Answer Happy

★10.23 Refer to the Hough transform discussed in Section 10.2.7. Note: Fig. 10.33 in the 3rd edition is Fig. 10.30 in the 4th edition. (a) Explain why the Hough mapping of point 1 in Fig. 10.33(a) is a straight line in Fig. 10.33(b) (b) Is this the only point that would produce that result? Explain.
10.2 Point, Line, and Edge Detection 757 Figure 10.33 illustrates the Hough transform based on Eq. (10.2-38). EXAMPLE 10.13: Figure 10.33(a) shows an image of size 101 x 101 pixels with five labeled An illustration of points, and Fig. 10.33(b) shows each of these points mapped onto the basic Hough po-plane using subdivisions of one unit for the p and 6 axes. The range of 9 values is +90°, and the range of the p axis is tV2D, where D is the dis- tance between corners in the image. As Fig. 10.33(c) shows, each curve has a different sinusoidal shape The horizontal line resulting from the map- ping of point 1 is a special case of a sinusoid with zero amplitude. transform properties. The points labeled A (not to be confused with accumulator values) and B in Fig. 10.33(b) show the colinearity detection property of the Hough transform. b FIGURE 10.33 (a) Image of size 101 x 101 pixels, containing five points. (b) Corresponding parameter space. (The points in (a) were enlarged to make them easier to sec.) -100-- -50- 0- 50- 100- Q 80 60 40 20 B R 30 40 -60