November 21, 2014

Matthias Odisio, Mathematica Algorithm R&D

Giulio Alessandrini, Mathematica Algorithm R&D

For most of us, taking bad pictures is incredibly easy. Band-Aid or remedy, digital post-processing can involve altering the photographed scene itself. Say you’re trekking through the mountains taking photos of the horizon, or you’re walking down the street and catch a beautiful perspective of the city, or it’s finally the right time to put the new, expensive phone camera to good use and capture the magic of this riverside… Just why do all the pictures look so bad? They’re all foggy! It’s not that you’re a bad photographer—OK, maybe you are—but that you’ve stumbled on a characteristic problem in outdoor photography: haze.

What is haze? Technically, haze is scattered light, photons bumped around by the molecules in the air and deprived of their original color, which they got by bouncing off the objects you are trying to see. The problem gets worse with distance: the more the light has to travel, the more it gets scattered around, and the more the scene takes that foggy appearance.

What can we do? What can possibly help our poor photographer? Science, of course.

Wolfram recently attended and sponsored the 2014 IEEE International Conference on Image Processing (ICIP), which ended October 30 in Paris. It was a good occasion to review the previous years’ best papers at the conference, and we noticed an interesting take on the haze problem proposed by Chen Feng, Shaojie Zhuo, Xiaopeng Zhang, Liang Shen, and Sabine Süsstrunk [1]. Let’s give their method a try and implement their “dehazing” algorithm.

The core idea behind the paper is to leverage the different susceptibilities of the light being scattered, which depend on the wavelength of the light. Light with a larger wavelength, such as red light, is more likely to travel around the dust, the smog, and all the other particles present in the air than shorter wavelength colors, like green or blue. Therefore, the red channel in an image carries better information about the non-hazy content of the scene.

But what if we could go even further? What prevents us from using the part of the spectrum slightly beyond the visible light? Nothing really—save for the fact we need an infrared camera.

Provided we are well equipped, we can then use the four channels of data (near infrared, red, green, and blue) to estimate the haze color and distribution and proceed to remove it from our image.

September 4, 2014 — Jon McLoone, International Business & Strategic Development

I first came across the knight’s tour problem in the early ’80s when a performer on the BBC’s *The Paul Daniels Magic Show* demonstrated that he could find a route for a knight to visit every square on the chess board, once and only once, from a random start point chosen by the audience. Of course, the act was mostly showmanship, but it was a few years before I realized that he had simply memorized a closed (or reentrant) tour (one that ended back where he started), so whatever the audience chose, he could continue the same sequence from that point.

In college a few years later, I spent some hours trying, and failing, to find any knight’s tour, using pencil and paper in various systematic and haphazard ways. And for no particular reason, this memory came to me while I was driving to work today, along with the realization that the problem can be reduced to finding a Hamiltonian cycle—a closed path that visits every vertex—of the graph of possible knight moves. Something that is easy to do in *Mathematica*. Here is how.

August 14, 2014 — Tom Sherlock, User Interface Group

The planet Mars comes into opposition, the point closest to the Earth, about every 780 days, or a bit over two years. The Martian opposition this year was on April 9. This past May, on a rare clear, warm night, I attempted to capture some images of the red planet. Unfortunately once I had my telescope set up, Mars had passed behind a large tree, so the images I captured were distorted by tree branches. Nevertheless, I did manage to capture a set of frames, and hoped that image processing with *Mathematica* could produce something usable.

May 30, 2014 — Wolfram Blog

Donald Barnhart is a self-proclaimed mad optical scientist and independent business owner. He’s been developing optical design and analysis software in *Mathematica* since 1991, he’s the creator of the popular Optica software package, and he’s the developer of the first successful high-resolution holographic instrument that measures three-dimensional velocity fields in fluids.

Now Barnhart has another invention to add to his list of accomplishments: a totally new kind of photo album called the SlideOScope.

