Human Vision Paradox Implicates Relaxation Model

HUMAN VISION PARADOX IMPLICATES RELAXATION MODEL*

LBL6469

F. S. Montalvo

Computer Science and Applied Mathematics Lawrence Berkeley Laboratory Berkeley, California 94720

The dual role of edges as boundaries and as periodic groupings is supported by human experi­ mental findings. A relaxation model (Zucker, et al., 1975) based on line detectors can underlie both mechanisms. The existence of these edge oper­ ators (Hubel and Wiesel, 1962) and parallel inter­ actions has strong neurophysiological support .

Edges or discontinuities in intensity play two rol es: 1) as outlines of boundaries between regions and 2) as uniform texture within regions. In this context, one can assume an equivalence be­ tween texture detection and spatial frequency/ orientation operators. Bajcsy (1973), for example, has successfully used measures of spatial frequency and directionality as a concise and complete de­ scription of texture . Other approaches to texture segmentation also take into account a dual role for edges . Marr's (1975) terminology for the two ways that lines interact is in curvilinear and theta aggregations. Lines grouped into boundaries rely on continuation of contour while lines grouped into uniform texture rely on similarity of orien­ tation and spacing for their enhancement and defi­ nition .

In addition to having utility in computer vision there is experimental evidence that human vision uses the dual role of edges in organizin~ the visual scene. An experiment by Frome and Levinson (1975) produces opposite results depend­ ing on whether a subject is asked to adjust the shape or the spacing of a row of squares. The ex­ periment is this. Subjects look at a vertical sine-wave grating for a few minutes. Then they look at a row of squares whose size and spacing (spatial frequency) is somewhat smaller (higher) than the size and spacing (spatial frequency) of the bars in the sine-wave grating. Size (spatial frequency) contrast (Blakemore and Sutton, 1969) predicts that the squares in the row will appear narrower (higher in spatial frequency) . However when subjects are asked to adjust the height of the row before and after adaptation to make the figures look square, the height is increased after adaptation to compensate for a wider (lower spa­ tial frequency) appearance . In the same experi­ ment, when subjects are asked to adjust the spac­ ing (spatial frequency), the squares appear more narrowly spaced (higher spatial frequency).

How does one resolve the paradox of wider size but higher spatial frequency? One does not have to resort to spatial frequency detectors operating independently of outline continuity detectors pre­ liminary to shape detection. All that is neces­ sary is a distribution of edge operators of various

*Work performed under the auspices of the Energy Research and Development Administration.

sizes and orientations and relational constraints (in relaxation network terminology) or facilitory connectivity (in neural network terminology) such that segments that line up to form continuous con­ tours facilitate each other and bars of a given width, w, facilitate same-sized, parallel bars at a distance 2w away. After adaptation to a grating the interconnections for that particular spatial frequency and orientation are less strong. Thus, perception of frequencies slightly higher than the adapting frequency will be biased away from the adapting frequency, toward even higher frequencies, and ver tical contours will be less distinct .than horizontal contours. These effects are all in the general class of feature . contrast effects modeled by Montalvo (1976). If we assume that less dis­ tinct contours appear shorter, as some computation­ al experiments (Zucker, 1975) would indicate , then squares after adaptation to vertical contours should appear squat. Human experimental evidence does show that longer contours are more easily de­ tected (Thomas, 1976). The converse, however, has not yet been verified.

In any case, if we accept such an explana­ tion for the paradox two conclusions important to image processing can be made: 1) the intensity of contours can affect shape qualitatively, and 2) local interactions between edge operators can support two different kinds of global organization simultaneously in the same network.