Kluwer - Handbook of Biomedical Image Analysis Vol

5.Let us consider a characteristic function in f : !2 → {0, 1} defined over a CF triangulation of !2. In this case, given a triangle, it can be verified (do it as an exercise) that it has exactly two transverse edges or it does not have transverse edges. Based on this property, write a pseudocode for an algorithm to generate the polygonal curves, after computing the intersections with the triangulation (see Section 7.2.3).

6.Would it be possible to design a T-surfaces model based on a cellular decomposition of the image domain? What would be the advantages over the traditional T-surfaces?

7.Choose a gray scale image, binarize it applying several values of thresholds. Later, with the same initial image, apply the following sequence of operations and compare the results: Canny’s edge detector of thresholds 30 and 80; invert the result; apply over the result the erosion operation with a cross structuring element. Observe the isolated regions with other values of thresholds of your choice.

8.Choose a binary image, apply the following sequence of operations and describe the net effect (B is the structuring element of your choice):

(a) XB = (X # B) B

(b) XB = (X B) # B

(c)XB = X/(X # B)

(d)XB = (X # Bob)/(X Bbk), where Bob is the set formed from pixels in B that should belong to the object, and Bbk is the set formed from pixels

in B that should belong to the background.

9. Considering the implicit representation of a curve, G(x, y) = 0, show that

−→

the normal n and the curvature K can be computed by:

respectively, where the gradient and the divergent ( ·) are computed with respect to the spatial coordinates (x, y).

10. Take the anisotropic diffusion scheme (see Section 7.8):

Show that if I < T, the edges are blurring and if I > T they become sharper.

11. Let us suppose h and g as constants in the GVF model given by the equation:

∂u = g u + h( f − u).

∂t

Consider the stationary solution and take the Fourier transform of the corresponding stationary equation to analyze the GVF in the frequency space.

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