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A process to find and extract data-points from graphs in pdf files
Ever since I discovered that it’s sometimes possible to extract the x/y values of the points/circles/diamonds appearing in a graph, within a pdf, I have been trying to automate the process.
Within a pdf there are two ways of encoding an image, such as the one below. The information can be specified using a graphics image format (e.g., jpeg, png, or svg), or it can be specified using a sequence of pdf’s internal virtual machine instructions.
After spotting an interesting graph containing data points, when reading a paper, the quickest way to find out whether the image is embedded in the pdf as an image file (the most common case) is to run pdfcpu (using the options extract -m image). If the graph is not contained in the image files extracted by pdfcpu, it may have been created using internal pdf commands (or be a format not yet support by pdfcpu).
Until recently, finding the sequence of internal pdf instructions used to visualise a particular graph was a tedious process. A few months ago, I discovered the tool pdfsyntax, which has an option to convert the pdf internals into a html page containing links between the various components (making it easy to go to a particular page and view the contents). However, pdfsyntax is still new, i.e., it regularly fails to convert a pdf file.
As distributed, pdf files are compressed. They can be converted to readable form using the command qpdf –stream-data=uncompress (images remain in their respective binary format). To locate the instructions that generate a graph, I search for a sequence of 3-4 characters appearing close to the graph in the displayed text (it is difficult to predict how words will be split for layout purposes, within a pdf). The instructions that generate the graph may appear later in the uncompressed file, with a named reference to these instructions appearing around this text (i.e., a pdf function call). LLM’s are great at describing the behavior of sequences of pdf instructions.
Why not grep uncompressed pdf files to find those containing the instructions used to generate graphs?
Surprisingly, apps that produce pdf files use a myriad of different instruction sequences to draw circles, diamonds, pluses, etc. While there is a pdf instruction to draw a circle, the most common technique uses four Bézier curves to draw each quadrant of a circle; a colored circle might be drawn by filling a specified area with a chosen color. The plus (+) symbol is sometimes drawn as a vertical line followed by a horizontal line (or the other order), and sometimes all the vertical lines are drawn followed by all the horizontal lines. Diamonds are created using four angled lines.
Fewer combinations of instructions are used to draw the values associated with the axis ticks, e.g., 10, 20, 30, etc.
The output from my script that searches pdf files for possible extractable data lists the line numbers of possible data points and possible tick labels, along with the totals for each. A graph will usually contain many points and 10+ labels. Lower totals usually suggest incidental matches.
If an appropriate instruction sequence is found, it is copied to a file, and a bespoke awk script (usually an edited version of a previous script) extracts the numeric values within the reference frame of the graph axis bounds. This extraction process first calculates the x/y coordinates of the center of the circle/diamond/plus, in the pdf frame, then calculates the x/y coordinates of the axis tick marks, in the pdf frame, then maps the x/y data points to the axis frame.
I’m not expecting the extraction of numeric values to have any degree of automation anytime soon. But then, this problem would make a great challenge for LLM coding apps…
When a graph is specified using an image format, WebPlotDigitizer is the extraction tool of choice.
My 2cents on the design of the contract language in Ethereum
My previous post on Ethereum contracts got me thinking about how Ethereum should be going about creating a language and virtual machine for the contracts aspect of their cryptocurrency.
I would base the contract development gui on Scratch. Contract development will involve business people and having been extensively field tested on children Scratch stands some chance of being usable for business types.
For the language itself I would find a language already being used for contract related programming and simply adopt it.
At the moment the internal specification of contracts is visible for all to see. I expect a lot of people will be unwilling to share contract information with anybody outside of those they are dealing with. The Ethereum Virtual Machine needs to include opcodes that perform Homomorphic encryption, i.e., operations on encrypted values producing a result that is the encrypted version of the result from performing the same operation on the unencrypted values. Homomorphic encryption operations would allow writers of contracts that keep sensitive numeric values secret, they get to decide who gets a copy of thee dencryption keys needed to see the plain-text result.
The only way I see of overcoming the denial-of-service attack outlined in my previous post is to require that the miner who receives payment for executing a contract prove that they did the work of executing the contract by including program values existing at various randomly chosen points of contract execution.
Christmas books for 2009
I thought it would be useful to list the books that gripped me one way or another this year (and may be last year since I don’t usually track such things closely); perhaps they will give you some ideas to add to your Christmas present wish list (please make your own suggestions in the Comments). Most of the books were published a few years ago, I maintain piles of books ordered by when I plan to read them and books migrate between piles until eventually read. Looking at the list I don’t seem to have read many good books this year, perhaps I am spending too much time reading blogs.
These books contain plenty of facts backed up by numbers and an analytic approach and are ordered by physical size.
The New Science of Strong Materials by J. E. Gordon. Ideal for train journeys since it is a small book that can be read in small chunks and is not too taxing. Offers lots of insight into those properties of various materials that are needed to build things (‘new’ here means postwar).
Europe at War 1939-1945 by Norman Davies. A fascinating analysis of the war from a numbers perspective. It is hard to escape the conclusion that in the grand scheme of things us plucky Brits made a rather small contribution, although subsequent Hollywood output has suggested otherwise. Also a contender for a train book.
Japanese English language and culture contact by James Stanlaw. If you are into Japanese culture you will love this, otherwise avoid.
Evolutionary Dynamics by Martin A. Nowak. For the more mathematical folk and plenty of thought power needed. Some very powerful general results from simple processes.
Analytic Combinatorics by Philippe Flajolet and Robert Sedgewick. Probably the toughest mathematical book I have kept at (yet to get close to the end) in a few years. If number sequences fascinate you then give it a try (a pdf is available).
Probability and Computing by Michael Mitzenmacher and Eli Upfal. For the more mathematical folk and plenty of thought power needed. Don’t let the density of Theorems put you off, the approach is broad brush. Plenty of interesting results with applications to solving problems using algorithms containing a randomizing component.
Network Algorithmics by George Varghese. A real hackers book. Not so much a book about algorithms used to solve networking problems but a book about making engineering trade-offs and using every ounce of computing functionality to solve problems having severe resource and real-time constraints.
Virtual Machines by James E. Smith and Ravi Nair. Everything you every wanted to know about virtual machines and more.
Biological Psychology by James W. Kalat. This might be a coffee table book for scientists. Great illustrations, concise explanations, the nuts and bolts of how our bodies runs at the protein/DNA level.
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