.In other words, when the colors are the same, then the matching error is described by differences in spatial position. For such mechanisms, B matches A better than B matches C, in agreement with intuition. Later we describe a simple matching mechanism that simultaneously compares both the spatial positions and the colors of object points. We surface that this mechanism produces matching results that are general ly more perceptually aware than those of template matching. Attribute matchingAnother well-known method of comparing groups is to measure mixed attributes or properties of the groups, and then represent the differences in the groups by differences in the measurable attributes (see, e. g. , Neisser, 1967 Rosenfeld & Kak, 1982 Selfridge, 1956 Sutherland, 1957). These attributes might be simple measures, such as the mean and discrepancy of the color, position, orientation, or size of the primitives in a group, or they might be more complex measures, such as the invariant shape moments. It is likely that perceptual organization in the human visual system involves both transformational matching and attribute matching.However, the specific models considered here involve transformational matching exclusively. The primary reason is that perceptual organization models based on transformational matching have relatively few free parameters, yet they are sensitive to differences in image str ucturean essential requirement for moving beyond existing filter- and feature-based models. For example, a simple transformational matching mechanism (described later) can detect small differences in arbitrary 2D shapes without requiring an explicit description of the shapes.On the other hand, specifying an attribute-matching model that can detect small differences in arbitrary shapes requires specifying a set of attributes that can describe all the relevant details of arbitrary shapes. This type of model would require many assumptions and/or free parameters. Our current view is that transformational matching (or something like it) may be the central mechanism for similarity/difference detection and that it is supplemented by certain forms of attribute matching. Matching groups to categoriesThe discussion so far has assumed implicitly that transformational and attribute matching occur between different groups extracted from the image. However, it is obvious that the brain is also ab le to compare groups with stored information because this is essential for memory. Thus, the visual system may also measure similarities and differences between groups and stored categories, and perform accompanying grouping using these similarities and differences. These stored categories might be represented by prototypes or sets of attributes.Rather than use stored categories, the visual system could also measure similarities and differences to categories that emerge during the perceptual processing of the image. For example, the visual system could extract categories corresponding to prevalent colors within the image, and then perform subsequent grouping on the basis of similarities between the colors of image primitives and these sudden color categories. Grouping Mechanisms Once similarities and differences among image parts are discovered, then the parts may be grouped into wholes.These wholes may then be grouped to form larger wholes, resegregated into a different collectio n of parts, or both. However, it is important to keep in mind that some grouping can occur before all of the relevant relationships between the parts have been discovered. For example, it is possible to group together all image regions that have a similar color, before discovering the geometrical relationships among the regions. As further relationships are discovered, the representations of wholes may be enriched, new wholes may be formed, or wholes may be broken into new parts and reformed.Thus, the discovery of structure is likely to be an asynchronous process that operates simultaneously at multiple levels, often involving an elaborate interleaving of similarity/difference detection and grouping. Within the theoretical framework proposed here we consider one grouping constraintthe generalized uniqueness principleand three grouping mechanisms transitive grouping, nontransitive grouping, and multilevel grouping. The uniqueness principle and the grouping mechanisms can be applied a t multiple levels and can be interleaved with similarity/difference detection.Generalized uniqueness principle The uniqueness principle proposed here is more general it enforces the constraint that at any time, and at any level in the hierarchy, a given object (part) can be designate to only one superordinate object (whole). An object at the lowest level (a primitive) in the hierarchy can be assigned to only one object at the next level, which in piece can be assigned to only one object at the next level, and so on. The sequence of nested objects in the hierarchy containing a given object is called the partwhole path of the object.The generalized uniqueness principle, if valid, constrains the possible perceptual organizations that can be found by the visual system. Nontransitive grouping Our working hypothesis is that similarity in spatial position (proximity) contributes light to nontransitive grouping. If proximity were making a dominant contribution, then separated objects cou ld not bind together separately from the background objects. Proximity contributes powerfully to a different grouping mechanism, transitive grouping, which is described next.We propose that transitive and nontransitive grouping are in some competition with each other and that the visual system uses both mechanisms in the search for image structure. References Beck, J. (Ed. ). (1982). Organization and representation in perception. Hillsdale, NJ Erlbaum. Beck, J. , Sutter, A. , & Ivry, R. (1987). 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