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Material Type: Assignment; Professor: Jacobs; Class: Computer Graphics; Subject: Computer Science; University: University of Maryland; Term: Fall 2007;
Typology: Assignments
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Introduction: This problem set will focus on writing a program to morph one image into another. You will implement the approach described in: “Feature-Based Image Metamorphosis,” by T. Beier and S. Neely, Computer Graphics , 26(2) 25-42 (available on-line at: http://www.cs.princeton.edu/courses/archive/fall00/cs426/papers/beier92.pdf).
You will be given some basic code, as well as an executable for finished code. Some things to notice about this code:
A maximum of 20 extra credit points are available.
c. Suppose we smooth the image with an averaging filter that has a width of one pixel, and then sample it as in (a). What will the image be then? d. Now let’s consider an even simpler image, in which f(x) = 255 for 0< x < k and f(x) = 0 for k <= x < 1, for some k. Suppose we use the sampling method in (a), and try to reconstruct f using linear interpolation. What value of k will produce the greatest possible error at some location? e. What about if we first apply the averaging filter in (c)? Challenge problem: Suppose that we smooth a signal by averaging. Prove that this smoothing cannot increase the number of points x, at which f(x) is a local maximum value. Note that in some sense this is a measure of how “wiggly” the curve is, so that this shows that smoothing cannot make a curve more wiggly. Hint: Instead of thinking about how smoothing affects f , try thinking about how the inverse process would affect g.