05.24.11

Gemini version available ♊︎

Software is Mathematics

Posted in Patents at 4:13 pm by Dr. Roy Schestowitz

Block diagram
Depiction of the framework for detection and classification of 3-D data such as faces or internal organs, as well as benchmarking

Summary: Personal take on why software is just symbiosis of maths

This post is a concise summary of something I have been working on (source code will be uploaded at a later date when I tidy everything up). The figure at the top shows a breakdown of our existing framework, which basically depicts a program as a set of black boxes. Each box merely performs mathematical operations on volumetric matrices. It’s maths. It can also be specified most precisely using equations (no need for explanation using code or pseudo-code). For the sake of simplicity, the block diagram contains only core components that are used irrespective of the approach tested. The file loaders, for example, are shown separately. They work very well and can elegantly load datasets based on a data selector. With the exception of test sets that are small (remnants of debugging), there are 6 families of data, some grouped in pairs, some grouped by training/target, some our lab’s data in isolation, others for FRGC data from NIST. There are also correct and incorrect matches in isolation. These simplify the plotting of ROC curves in a largely streamlined fashion. The goal is the program is to test new metrics that can be used to analyse anything elastic such as tissue. It has uses in cardiac analysis, brains, and even faces (I have dealt with each of these data types). For large quantiles of 3-D data, about 70 GB of face data gets used.

The nose-finding part may as well be treated as a component that provides orientation o a form of segmentation (it can be a face or even an internal organ which we wish to model and perform binary diagnosis on). Depending on the datasets, different methods are used. Commonly, FRGC data is better off interpreted by finding nearest point, excepting noise. For the lab’s data, it is preferable to choose the nearest point within a specified region (usually around the centre, no weighting/scoring based on location although that too would work). This can also be done using ICP, as described later (settings inherited from another box/module) or a Viola-Jones approach with face templates for training, although it is only partly implemented so far. Sphere intersection with plane, as per Mian et al. (with separate slider for radius), is another existing option, but it does not appear to outperform the simpler methods, which work most of the time given some reasonable boundaries (e.g. boundaries to dodge the hair region).

Having identified the tip of the nose correctly, we are cropping out what is left for rigid areas to be isolated. It is quite customisable. Various separation methods and boundary types like circle, ellipsoid, and rectangle have been tested, where circle is the most commonly used one that works in conjunction with binary masks. These come with many sliders and use measurements in X and Y to estimate real physical distances and then factorise pixel-space units, accordingly. There is also a slider for further manual tweaking. And still, it’s all maths.

There are some other bits of operation that are worth mentioning; left out from the diagram in order to reduce clutter are smoothers, hole removers, outlier eliminators, and rounding up of values, all of which are optional and very much depend on the data at hand and how it ought to be treated. For instance, FRGC data hardly requires any smoothing. Lab data has offsets that need to be handled systematically depending on the image number. In fact, both datasets do need a lot of branching/forking in the code as their handling and even their size varies (the program is built to handle any image side with any aspect ratio, but for sub-regions to be defined it uses absolute and not relative coordinate inputs).

Then we come to the key part, which actually does more to contribute toward similarity measures. ICP becomes very important in case the initial alignment of the noses is deemed incorrect or the faces are tilted. In practice, assuming the faces are forward-looking and bend neither to the sides or top/bottom, ICP is not supposed to change much. The methods already available are Mian’s early ICP method, Mian’s most recent ICP method, Raviv’s ICP implementation from 2008, and Raviv/Rosman ICP implementation from recent months or years. The program optionally applies translation and optionally it applies the rotation too. In many cases this does not seem necessary as ICP hardly modifies anything substantial.

The model part is not included in the diagram as there are many different things are can be done with a model. PCA, model-building, model assessment, file loaders for models (about 2 gigabytes for some), in addition to more basic measures on which assessment is applied, are basically all sorts of comparators which yield one value for each pair, then proceeding to the plotting of ROC curves (mostly automated following experimental design).

