Perimeter

Abstract: In regulated rivers, the relationship between wetted perimeter and discharge is sometimes used as an expedient technique for determining the minimum flow allowable for environmental purposes. The critical minimum discharge is supposed to correspond to the point where there is a break in the shape of the curve (usually a logarithmic or power function). Below this discharge, wetted perimeter declines rapidly. This critical point on the curve is almost universally, but incorrectly, termed an ‘inflection’ point, and is usually determined subjectively by eye from a graph. The appearance of a break in the shape of the curve is strongly dependent on the relative scaling of the axes of the graph. This subjectivity can be overcome by defining the break in shape using mathematical techniques. The important break in the shape of the curve can be systematically defined by the point where the slope equals 1, or where the curvature is maximized. The technique can be applied to other habitat‐discharge relationships, provided the habitat variable increases with discharge. These techniques were applied to two regulated headwater streams located in the Melbourne catchment area. Channel survey data were used to model the relationship between discharge and wetted perimeter, flowing water perimeter and blackfish habitat area. A logarithmic function could be fitted to the wetted perimeter data for Starvation Creek, but the relationship for Armstrong Creek was linear. Both streams showed logarithmic relationships between discharge and flowing water perimeter. For these streams, the wetted perimeter relationships did not suggest an optimum environmental flow, nor did they suggest a flow level that would maintain the macroinvertebrate community in its unregulated state if it was applied for a long period of time. Fish habitat area does not necessarily increase with discharge, so the method of curve analysis suggested here for wetted perimeter may not be applicable to some fish habitat area data. Flowing water perimeter is preferable over wetted perimeter as a variable to define habitat suitable for macroinvertebrates. © 1998 John Wiley & Sons, Ltd.

Abstract: An autosegmentation/autocontouring method that may be used for quickly and accurately contouring the regions and boundaries around regions for the development of cross sections that may be linearly disposed for the three-dimensional reconstruction of an image is described and claimed. The autosegmentation/autocontouring method includes at least four steps. The first step is to digitize a CT, MRI, or other suitable image and display it on a display screen. The two-dimensional image on the display screen will include gray-scale representations of the internal organs and tissue masses of the anatomical site through which the cross section was made. The second step is to select the interior of a ROI and draw a polygon within the boundaries of the cross-sectional view of this ROI. This polygon could also be drawn in the interior of a cancerous mass or other diseased tissue. The third step of the method of the present invention is to expand the polygon in a novel manner by iteratively testing pixels of the image on the display outside of, but adjacent to, the pixels that the polygon currently subtends. Pixels will be added to the polygon if the value of a decision rule function has a predetermined value. The expansion of the polygon is continued until none of the pixels at the perimeter of the polygon can satisfy the decision rule. Once it is found that none of the perimeter pixels satisfy the decision rule, the perimeter of the polygon is considered the boundary of the ROI. And the fourth step is that the boundary of the ROI is computed and a contour is developed based on this boundary. This same process is repeated for other ROIs that the user may select.