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[SOLVED] (csc420) assignment 1 1. (a) [2 points] write your own code for computing convolution of the 2d

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1. (a) [2 points] Write your own code for computing convolution of the 2D (grayscale)
image and a 2D filter. Make the output matrix be the same size as the input
image. Be careful to correctly deal with the border of the image. The easiest way
to do this is to “zero-pad” the image prior to convolution.(b) [1.5 points] Is it possible to write a convolution in one pixel as a dot product
between two vectors? Is it possible to write the full convolution between the image
and the filter via matrix multiplication?2. (a) [1 points] Given a n×n image, I, and m×m filter, h, what is the computational
cost of computing h × I (the convolution)? What is the computational cost if h
is a separable filter?(b) [1 points] If I first convolve an image with a Gaussian filter with σ = 3, and then
convolve the output with a Gaussian with σ = 8, this gives an equivalent result
as if I just convolve the image with a Gaussian with what σ?(c) [1 points] Write your own function that creates an anisotropic Gaussian filter
with σx and σy as an input parameter.(d) [1 points] Convolve the attached cat.jpg with a (2D) Gaussian filter with σx = 15
and σy = 2 and visualize the result (display the result of the convolution). You
can use built-in functions for convolution.(e) [1 points] The Gaussian filter in question 2.d is separable. How can you use this
fact to speed up convolution? What are the vertical and horizontal filters? No
need to write code.3. (a) [1.5 points] Compute magnitude of gradients for the attached images templateNoise.png and waldoNoise.png using convolution at three different scales.(b) [1 points] Write a function that localizes the template (templateNoise.png) in
the image waldoNoise.png based on the magnitude of gradients. You can help
yourself using findWaldo.m.4. (a) [1 points] Run the Canny edge detector on tennisCourt.jpg. Play with the
parameters so that you get rid of low-contrast edges. In Matlab you can help
yourself with function edge.(b) [1 points] Any idea how you could find the bounds of the court in the image?
No need to write code, just brainstorm!5. [3 points] total (this is an optional exercise) Implement seam carving using Dijkstra’s algorithm for shortest paths:
(a) Compute magnitude of gradients of an image(b) Build a directed image graph with a source and a sink(c) Find the connected path of pixels that has the smallest sum of gradients. A path
is valid if it is connected (the neighboring points in the path are also neighboring
pixels in the image), it starts in the first row of the image and in each step
continues one row down. It finishes in the last row of the image. Hint: It is easier
to restrict your graph, than to modify Dijkstra’s to exhibit this property.(d) You do not have to write your own Dijkstra’s algorithm. In Matlab you can use
graphshortestpath.
(e) Remove the pixels in the path from the image. This gives you a new image with
one column less.(f) [2 points] Remove a few paths with the lowest sum of gradients. Create (fun!)
examples with a few of your own images.(g) [1 points] Could you use this algorithm (with minor modifications) to segment
the bull in cattle.png? A segmentation is a closed path following the boundary
of the object. You can use mouse-clicks, e.g. ginput, to specify initial points on
the object boundary. You will need at least two points, try to get it working with
as few as possible.1 Sources
1. cat.jpg Osamu, Uchida, https://www.flickr.com/photos/13975275@N00/
2. tennisCourt.jpg Michael, Coghlan, https://www.flickr.com/photos/mikecogh/