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).

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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.

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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?

Movies in sequence image

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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:

fictional character curves

fictional character curves

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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:

maxMemoryInBytes0 = 7 1024^3 ; maxWidth0 = Floor[Sqrt[maxMemoryInBytes0/3.0]]

50053

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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.

Defining the new image

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:

myfunction[{r_, g_, b_}] := {r, g^1.5, 0} ImageApply[myfunction, image]

Image with the blue channel removed and a gamma correction only on the green channel

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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.”

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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.

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:

b = FillingTransform[ColorNegate[Binarize[rbc]]]

Using Binarize and FillingTransform to show cell segmentation and hole filling

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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.

John F. Kennedy and John F. Kennedy Jr.

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.

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September 9, 2011 — Jon McLoone, International Business & Strategic Development

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.

Photograph of 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.

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