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 signature of each boundary, we can start by defining the boundaries parametrically. Then we can compute the distance between each point on the boundary and a reference point (e.g., centroid), and plot these distances as a function of the angle. Let's derive the expressions for each shape:
i) Equilateral Triangle:
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Apply Prewitt operators and Sobel operators for the image given below:
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
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.
Write an expression for 2-D continuous convolution.
a) Two images, f (x,y) and g (x,y), have histograms and
Give the condition under which you can determine the histograms of
i)
ii)
iii)
iv)
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
Suppose that an image )y,x(f is convolved with a mask of size n × n (with cofficients 1/n2 ) to produce a smoothed image ).y,x(f (5) i) Derive an expression for edge strength (edge magnitude) of the smoothed image as a function of mask size. Assume for simplicity that n is odd and that edges are obtained using the partial derivatives
and
ii) Show that the ratio of the maximum edge strength of the smoothed image to the maximum edge strength of the orginal is 1/n. In other words, edge strength is inversely proportional to the size of the smoothing mask.