CSE252 – Computer Vision – Assignment #4
Instructor: Prof. Serge Belongie.
http://www-cse.ucsd.edu/classes/sp03/cse252
Target Due Date: Tue. May 27, 2003.
1. Optical Flow.
(a) Implement the Lucas-Kanade optical flow algorithm. Demonstrate it on the translating
square sequence in frames.mat.
Matlab hints: quiver.
(b) Use the eigenvalues of ATAto identify the regions with reliable optical flow.
2. Spline Interpolation.
(a) Let U(x) = |x|3denote the cubic spline, which is the 1D counterpart to the thin plate
spline (TPS). Prove that in order for the function
f(x) = a+bx +
n
X
i=1
wiU(x−xi)
to have a square integrable second derivative, the following constraints must be satisfied:
n
X
i=1
wi= 0 and
n
X
i=1
wixi= 0.
(b) Reproduce Fig. 4 in Bookstein’s 1989 PAMI paper. You do not need to reproduce the
principal warps part (i.e. the signed segments or the little table), but you do need to show
the interpolated grid points and compute the integral bending norm.
(c) Repeat the previous step using regularization, i.e. replace Kby K+λI , and demonstrate
the effect of varying λ.
3. Pairwise Clustering.
(a) Run the script make_pointset.m to produce the p ointset shown in class consisting of
an annulus and an off-center clump. Calculate and display the affinity matrix using the
Gaussian weighted Euclidean distance wij =e−(dij/α)2.
(b) Implement the Normalized Cuts algorithm to partition this pointset into two clusters.
Run your algorithm with several choices of αand discuss the resulting partitions.
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