## Making Formulas… for Everything—From Pi to the Pink Panther to Sir Isaac Newton

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:

## Gigapixel Images in Mathematica

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:

## Image Effects in Mathematica

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:

## Image Quality Analysis with Mathematica

January 29, 2013 — Wolfram Blog Team

With Mathematica, you can bring new ideas into focus. No one knows that better than Fritz Lebowsky. He’s a senior principal engineer who does image-quality-related algorithm development for STMicroelectronics, a global manufacturer of electronics and semiconductors with advanced image processing technologies.

Thanks to Mathematica‘s advanced programming language and computational power, Lebowsky is seeing major advancements in his image processing development work, with his latest color imaging project set to double performance while reducing cost by half.

About the development, he says, “For the very first time in my research career I could combine several simple non-linear functions/dimensions to overcome some fundamental weaknesses in today’s linear mathematics applied to image processing.”

## How to Count Cells, Annihilate Sailboats, and Warp the Mona Lisa

January 4, 2012 — Shadi Ashnai, Manager, Image Processing

In a recent series of Image Processing with Mathematica workshops held at universities across the United States, we presented Mathematica‘s new image processing functionality and applied it on the spot to attendees’ real-world problems. It was amazing to me to see how rapidly and flexibly Mathematica could be applied to solve complex image processing problems. For example, it might seem like writing a program to automatically count cells in an image would be a master’s research project, but amazingly you can do it with a few lines of Mathematica code.

Below I am using morphological operations and measurement tools to segment and analyze red blood cells in a microscopy image.

Cell segmentation and hole filling can be done with an intensity thresholding using Binarize and FillingTransform:

## Detecting Kinship from a Pair of Images

November 21, 2011 — Matthias Odisio, Mathematica Algorithm R&D

We just attended the International Conference on Image Processing (ICIP) in Brussels and the 14th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) in Toronto. Both events proved to be great occasions to demonstrate how Mathematica can aid research in image processing, from investigation and prototyping to deployment. Last but not least, we seized the opportunity to listen to the experts in the field to extend the functionality of Mathematica in the right direction.

Last year, Ruogu Fang, Kevin D. Tang, Noah Snavely, and Tsuhan Chen received the best paper award at ICIP for their study of kinship detection from pairs of images. I decided to build a detector by following their proposed framework with Mathematica.

A lot has been said and studied about our human ability to recognize faces; computer programs can be quite good at it, too. Similarly, when looking at faces, we may display a canny ability to detect an ancestry relationship, or kinship.

In these pictures, is the person on the left the father of the person on the right? Yes, and we can figure it out with Mathematica.

## Building a Microscopy Application in Mathematica

September 9, 2011 — Jon McLoone, Director, Technical Communication & Strategy

As a change from my usual recreational content, today I thought I would describe a real Mathematica application that I wrote. The project came from my most important Mathematica user—not because she spends a lot of money with Wolfram Research, but because I am married to her!

Her company, Particle Therapeutics, works on needle-free injection devices that fire powdered drug particles into the skin on a supersonic gas shock wave. She was trying to analyze the penetration characteristics on a test medium by photographing thin slices of a target under a microscope and measuring the locations of the particles.

The problem was that her expensive image processing software was doing a poor job of identifying overlapping particles and gave her no manual override for its mistakes.

Faced with the alternative of holding rulers up to her screen and recording each value by hand, I promised that I could do better in Mathematica, with the added advantage that now her image processing tool would be integrated into her analysis code to go from image file to report document in a single workflow.

## Mission Mathematica: Making a Photo Booth App in Three Steps

June 23, 2011 — Yu-Sung Chang, Technical Communication & Strategy

Creating an interactive app could be a complex and painstaking task. Not with Mathematica. Here I will present how I created a photo booth program in three easy steps—mostly during my lunch breaks.

Step One: Architecture

The application will have four main stages. Stage one: We show live webcam images with different image effects applied (possibly multiple pages of them) as a preview, and let the user choose one. Stage two: The chosen image takes up the window, waiting for the user to click a button. Stage three: Count down. Stage four: Capture an image, apply the effect, and add it in a film strip. Repeat.

## Retreat from Blenheim

February 1, 2011 — Daniel Lichtblau, Symbolic Algorithms Developer, Algorithms R&D

When last seen in the whereabouts of the Marlborough Maze, I was slinking off stage left, having been upstaged by Jon McCloone and his mix of image processing and graph theory alchemy. In a comment on my post, Jaebum Jung showed similar methods.

Me, I only wanted to compute a bunch of distances from the entrance, then walk the maze. But I was not at that time able to show which was the shortest path, or even to prune off the dead ends. I’m over that lapse now. In this post I will provide brief Mathematica code to take the grid of maze pathway distances that I computed, and get the hopeless paths to melt away. Technically this is referred to as a retraction—not in the sense of an apology, but, rather, topology.

## The Battle of the Marlborough Maze at Blenheim Palace Continues

December 21, 2010 — Jon McLoone, Director, Technical Communication & Strategy

Regular readers of the Wolfram Blog will have seen that the item that I wrote on solving mazes using morphological image processing was thoroughly beaten by the much smarter and better read, Daniel Lichtblau from our Scientific Information Group in his post “Navigating the Blenheim Maze”.

Always up for a challenge (and feeling a little guilty about the rather hacky and lazy way I tried to deal with loops and multiple paths the first time), I am back for another go.

My first approach with any new problem is to think about the nearest available Mathematica command. In the new Mathematica 8 features is a graph theory command FindShortestPath. That certainly sounds promising.

Mixing image processing and graph theory may sound complicated, but one of the central strengths of Mathematica‘s integrated all-in-one design is that different functionality works together, and in this case it proves to be quite easy.