All the above is just mathematics. It can all be described using equations. To patent such stuff would be to claim a monopoly on equations, which means the monopoly covers a wide range (infinite even) of implementations. How can anybody defend the argument that software is not maths? Or that “innovative” software is somehow the exception? If many equations are already patented, how is one supposed to code safely? How can existing methods be enhanced without a violation?

Share in other sites/networks: These icons link to social bookmarking sites where readers can share and discover new web pages.
  • Reddit
  • email

Decor ᶃ Gemini Space

Below is a Web proxy. We recommend getting a Gemini client/browser.

Black/white/grey bullet button This post is also available in Gemini over at this address (requires a Gemini client/browser to open).

Decor ✐ Cross-references

Black/white/grey bullet button Pages that cross-reference this one, if any exist, are listed below or will be listed below over time.

Decor ▢ Respond and Discuss

Black/white/grey bullet button If you liked this post, consider subscribing to the RSS feed or join us now at the IRC channels.

2 Comments

  1. Needs Sunlight said,

    May 25, 2011 at 4:42 am

    Gravatar

    “It can all be described using equations.”

    That is why the expression of these ideas is governed by copyright, rather than allowing a blanket monopoly on using the general idea.

    Dr. Roy Schestowitz Reply:

    It’s more like an explanation or formulation than an observation. Ideas are sometimes just opinions and are relative.

    Can one patent Newton’s Laws to get a monopoly on software/games where gravity and force impacts are simulated (e.g. Angry Birds)? It would be like getting a monopoly on Mother Nature.

DecorWhat Else is New


  1. [Meme] [Teaser] Oligarchs-Controlled Patent Offices With Media Connections That Cover Up Corruption

    As we shall see later today, the ‘underworld’ in Bulgaria played a role or pulled the strings of politically-appointed administrators who guarded Benoît Battistelli‘s liberticidal regime at the EPO



  2. IRC Proceedings: Sunday, October 24, 2021

    IRC logs for Sunday, October 24, 2021



  3. Links 25/10/2021: EasyOS 3.1 and Bareflank 3.0

    Links for the day



  4. The Demolition of the EPO Was Made Possible With Assistance From Countries That Barely Have European Patents

    The legal basis of today's EPO has been crushed; a lot of this was made possible by countries with barely any stakes in the outcome



  5. The EPO’s Overseer/Overseen Collusion — Part XXII: The Balkan League - North Macedonia and Albania

    We continue to look at Benoît Battistelli‘s enablers at the EPO



  6. Links 24/10/2021: GPS Daemon (GPSD) Bug and Lots of Openwashing

    Links for the day



  7. Links 24/10/2021: XWayland 21.1.3 and Ubuntu Linux 22.04 LTS Daily Build

    Links for the day



  8. IRC Proceedings: Saturday, October 23, 2021

    IRC logs for Saturday, October 23, 2021



  9. Links 24/10/2021: Ceph Boss Sage Weil Resigns and Many GPL Enforcement Stories

    Links for the day



  10. GAFAM-Funded NPR Reports That Facebook Let Millions of People Like Trump Flout the So-called Rules. Not Just “a Few”.

    Guest post by Ryan, reprinted with permission



  11. Some Memes About What Croatia Means to the European Patent Office

    Before we proceed to other countries in the region, let’s not forget or let’s immortalise the role played by Croatia in the EPO (memes are memorable)



  12. Gangster Culture in the EPO

    The EPO‘s Administrative Council was gamed by a gangster from Croatia; today we start the segment of the series which deals with the Balkan region



  13. The EPO’s Overseer/Overseen Collusion — Part XXI: The Balkan League – The Doyen and His “Protégée”

    The EPO‘s circle of corruption in the Balkan region will be the focus of today’s (and upcoming) coverage, showing some of the controversial enablers of Benoît Battistelli and António Campinos, two deeply corrupt French officials who rapidly drive the Office into the ground for personal gain (at Europe’s expense!)



