数字图像处理（第二版）课后答案.pdf

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Digital Image Processing Second Edition Problem SolutionswStudent Set Rafael C. Gonzalez Richard E. Woods Prentice Hall Upper Saddle River, NJ 07458 www.prenhall.com/gonzalezwoods or www.imageprocessingbook.com

ii Revision history 10 9 8 7 6 5 4 3 2 1 Copyright c°19922002 by Rafael C. Gonzalez and Richard E. Woods

1 Preface This abbreviated manual contains detailed solutions to all problems marked with a star in Digital Image Processing, 2nd Edition. These solutions can also be downloaded from the book web site (www.imageprocessingbook.com).

2 Solutions (Students) Problem 2.1 The diameter, x, of the retinal image corresponding to the dot is obtained from similar triangles, as shown in Fig. P2.1. That is, (d=2) 0:2 (x=2) 0:014 = which gives x = 0:07d. From the discussion in Section 2.1.1, and taking some liberties of interpretation, we can think of the fovea as a square sensor array having on the order of 337,000 elements, which translates into an array of size 580 £ 580 elements. Assuming equal spacing between elements, this gives 580 elements and 579 spaces on a line 1.5 mm long. The size of each element and each space is then s = [(1:5mm)=1; 159] = 1:3£ 10¡6 m. If the size (on the fovea) of the imaged dot is less than the size of a single resolution element, we assume that the dot will be invisible to the eye. In other words, the eye will not detect a dot if its diameter, d, is such that 0:07(d) < 1:3 £ 10¡6 m, or d < 18:6 £ 10¡6 m. Figure P2.1

4 Chapter 2 Solutions (Students) Problem 2.3 ¸ = c=v = 2:998 £ 108(m/s)=60(1/s) = 4:99 £ 106m = 5000 Km. Problem 2.6 Problem 2.9 Problem 2.11 One possible solution is to equip a monochrome camera with a mechanical device that sequentially places a red, a green, and a blue pass ﬁlter in front of the lens. The strongest camera response determines the color. If all three responses are approximately equal, the object is white. A faster system would utilize three different cameras, each equipped with an individual ﬁlter. The analysis would be then based on polling the response of each camera. This system would be a little more expensive, but it would be faster and more reliable. Note that both solutions assume that the ﬁeld of view of the camera(s) is such that it is completely ﬁlled by a uniform color [i.e., the camera(s) is(are) focused on a part of the vehicle where only its color is seen. Otherwise further analysis would be required to isolate the region of uniform color, which is all that is of interest in solving this problem]. (a) The total amount of data (including the start and stop bit) in an 8bit, 1024 £ 1024 image, is (1024)2 £ [8 + 2] bits. The total time required to transmit this image over a At 56K baud link is (1024)2 £ [8 + 2]=56000 = 187:25 sec or about 3.1 min. (b) At 750K this time goes down to about 14 sec. Let p and q be as shown in Fig. P2.11. Then, (a) S1 and S2 are not 4connected because q is not in the set N4(p)u (b) S1 and S2 are 8connected because q is in the set N8(p)u (c) S1 and S2 are mconnected because (i) q is in ND(p), and (ii) the set N4(p) \ N4(q) is empty.

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