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# CSE 5524 Homework Assignment #6 solved

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## Covariance Tracking:

1) Use the covariance matching technique to find the correct match in the color image
given on the WWW site (target.jpg). The model covariance matrix (of <x,y,R,G,B>
features) is given below (notice x,y vs. row,col!).
modelCovMatrix = [47.917 0 -146.636 -141.572 -123.269;
0 408.250 68.487 69.828 53.479;
-146.636 68.487 2654.285 2621.672 2440.381;
-141.572 69.828 2621.672 2597.818 2435.368;
-123.269 53.479 2440.381 2435.368 2404.923];
Test all possible 1-pixel overlapping windows (each of size 70 rows by 24 columns,
with the upperleft-corner as the window origin) in the image with the given model.
Save the match distance for each box location in the image at each pixel location (for
the origin of the window). Plot/display the match-distance-image. Provide the
location of the best match distance for the best candidate. Note that the above given
covariance matrix is biased (normalized with 1/(M*N)), and Matlab’s cov function is
unbiased by default using 1/(M*N-1), so call cov( X, 1 ) to make it consistent
(biased). Leave the image with colors ranging 0-255 (do not scale/normalize the
colors). NOTE: make sure not to take a log() of zero at any time! [5 pts]

## Mean-Shift:

2) Create a function to extract a feature vector for each pixel in a circular neighborhood
[ X ]=circularNeighbors(img, x, y, radius);
For each pixel, use the same format to return as used above (<xi,yi,R,G,B>). That is, X
should be a Kx5 matrix, where each row is for one of the pixels in the neighborhood.
Assume that the (x,y) passed into the function are real (non-integer) values, and do
NOT round them in the function for computation of the neighborhood. [2 pts]
[ Next Page ]
3) Create a function to build a color histogram from a neighborhood of points:
[ hist ]=colorHistogram(X, bins, x, y, h);
The histogram (hist) should be a bins x bins x bins color cube (RxGxB). The bins
should be evenly spaced. For example, if bins=4 then the pixel-value limits for each
bin will be {0-63, 64-127, 128-191, 192-255}. Be sure to test your code on pixels
with RGB values 0 and 255. Weight the construction of the histogram using an
Epanechnikov kernel centered at real-valued (x, y) and with bandwidth h. Normalize
the histogram/cube so it sums to 1. (This function will be used to make your model
histogram “q_model” and to make the candidate test histogram “p_test”) [3 pts]
4) Create a function to calculate a vector of the mean-shift weights (w), where there is a
weight wi for each pixel i in the neighborhood: [2 pts]
[ w ]=meanshiftWeights(X, q_model, p_test, bins);
5) Load the images img1.jpg and img2.jpg (from the website), and use the functions
above to perform mean-shift tracking.
Build a model from img1 using a circular neighborhood with a radius of 25 pixels
centered at (x0,y0) = (150.0, 175.0) and a color histogram of size 16x16x16 (cube).
Build the weighted cube histogram using an Epanechnikov kernel with bandwidth
h = 25 (same as the earlier radius).
Run 25 iterations of mean-shift tracking on img2. DO NOT ROUND coordinates or
values at any time!
Report the final (x, y) location (DO NOT ROUND) and Euclidean distance between
the last two iterations (see Step 4 on the Algorithm slide). [3 pts]