Wine & Cheese visited again

A while back we talked about the jpeg artifacts in an image give to me by my good friend Justin Lau. Apparently, my solution did not please him very much. So, I am revisiting the poster again. Here is the output I got with my new algorithm. I will revisit the algorithm again as I know Justin's objections in advance.

The code that generated the following output is up for auction. (Minimum bid is $2500)

Meanwhile, I will keep thinking about how to approach the quality of the poster obtained in pdf format.

Output of my new algorithm that corrects jpeg artifacts

Compare the above result to the original image below ...

The original image with severe jpeg artifacts.

Automatic makeup!

Today, I will post results of my new algorithm called 'automatic make up'.
Below is the original image and the image produced by my automatic make up algorithm.

Original image

Automatic make up!

Nordstrom

Anisosotropic diffusion may be awesome, but as we have seen, we don't know where to stop. Nordstrom an electrical engineer showed (1992) that if by adding f-u on the right hand of the Perona Malik equation makes its steady state non-trivial. Below is the steady state that was reached at t=1.05.

Non-trivial steady state

Difference between the original and the steady state of Norstrom eq.

Anisotropic diffusion is awesome

We know that the heat equation diffuses an image isotropically. This is not good, because it destroys the edges too.  Somehow one must find a way for isotropic diffusion, only in a flat region and stop the diffusion near the edges. This is the motivation for Peitro Perona and Jitendra Malik's original formulation of anisotropic diffusion.

The heat equation is $\frac{\partial u}{\partial t}=\Delta u$ i.e. $\frac{\partial u}{\partial t}=\mbox{div}\,(\nabla u)$ with $u(0)=f$.

The idea behind the anisotropic diffusion is to multiply the gradient by a function g that equals 1 when the $\nabla u=0$ i.e. flat regions and goes to 0 as the gradient increases, i.e. near the edges. A typical function that works is $g(x)=\frac{1}{1+(x/b)^2}$. for some constant $b$.

That is $\frac{\partial u}{\partial t}= \mbox{div}\,(g(\Vert\nabla u \Vert^2) \nabla u)$.

Alternatively, this can also be viewed as the gradient descent for the minimization of the energy
$$E(u):=\frac{1}{2}\int_{\Omega} g(\Vert\nabla u\Vert^2).$$
Let us look at some experiments, now.


Here is an experiment with Perona Malik model with b=0.01, at t=4.

Perona Malik at t=4.

There is hardly any loss of visual quality of the image. Compare it to the original below. Notice there is some loss of quality in her hair.

The original

Let us see what happens as we continue to t=10 below. Ok, the image is a bit too smooth, rather artistic.

Perona Malik at t=10

Comparison with heat equation



Compare these results with the heat equation at t=4 below. Very smooth, edges are lost. Not good.

Heat equation at t=4.

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