Define the terms ‘Sampling’ and ‘Quantization’ in context of digital image processing. A medical image has size 8 × 8 inches, the sampling reduction is 5 cycles/mm, calculate the number of pixels required for the medical image.
Sampling and Quantization in Digital Image Processing
Sampling and quantization are fundamental processes in digital image processing that convert continuous images into digital form, allowing computers to process and manipulate them effectively.
1. Sampling:
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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 8 × 8 inches, the sampling reduction is 5 cycles/mm, calculate the number of pixels required for the medical image.
Consider a 3 × 3 spatial mask that averages the four closet neighbours of a point but excludes the point itself from the average.
i) Find the equivalent filter, H (u, v), in the frequency domain.
ii) Show that your result is a lowpass filter.
Prove that both 2-D continuous and discrete Fourier transforms are linear operations.
Consider a linear, position-invariant image degradation system with impulse response
h(
Supose that the input to the system is an image cosnsiting of a line of infinitesimal width located at x = a, and modeled by where δ is an impulse. Assuming no noise, what is the output image g
Write an expression for 2-D continuous convolution.
a) Consider an 8-pixel line of intensity data, {108,139,135,244,172,173 56, 99, }. If it is uniformly quantized with 4-bit accuracy, compute the rms error and rms signal-tonoise ratios for the quantized data.
b) 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