  14. Links 23/10/2021: FreeBSD 12.3 Beta, Wine 6.20, and NuTyX 21.10.0

    Links for the day



  15. IRC Proceedings: Friday, October 22, 2021

    IRC logs for Friday, October 22, 2021



  16. [Meme] [Teaser] Crime Express

    The series about Battistelli's "Strike Regulations" (20 parts thus far) culminates as the next station is the Balkan region



  17. Links 23/10/2021: Star Labs/StarLite, Ventoy 1.0.56

    Links for the day



  18. Gemini on Sourcehut and Further Expansion of Gemini Space

    Gemini protocol is becoming a widely adopted de facto standard for many who want to de-clutter the Internet by moving away from the World Wide Web and HTML (nowadays plagued by JavaScript, CSS, and many bloated frameworks that spy)



  19. Unlawful Regimes Even Hungary and Poland Would Envy

    There’s plenty of news reports about Polish and Hungarian heads of states violating human rights, but never can one find criticism of the EPO’s management doing the same (the mainstream avoids this subject altogether); today we examine how that area of Europe voted on the illegal "Strike Regulations" of Benoît Battistelli



  20. The EPO’s Overseer/Overseen Collusion — Part XX: The Visegrád Group

    The EPO‘s unlawful “Strike Regulations” (which helped Benoît Battistelli and António Campinos illegally crush or repress EPO staff) were supported by only one among 4 Visegrád delegates



  21. [Meme] IBM Has Paid ZDNet to Troll the Community

    Over the past few weeks ZDNet has constantly published courses with the word "master" in their headlines (we caught several examples; a few are shown above); years ago this was common, also in relation to IBM itself; clearly IBM thinks that the word is racially sensitive and offensive only when it's not IBM using the word and nowadays IBM pays ZDNet — sometimes proxying through the Linux Foundation — to relay this self-contradictory message whose objective is to shame programmers, Free software communities etc. (through guilt they can leverage more power and resort to projection tactics, sometimes outright slander which distracts)



  22. [Meme] ILO Designed to Fail: EPO Presidents Cannot be Held Accountable If ILOAT Takes Almost a Decade to Issue a Simple Ruling

    The recent ILOAT ruling (a trivial no-brainer) inadvertently reminds one of the severe weaknesses of ILOAT; what good is a system of accountability that issues rulings on decisions that are barely relevant anymore (or too late to correct)?



  23. Links 22/10/2021: Trump's AGPL Violations and Chrome 95 Released

    Links for the day



  24. [Meme] How Corporate Monopolies Demonise Critics of Their Technically and Legally Problematic 'Products'

    When the technical substance of some criticism stands (defensible based upon evidence), and is increasingly difficult to refute based on facts, make up some fictional issue — a straw man argument — and then respond to that phony issue based on no facts at all



  25. Links 22/10/2021: Global Encryption Day

    Links for the day



  26. [Meme] Speaking the Same Language

    Language inside the EPO is misleading. Francophones Benoît Battistelli and António Campinos casually misuse the word “social”.



  27. António Campinos Thinks Salary Reductions Months Before He Leaves is “Exceptional Social Gesture”

    Just as Benoît Battistelli had a profound misunderstanding of the concept of “social democracy” his mate seems to completely misunderstand what a “social gesture” is (should have asked his father)



  28. IRC Proceedings: Thursday, October 21, 2021

    IRC logs for Thursday, October 21, 2021



  29. Links 21/10/2021: MX Linux 21 and Git Contributors’ Summit in a Nutshell

    Links for the day



  30. [Meme] [Teaser] Miguel de Icaza on CEO of Microsoft GitHub

    Our ongoing series, which is very long, will shed much-needed light on GitHub and its goals (the dark side is a lot darker than people care to realise)


RSS 64x64RSS Feed: subscribe to the RSS feed for regular updates

Home iconSite Wiki: You can improve this site by helping the extension of the site's content

Home iconSite Home: Background about the site and some key features in the front page

Chat iconIRC Channel: Come and chat with us in real time

Recent Posts