Holiday wine & cheese event is fun

Today, my dear friend Justin Lau, showed me a jpeg poster that he complained was not very good.Of course ! It produces strange artifacts. Below is the poster he showed me:

Original poster

Here is the detail of the artifact:

Details of the artifact

So, I asked him if I could try to correct the image. And this is what I got with the parameters: 0.01, 6 and 8 in my new algorithm, which is also for auction ($1000 minimum bid).

Details of the artifact removal algorithm

Complete poster corrected ... sort of see this post also!

Boo, the sharpest dog in the world !

I do not like Matlab's unsharp filter. Aside from the fact that the name is stupid, this filter overshoots the edges.

Here is today's fun assignment: design a filter using linear combination of derivatives of the image that does not overshoot.

Here is the output where I sharpen Boo, without overshooting him.

Boo, the sharpest dog in the world

Compare the above image with the original below. There is a subtle change in the image, which I personally believe makes it pleasing to look at.

Original Boo

A new fast denoising algorithm for auction

Here is a novel denoising algorithm. It denoises a 256x256 color image in 2.17 seconds, grayscale in 0.58 seconds (should this be plural or singular?) in Matlab.

I will give the code with explanation to the highest bidder. Minimum bid $1000 USD.

Noisy image

Denoised image

Details of the noisy image

Details of denoised image:
Notice the texture of the wig is almost perfectly maintained.

Nostaligia

It is snowing in Toronto and it is depressing and gloomy to look outside my window. This is a perfect time to think about the past. When I was a child we used to have a film camera. Tricky contraption, if you ask me. The light would be imparted on a film, we would call it a 'negative'. This film is then developed into a photograph. For some reason, I was more fascinated by the negative. Somehow I would think that all my negativity is captured in that. So, on this gloomy day I found an old picture of mine and made its negative. Can you figure out a one line code to do this?

Me and my alter ego

A quick divergence to the cutest Laplacian in the world.

Let $\mathbf{u}=(u_1, u_2)$ be a vector valued function. Then the divergence operator: $\mbox{div }\mathbf{u}:=\frac{du_1}{dx}+\frac{du_2}{dx}$ is a very useful thing to have on our side. Again, I will leave this little code upto you. It is really a one liner!

Note, that if $\nabla u=(u_x, u_y)$ then $\mbox{div}(\nabla u)$ gives the Laplacian $\Delta u$ of the image $u$. This could be useful.

Here is the Laplacian of Boo displayed between -50 to 50.
i.e. use the commands to display the Laplacian d :
>> m=-50; M=50; figure; imshow((d-m)/(M-m));

Laplacian of Boo (-50 to 50)

Here is the original.

Boo, the cutest dog in the world

The edge of darkness is upon us!

I assume that now we know how to find edges in a given image u. It's simple, just take the derivative!

Today, I want to find the smooth regions. Well, it's kind of silly, as now that we have edges, the rest of the image is kind of edgeless. Right... but I would like to assign a number from 0 to 1 to it ... where 1 indicates a flat region and zero indicates an edge, in other words I want to make the edges appear dark.

There are many ways to do it. One of the ways to do it is to look at the function $$g(x, y):=\frac{1}{\sqrt{1+|K*\nabla u(x, y)|}}.$$Where, K is your favourite smoothing kernel. (I will leave it to you to code this as an exercise. It is a four liner.)

Staring at this function is a refreshing activity, something that I love to do in my spare time.

Boo in the edge of darkness

Lenna in the edge of darkness

Barbara in the edge of darkness

Boo, the smoothest dog in the world!

Yesterday night I was too sleepy to code, so I wrote a code for filtering with a kernel that is more than 3x3. Btw, I still like my kernel to be of odd sized and square.

Let's use the image of Boo, the cutest dog in the world and make it the smoothest dog in the world. By using a 5x5 averaging kernel.


>> h=ones(5)/25;
>> u=double(imread('boo.jpg'));
>> uf=ifilter(u, h);m=min(min(min(uf))); M=max(max(max(uf))); figure; imshow((uf-m)/(M-m));

Boo, the cutest dog in the world!

Boo, after smoothing with a 5x5 kernel becomes the smoothest dog in the world!