Showing papers by "Azriel Rosenfeld published in 1974"

Digital Straight Line Segments

Abstract: It is shown that a digital arc S is the digitization of a straight line segment if and only if it has the "chord property:" the line segment joining any two points of S lies everywhere within distance 1 of S. This result is used to derive several regularity properties of digitizations of straight line segments.

A Threshold Selection Technique

Abstract: Threshold selection for picture segmentation is relatively easy when the frequency distribution of gray levels in the picture is strongly bimodal, with the two peaks comparable insize and separated by a deep valley. This report describes a method of handling cases in which the peaks are very unequal in size and the valley is broad. A Laplacian operation is applied to the picture to determine points that lie on or near the edges of objects. Threshold selection becomes easier when the frequency distribution of gray levels of these points is used.

Adjacency in digital pictures

Abstract: Let S be a subset of a digital picture, and let s be the complement of S. It is well known that the connected components of S and s, under the relation “is adjacent to,≓ form a tree, and algorithms for constructing this tree have been devised. The main purpose of this paper is to prove that the components do form a tree, and in the process, to provide a basis for proving the validity of the tree-constructing algorithms.

Compact Figures in Digital Pictures

Abstract: The square of the perimeter of a figure divided by its area P2/A is a classical measure of the noncompactness of the figure. In Euclidean geometry, P2/A is always at least 4?, and takes on this minimum value only if the figure is a circle; larger values correspond to figures that are less compact than circles. In digital pictures, however, certain squares or octagons?depending on how P is measured?yield smaller values than do digitized circles. Thus for digital pictures, though P2/A may be useful as a practical measure of noncompactness, it possesses certain pathological features of which users should be aware.

A note on perimeter and diameter in digital pictures

Abstract: It is shown that the “intrinsic diameter” of a connected digital object C—i.e., the maximum distance in C between any two points of C—never exceeds half of C's total perimeter (counting all of C's borders, including hole borders). As a preliminary result, it is shown that a simply connected digital object is a simple arc if and only if it has at most two “end” or “corner” points (and, in fact, it can then only have two “end” points).

Threshold Selection, 4.

Abstract: : If a picture contains dark objects on a light background, or vice versa, the objects can be separated from the background by thresholding the picture. A good place to choose the threshold is at the average gray level of those picture points where the value of some difference operation is high (e.g., above the p-title, for p = .85 or so). This idea, suggested over then years ago by Yale Katz, is verified for several classes of pictures (handwriting, chromosomes, cloud cover) and various difference operations. Another standard method of choosing a threshold is to examine the histogram of gray levels that occur in the picture. If this has two peaks, corresponding to the gray level ranges of object points and background points, then a good place to choose the threshold is at the bottom of the valley between these peaks. Mason et al recently describes a method of deepening this valley bottom, to make the choice of threshold easier. This method was tested on the pictures mentioned above; it yielded reasonable thresholds, but the valley deepening effect was not as strong as that obtained using other methods.