Write an expression for 2-D continuous convolution.
In the context of pattern recognition and image processing, the 2-D continuous convolution is a mathematical operation used to combine two functions (such as an image and a filter or kernel) _____ _______ ___ ______ ________ _______ ___ ______ _______ __________ ____.
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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.
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
The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model.
| Symbol | Probability |
| a | 0.2 |
| e | 0.3 |
| i | 0.1 |
| o | 0.2 |
| u | 0.1 |
| ! | 0.1 |
Consider a 3x3 spatial mask that averages the four closet neighbours of a point
(x, y), 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.
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.
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 7x7 arithmetic mean filter?
iii) A 9×9 arithmetic mean filter?
