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# Homework 3: Scale-space blob detection

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Computer Vision
Homework 3: Scale-space blob detection

Basic project outline
1. Generate and apply a Laplacian of Gaussian filter at a variety of scales.
2. You will develop two separate implementations.
○ First, try increasing the size of the filter to detect blobs at different sizes.
○ Next, write code to instead scale the image down, and apply the filter.
3. Perform nonmaximum suppression in each scale space.
4. Display resulting circles.
Test images
The data folder contains four images to test your code, and the output folder contains sample
output images for your reference. Keep in mind, though, that your output may look different
depending on your threshold, range of scales, and other implementation details. In addition to
the images provided, also run your code on at least four images of your own choosing.
Running the code
Download the code and data and run evalCode.m. It runs a dummy implementation of the code
and draws the blob (a circle in the center of the image). On running the code the ouput should
be something like this (exact times will vary based on the machine):
evalCode
Elapsed time is 0.007286 seconds.
Elapsed time is 0.002676 seconds.
And two identical images:
Detailed instructions
Here are the key steps to implement the blob detector:
● Don’t forget to convert images to grayscale (rgb2gray command) and double
(im2double).

● For creating the Laplacian filter, use the fspecial function (check the options). Pay careful
attention to setting the right filter mask size. Hint: Should the filter width be odd or even?

● It is relatively inefficient to repeatedly filter the image with a kernel of increasing size.
Instead of increasing the kernel size by a factor of k, you should downsample the image
by a factor 1/k. In that case, you will have to upsample the result or do some
interpolation in order to find maxima in scale space. For full credit, you should turn in
both implementations: one that increases filter size detectBlobsScaleFilter.m, and
one that downsamples the image detectBlobsScaleImage.m. In your report, list the
running times for both versions of the algorithm and discuss differences (if any) in the
detector output. For timing, use tic and toc commands.
● Hint 1: think about whether you still need scale normalization when you downsample the
image instead of increasing the scale of the filter.
● Hint 2: For the efficient implementation, pay attention to the interpolation method you’re
using to upsample the filtered images (see the options of the imresize function). What
kind of interpolation works best?
● You have to choose the initial scale, the factor k by which the scale is multiplied each
time, and the number of levels in the scale space. I typically set the initial scale to 2, and
use 10 to 15 levels in the scale pyramid. The multiplication factor should depend on the
largest scale at which you want regions to be detected.

● You may want to use a three-dimensional array to represent your scale space. It would
be declared as follows:
● scaleSpace = zeros(h,w,n); % [h,w] – dimensions of image, n – number of levels in scale
space
● Then scaleSpace(:,:,i) would give you the ith level of the scale space. Alternatively, if you
are storing different levels of the scale pyramid at different resolutions, you may want to
use a cell array, where each “slot” can accommodate a different data type or a matrix of
different dimensions. Here is how you would use it:
● scaleSpace = cell(n,1); %creates a cell array with n “slots”
● scaleSpace{i} = myMatrix; % store a matrix at level i
● To perform nonmaximum suppression in scale space, you should first do nonmaximum
suppression in each 2D slice separately. For this, you may find functions nlfilter, colfilt or
ordfilt2 useful. Play around with these functions, and try to find the one that works the
fastest. To extract the final nonzero values (corresponding to detected regions), you may
want to use the find function.

● You also have to set a threshold above which the Laplacian response will count as a
detection. You should play around with different values and choose one you like best.

● To display the detected regions as circles, you can use the drawBlobs.m. You should
display the highest scoring 1000 detected blobs for each image. If your code returns
fewer than 1000 blobs then you may have to lower your threshold. Hint: Don’t forget that
there is a multiplication factor that relates the scale at which a region is detected to the
radius of the circle that most closely “approximates” the region.

For extra credit
● Implement the difference-of-Gaussian pyramid as mentioned in class and described in
David Lowe’s paper. Compare the results and the running time to the direct Laplacian
implementation.

● Implement the affine adaptation step to turn circular blobs into ellipses as shown in the
lecture (just one iteration is sufficient). The selection of the correct window function is
essential here. You should use a Gaussian window that is a factor of 1.5 or 2 larger than
the characteristic scale of the blob. Note that the lecture slides show how to find the
relative shape of the second moment ellipse, but not the absolute scale (i.e., the axis
lengths are defined up to some arbitrary constant multiplier). A good choice for the
absolute scale is to set the sum of the major and minor axis half-lengths to the diameter
of the corresponding Laplacian circle. To display the resulting ellipses, you should
modify the circle-drawing function or look for a better function in the MATLAB
documentation or on the Internet.

● The Laplacian has a strong response not only at blobs, but also along edges. However,
edge points are not “repeatable”. So, implement an additional thresholding step that
computes the Harris response at each detected Laplacian region and rejects the regions
that have only one dominant gradient orientation (i.e., regions along edges). If you have
implemented the affine adaptation step, these would be the regions whose characteristic
ellipses are close to being degenerate (i.e., one of the eigenvalues is close to zero).
Show both “before” and “after” detection results.
● Blob detection on Wikipedia.
● D. Lowe, “Distinctive image features from scale-invariant keypoints,” International
Journal of Computer Vision, 60 (2), pp. 91-110, 2004. This paper contains details about
efficient implementation of a Difference-of-Gaussians scale space.
● T. Lindeberg, “Feature detection with automatic scale selection,” International Journal of
Computer Vision 30 (2), pp. 77-116, 1998. This is advanced reading for those of you
who are really interested in the gory mathematical details.
the following items:
1. The output of your circle detector on all the images (four provided and four of your own
choice), together with running times for both the “efficient” and the “inefficient”
implementation.
2. An explanation of any “interesting” implementation choices that you made.
3. An explanation of parameter values you have tried and which ones you found to be
optimal.
4. Discussion and results of any extensions or bonus features you have implemented.
Instructions for submitting the homework
On CTools submit the following files:
● detectBlobsScaleFilter.m
● detectBlobsScaleImage.m
● report.pdf
Also include additional code (e.g. for extra credit) and explain it in the report what each file
does.