Refer to the three vertical edge models and corresponding profiles in Fig.FIGURE From left...

Refer to the three vertical edge models and corresponding profiles in Fig.

FIGURE From left to right, models (ideal representations) of a step, a ramp, and a roof edge, and their corresponding intensity profiles.

(a) Suppose that we compute the gradient magnitude of each of the three edge models using the Sobel masks. Sketch the horizontal intensity profiles of the three gradient images.

---

(b) Sketch the horizontal intensity profiles of the three Laplacian images, assuming that the Laplacian is computed using the 3×3 mask in Fig.

FIGURE (a) Point detection (Laplacian) mask. (b) X-ray image of turbine blade with a porosity. The porosity contains a single black pixel. (c) Result of convolving the mask with the image. (d) Result of using Eq. showing a single point (the point was enlarged to make it easier to see). (Original image courtesy of X-TEK Systems, Ltd.)

---

(c) Repeat for an image generated using only the first two steps of the Marr-Hildreth edge detector.

---

(d) Repeat for the first two steps of the Canny edge detector. You may ignore the angle images.

---

(e) Sketch the horizontal profile of the angle images for the Canny edge detector.

(Note: Answer this question without generating the images. Simply provide sketches of the profiles that show what you would expect the profiles of the images to look like.)