Find an expression for the signature of each of the following boundaries, and plot the signatures.
i) An equilateral triangle
ii) A rectangle
iii) An ellipse
To find the signatures for the boundaries of these shapes, we need to first define what a "signature" means in the context of image processing. The signature of a boundary is typically a function of the distance from a reference point along the boundary, as the boundary is traced.
### i) Equilateral Triangle
For an equilateral triangle, let the vertices be at points \( A(0, h) \), \( B(-b, 0) \), and \( C(b, 0) \), where \( h \) is the height of the triangle and \( b \) is half of its base.
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Prove that, for a zero-memory source with q symbols, the maximum value of the entropy is log q, which is achieved if and only if all source symbols are equiprobable. [Hint: Consider the quantity log q-H(z) and note the inequality In x ≤x-1]
Write an expression for 2-D continuous convolution.
Find an expression for the signature of each of the following boundaries, and plot the signatures.
i) An equilateral triangle
ii) A rectangle
iii) An ellipse
Define the terms 'Sampling' and 'Quantization' in context of digital image processing. A medical image has size 8x8 inches, the sampling reduction is 5 cycles/mm, calculate the number of pixels required for the medical image.
What do you understand by the term "Entropy" in context of any digital image? Calculate the entropy for the symbols, where probability distribution is given below:
| Symbol | Probability |
| 1 | 0.4 |
| 2 | 0.3 |
| 3 | 0.1 |
| 4 | 0.1 |
| 5 | 0.1 |
A binary image contains straight lines oriented horizontally, vertically, at 45°, and at - 45°. Give a set of 3 x 3 masks that can be used to detect 1-pixel breaks in these lines. Assume that the intensities of the lines and background are 1 and 0, respectively.
Consider a linear, position-invariant image degradation system with impulse response
Supose that the input to the system is an image cosnsiting of a line of infinitesimal width located at x = a, and modeled by f(x, y) = 8(x-a), where 8 is an impulse. Assuming no noise, what is the output image g(x, y)?