February 1, 2011 — Daniel Lichtblau, Scientific Information Group

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.

Marlborough Maze

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December 21, 2010 — Jon McLoone, International Business & Strategic Development

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.

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December 7, 2010 — Daniel Lichtblau, Scientific Information Group

I read Jon McLoone’s recent “aMazeing Image Processing in Mathematica” post with some interest.

It showed how to import an image of a maze, and then use image processing functions in Mathematica (some new to Version 8) to draw paths through the maze. What fun! I then observed, to my dismay, that there was no way to determine a “good” path. Frankly, I was disappointed.

I decided that there must be ways to do this in Mathematica. One approach would involve forming a graph. We would have vertices at points where the maze path forks, and we would make weighted edges from approximated distances between these vertices. New functionality in Mathematica supports these graph methods. Unfortunately I am not yet familiar with it.

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November 10, 2010 — Jon McLoone, International Business & Strategic Development

Ever since I wrote the “Doing Spy Stuff with Mathematica” blog post, I have had a feeling that I am being watched. Time to build some office security using Mathematica Home Edition!

First, I am going to make use of an imminent new Mathematica command CurrentImage, which will import a real-time image from a video device. Let’s get some test images using the webcam on my laptop.

Imported real-time test image

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November 3, 2010 — Jon McLoone, International Business & Strategic Development

A little over a mile from the Wolfram Research Europe Ltd. office, where I work, lies Blenheim Palace, which has a rather nice hedge maze. As I was walking around it on the weekend, I remembered a map solving example by Peter Overmann using new image processing features in an upcoming version of Mathematica. I was excited to apply the idea to this real-world example.

Once back at my computer, I started by using Bing Maps to get the aerial photo (data created by Intermap, NAVTEQ, and Getmapping plc).

The maze is meant to depict a cannon with cannon balls below it and flags and trumpets above.

Aerial photo of the maze

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October 27, 2010 — Andrew Moylan, Technical Communication & Strategy

Practically everything I know about British art history would fit in one BBC documentary—the very BBC documentary I watched a little while ago.

I was intrigued to learn about the The Ambassadors, a sixteenth-century painting by Holbein. Among other things, this painting is famous for containing a human skull hidden in plain sight. Can you see it?

The Ambassadors

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September 1, 2010 — Jon McLoone, International Business & Strategic Development

I have a lot to study at the moment, as I learn how to use the technology that’s in our development pipeline. One of the first features I played with was so much fun I thought I would share it with you. You will be able to efficiently and easily texture map over any 3D image.

Texture mapping has all kinds of practical uses for improving visualization, but the first thing that I thought of was setting fire to a plot…

Importing a texture and creating the plot
The resulting textured plot

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September 8, 2009 — Doug McClintic, Commercial Account Executive

Are you a die-hard video gamer? Can you spend hours at a time sacrificing sleep to play your favorite real-time action console game? Or maybe you find yourself captivated by the amazing animation found in movies such as Pixar’s latest release, Up. Whatever your form of diversion, have you ever stopped to wonder what makes 3D games so realistic or how Pixar managed to animate thousands of balloons lifting Carl’s house? We at Wolfram Research have the inside scoop—it’s all about the math and physics.

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June 23, 2009 — Jon McLoone, International Business & Strategic Development

While tidying up after my kids once again, I found myself staring at the toy shown below and thinking of a conversation that I had had with an archaeologist Mathematica user a few days before. He had been interested in image processing of aerial photographs, but it occurred to me that image processing would also allow reconstruction of the musical secrets of this precious artifact that I had just uncovered in the remains of a lost toy civilization.

Well, this should be fun for 5–10 minutes. The toy is a music box, where you crank the handle to turn the drum that has pins on it to pluck the prongs to the left. Can I discover the tune, without having to move the parts?

Music box

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April 24, 2009 — Jon McLoone, International Business & Strategic Development

The “Droste effect” is when images recursively include themselves. The name comes from Droste brand cocoa powder, which was sold in 1904 in a box that showed a nurse carrying the same box which, in turn, showed the nurse carrying the box, and so on. The simplest form is to use a scale and transform on an image to place an exact copy within it, and then repeat. Take a look at this Demonstration using the original Droste box artwork. But much more interesting results can be achieved when you get complex analysis involved. M.C. Escher was the first to popularize applying conformal mapping to images, but with computers we can easily apply the same ideas to photographs, to get results like this:

A photograph conformally mapped in Mathematica

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