Natural Image Statistics

I’m doing some simple exploration of image statistics on a large database of natural images. The first thing that I tried was computing the histogram of neighboring image pixel intensity differences. Here is the graph for that using a log y axis, for a few pixel separations.

Pixel differences histogramIt is clear that large differences occur much more rarely and that the most probable pixel to pixel spatial change in intensity is zero. However the tails are heavy, so it is nothing like a Gaussian distribution. The adjacent pixel intensity difference log probabilities were fairly well fitted by a function that goes like -|kx|^{0.5} , and the pixels further apart require a smaller exponent.
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Check out the new Tree Crafter Web Site

Tree CrafterI created a graphic design app for the iPad last year called Tree Crafter that lets you create tree inspired organic vector art and animations. It is fun to play with and quite relaxing. Also you can create great designs for web graphics or for merchandise with relative ease.

Recently I built a new web site for this app: http://treecrafter.com

If you have an iPad you should give it a go and let me know what you think. I am very keen to get it reviewed, so if you are an app reviewer, I can give you a promo code if you would like to write about it.

Calculating Engine Accepted at Maker Faire

Maker FaireI received the good news that my Relay Calculating Engine has been accepted for showing at the Maker Faire in San Francisco in May. I’m looking forward to taking it down there and showing it to interested people.

Make Magazine also interviewed me about this project and plan to feature the work too. I’m excited to see what they write about it.

My main concern is to finish it and get it all working in time for May. This should not be a problem since I currently have the luxury to be able to work full time on the project and at present, I am about 90% complete.

I hope that you can come along and check it out. I will also be showing some of the other projects on which I have been working. I’ll also be attending the Seattle Mini Maker Faire, but not showing anything off there.

Analyzing the Market – Part 3

BitcoinThis is part 3 of my series of posts on the statistics of financial markets. Part 1 is here.

In previous posts, I have found that working in log prices makes sense and that the double exponential distribution is a good fit to price change data. In this post, I will look at correlations over time in price changes.

Let’s ask a simple question: Does yesterday’s price change predict today’s price change? Continue reading

Analyzing the Market – Part 2

BitcoinThis is part 2 of my series of posts on the statistics of financial markets. Part 1 is here.

I have established that a double exponential distribution fits price movements when they are converted to log prices, at least for bitcoin, Apple, and Dell. (Actually I have checked it on a few other NASDAQ stocks too.)

Once we have a statistical model, we can generate some data to see if it produces results that look like the actual price graph. Below you can see the real 2 month bitcoin price graph, together with two graphs that were obtained by using a model based on the Continue reading

Analyzing the Market – Part 1

BitcoinThis series of blog posts is intended to document some mathematical analysis that I have been doing on the bitcoin price graph and on price histories of securities in the stock market. The purpose is to understand something about the statistics of these price movements, and to learn about the behavior of the stock market in general.

One thing that is useful about bitcoin is that trading is never stopped. Because everything runs 24 hours 7 days per week, there are no artifacts to do with starting and stopping trading on specific exchanges and transitioning between financial Continue reading

Bitcoin and Credit Cards: Scams and Money Laundering

chinabitcoinBitcoin has been facing trouble this week due to a series of crackdowns by the Chinese government. First, the People’s Bank of China stated that bitcoins did not qualify as currency and barred its banks and payment systems from being involved. Later, this ruling was extended to third party payment processors, meaning that bitcoin could only be exchanged in private transactions. The initial justification given was that people must be protected from speculation and wild changes in price – but the chilling effect has led to bitcoin losing half of its value. Presumably Chinese investors must now return to property speculation.

Negative reactions from government agencies, law enforcement, and established financial businesses are to be expected because they see digital currencies as a threat to their existing systems of checks and controls over financial transactions, their ability to regulate the market, to implement monetary policy, to protect consumers, and to oppose organized
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Bitcoin – How high can it go?

BitcoinWith all the recent interest in Bitcoin and crypto-currencies, many people have been moving money into the Bitcoin system and stories abound of people making a rapid fortune, or finding that forgotten wallets from the early days now contain life-changing amounts of money. This week has seen US Congress hearing information about opportunities and threats from digital peer-to-peer currencies. In the news, hopeful people have been quoted saying that they expect to be millionaires by next year after buying $100 worth of Bitcoin.

In this article, I examine the possible investment upside of virtual currencies, and Bitcoin in particular. I then discuss some of the threats that investors and adopters must watch out Continue reading