A binary image contains straight lines oriented horizontally, vertically, at 450 , and at – 45o . Give a set of 3 × 3masks 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.
### Stratified Sampling Stratified sampling is a statistical technique where a population is divided into smaller, homogeneous groups called strata before selecting samples. The purpose of this method is to ensure ______ _________ _______ _____ __________ _________ __________ _____ ___ __________ ____.
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Prove that both 2-D continuous and discrete Fourier transforms are linear operations.
The white bars in the test pattern shown are 7 pixels wide and 210 pixels high. The separation between bars is 17 pixels. What would this image look like after application of
i) A 3 × 3 arithmetic mean filter?
ii) A 7 × 7 arithmetic mean filter?
iii) A 9 × 9 arithmetic mean filter?
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
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 |
An automobile manufacturer is automating the placement of certain components on the bumpers of a limited-edition line of sports cars. The components are colour coordinated, so the robots need to know the colour of each car in order to select the appropriate bumper component. Models come in only four colours: blue, green, red, and white. Find a solution based on imaging and determine the colour of each car, keeping in mind that cost is the most important consideration.
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.
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