Apply the following image mask to image 2 2 3 4 7 3. Apply Ml at the left and Mr at the right.
Write down a sparse quad tree representation for the following image. In this case, label a node if all leaves below it have the same pixel value.
Given the Haar wavelet representation of an image, compute the image. Do the reverse (for example, for the above image, compute its Haar wavelet representation).
Show that given composite color (r,g,b) and background color (r',g',b') you can not in general compute the foreground pixel (r0,g0,b0,alpha0).
Explain two ways the above matting problem can be restricted so that it can be solved.
Write a simple, efficient algorithm which draws a line with slope 2/3 starting at point (x,y) within image coordinates and stops at the image boundary. The image has width w and height h and origin at the bottom left. You can plot a few points beyond the boundary.
Consider the following mask What can it be used for? Explain how to use it. What is it an approximation for?
Explain why we use the LoG for edge detection? Can a Gaussian be used for edge detection? Can a Laplacian be used?
Describe how you can give an image a painterly effect. What does this have to do with edge detection?
True or false: The following is a good example of a Gaussian mask. Explain.
Explain the intelligent scissors paper.
The following is a Haar Wavelet representation of an image. Compute the original image.
Explain what is meant by Haar is an invertible, but not in practice.
Find n such that, I=Haar^-1(Haar(I * 2ⁿ))/2ⁿ if only integer arithmetic is allowed (with large integers).
Do test 1, Bresenham's algorithm, definitions, triangulation matting, bi-linear interpolation ...
Image gradient, what is it, how do you calculate it, given a image, calculate the gradient at a point, calculate the gradient magnitude, gradient orientation
Derive a 1D mask approximating the first derivative
Show how to derive a 1D mask approximating the second derivative Hint: use f'(x) is almost (f(x+h/2)-f(x-h/2))/h then do it again
How do you detect an edge using the first derivative, second derivative, Laplacian?
Explain how you compute a Gaussian mask given sigma. Do the same for a LoG mask.
Explain how you compute a Laplacian pyramid of an image.
Compute the Fourier transform of a simple signal (do the example in the week 05 lecture notes).
Answer Kira's question, why does the sun seem to stay still and the trees move?
Given a set of points in 3 space, compute the perspective transform of the points (ie onto the plane z=1). Compute the orthographic projection of these points.
Explain how, given 2 quadrilaterals you map one onto the other using a projective 2D linear map (ie start with page 8 of the week 7 lecture notes and describe the linear system that arises, where do the 8 equations and 8 unknowns come from).