Hình là một phác thảo của một lợi thế cạnh hai chiều. Ngoài ra các thông số cạnh của một lợi thế cạnh một chiều, định hướng của các sườn núi cạnh đối với một trục tham chiếu cũng rất quan trọng. Hình xác định danh mục định hướng cạnh cạnh của một đối tượng octagonally hình mà | 628 SHAPE ANALYSIS 1 if C p 0 Ak p 0 if C p 1 or 3 . -1 if C p - 2 Table gives an example of computation of the enclosed area of the following four-pixel object 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 TABLE . Example of Perimeter and Area Computation p C p A j p A k p j p A p 1 0 0 1 0 0 2 3 -1 0 -1 0 3 0 0 1 -1 -1 4 1 1 0 0 -1 5 0 0 1 0 -1 6 3 -1 0 -1 -1 7 2 0 -1 -1 0 8 3 -1 0 -2 0 9 2 0 -1 -2 2 10 2 0 -1 -2 4 11 1 1 0 -1 4 12 1 1 0 0 4 . Bit Quads Gray 16 has devised a systematic method of computing the area and perimeter of binary objects based on matching the logical state of regions of an image to binary patterns. Let n Q represent the count of the number of matches between image pixels and the pattern Q within the curly brackets. By this definition the object area is then Ao n 1 DISTANCE PERIMETER AND AREA MEASURES 629 If the object is enclosed completely by a border of white pixels its perimeter is equal to PO 2n 0 1 2n Now consider the following set of 2 X 2 pixel patterns called bit quads defined in Figure . The object area and object perimeter of an image can be expressed in terms of the number of bit quad counts in the image as FIGURE . Bit quad patterns. AO 4 n Q1 2n Q2 3n Q3 4n Q4 2n QD PO n Q1 n Q2 n Q3 2n QD 630 SHAPE ANALYSIS These area and perimeter formulas may be in considerable error if they are utilized to represent the area of a continuous object that has been coarsely discretized. More accurate formulas for such applications have been derived by Duda 17 Afl 1n Q 1n Q 7n Q n Ổ4 3n Qr O 412283 44 D Po n Q2 -7 n Q1 n Q3 2n QD V2 Bit quad counting provides a very simple means of determining the Euler number of an image. Gray 16 has determined that under the definition of four-connectivity the Euler number can be computed as E 4 n Q1 - n Q3 2n Qd and for eight-connectivity E 4 n Q1 - n Q3 - 2n Qd It should be noted that although it