August 15, 2013 — Michael Trott, Chief Scientist

This blog post is the continuation of my last two posts (1, 2) about formulas for curves. So far, we have discussed how to make plane curves that are sketches of animals, faces, fictional characters, and more. In this post, we will discuss the constructions of some filled curves (laminae).

July 19, 2013 — Michael Trott, Chief Scientist

In my last blog post, I discussed how to construct closed-form trigonometric formulas for sketches of people’s faces. Using similar techniques, Wolfram|Alpha has recently added a collection of hundreds of such closed-form curves for faces, shapes, animals, logos, and signatures.

July 15, 2013 — Matthias Odisio, Mathematica Algorithm R&D

Or: How I Learned to Watch the Best Movies in the Best Way

I remember when I lived across the street from an art movie theater called Le Club, looking at the movie posters on my way back home was often enough to get me in the ticket line. The director or main actors would ring a bell, or a close friend had recommended the title. Sometimes the poster alone would be appealing enough to lure me in. Even today there are still occasions when I make decisions from limited visual information, like when flipping through movie kiosks, TV guides, or a stack of DVDs written in languages I can’t read.

So how can *Mathematica* help? We’ll take a look at the top 250 movies rated on IMDb. Based on their posters and genres, how can one create a program that suggests which movies to see? What is the best way to see the most popular movies in sequence?

May 17, 2013 — Michael Trott, Chief Scientist

Here at Wolfram Research and at Wolfram|Alpha we love mathematics and computations. Our favorite topics are algorithms, followed by formulas and equations. For instance, *Mathematica* can calculate millions of (more precisely, for all practical purposes, infinitely many) integrals, and Wolfram|Alpha knows hundreds of thousands of mathematical formulas (from Euler’s formula and BBP-type formulas for pi to complicated definite integrals containing sin(x)) and plenty of physics formulas (e.g from Poiseuille’s law to the classical mechanics solutions of a point particle in a rectangle to the inverse-distance potential in 4D in hyperspherical coordinates), as well as lesser-known formulas, such as formulas for the shaking frequency of a wet dog, the maximal height of a sandcastle, or the cooking time of a turkey.

Recently we added formulas for a variety of shapes and forms, and the Wolfram|Alpha Blog showed some examples of shapes that were represented through mathematical equations and inequalities. These included fictional character curves:

April 29, 2013 — Piotr Wendykier, Mathematica Algorithm R&D

Professional cameras offer a resolution of 50 megapixels and more. In addition, projects like GigaPan allow one to create gigapixel panoramas with billions of pixels. How can we process these images on a desktop computer with 8 GB of RAM?

One of *Mathematica* 9′s new and exciting features is out-of-core image processing. What does the out-of-core term really mean? It is a way to process very large images that are too big to fit into main memory. Let’s say we have a machine with 8 GB of RAM, and let’s assume that *Mathematica* can use up to 7.2 GB of that memory (the remaining 0.8 GB will be used by the operating system). Freshly started, *Mathematica* 9 on Windows 8 takes up about 200 MB of memory, so the kernel can use about 7 GB of RAM. What is the maximal size of the image that we can load into the kernel (we don’t want to visualize it at this point)? If we assume that the image is in the RGB color space and a single byte encoding, then the following formula gives a maximal width (and height) of an image that can be loaded at once into the memory:

February 14, 2013 — Giulio Alessandrini, Mathematica Algorithm R&D

*Mathematica* 9 has just been released with many new or enhanced capabilities for image processing. You can perform morphological operations, color manipulation, segmentation analysis, feature detection, and more, most of which can be applied to the new `Image3D` object as well.

A byproduct of this whole ecosystem is that now it is easier than ever to use *Mathematica* to create and apply effects to your images.

Two *Mathematica* super functions that can be used to apply transformations directly to an image are `ImageApply`, which is a pixel operator, and `ImageFilter`, which considers the pixel as well as a neighborhood of pixels around it and works as a local filter.

For example, you can remove the blue channel and perform a gamma correction only on the green channel by doing the following: