Bonum Certa Men Certa

Software is Mathematics

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?

Comments

Recent Techrights' Posts

Microsoft 'Studies' Again? Leon Musolff is Writing Papers With Microsoft.
Even if one can see/find a link to "the study" (in the Bezos-controlled publication), most people won't look any further and just take everything at face value.
RMS is Done at KCL, Next Stop is Oxford
The message of RMS has long resonated well in India
US Government Already Bailing Out OpenAI/Microsoft With "Contracts", As Usual, Back Doors You Cannot Remove Becoming 'a Step Closer' on New PCs (Unless Everyone Acts ASAP)
The next "logical" step towards digital prisons
Towards GNU World Domination
The FSF led by Geoffrey S. Knauth with his friend Richard Stallman in the FSF's Board [...] Let's encourage people to adopt GNU/Linux. There has never been a better time.
GNOME, Microsoft, and GitHub: The Lack of Reporting on Abusive Colleagues Contributed to Profound Media Vacuum (or Blackout), Now Resorting to SLAPPs
This lack of morality/courage has helped enable further abuse, lining up more victims
 
Links 23/04/2025: Tesla Profits Plunge 71%, Intel Ready to Lay Off 20% of Staff, Microsoft and IBM Layoffs
Links for the day
Microsoft's Most Profound Issue is That People Moved to 'Mobile' and "App Stores" (Microsoft's Presence There is Negligible)
Expect a wild ride for Microsoft this year
Google News is Amplifying FUD and Lies About Linux (and OpenSSH/SSH) by Promoting Slopfarms With Machine-Generated FUD and Slop Images
Google should know better
Gemini Links 23/04/2025: Librarians, Anubis, and Refactoring a Gemini Capsule
Links for the day
Over at Tux Machines...
GNU/Linux news for the past day
IRC Proceedings: Tuesday, April 22, 2025
IRC logs for Tuesday, April 22, 2025
Links 22/04/2025: Ending DEI Policies at Adobe, FTC Sues Uber
Links for the day
Microsoft Devises PR Stunts to Distract From Impending Mass Layoffs and Likely Bad Results Preceding Those Mass Layoffs
A "voluntary exit plan"
Gemini Links 22/04/2025: Deaths, HamsterCMS, and More
Links for the day
Links 22/04/2025: FTC v. Meta Trial and Google Remedies
Links for the day
In Turkey, Windows Down Rapidly While GNU/Linux Grows
Although Turkey is in NATO (but not the EU), it cannot quite trust computer systems controlled by the United States
Richard Stallman Has Updated His Article on Why "Free Software Is Even More Important Now"
Richard Stallman is about to give a talk here in the UK in a few hours
Microsoft Already Attacks the BSDs as Well (the E.E.E. Way, as Usual)
Bearers of bad news
The Open Source Initiative (OSI) is in Trouble, May Soon be Out of Business
Openwashing needs to end
Microsoft's Debt Grew Over 6 Billion Dollars in the Last Reporting Quarter (Before Inauguration), Expect Worse Next Week When 'Results' Are Disclosed and Mass Layoffs Resume
Microsoft is bleeding. It does not want people to notice.
Over at Tux Machines...
GNU/Linux news for the past day
IRC Proceedings: Monday, April 21, 2025
IRC logs for Monday, April 21, 2025
Richard Stallman Gives Public Talk in London in 7 Hours (Need to Register as Venue Limited to 150 Seats), Public Announcements Begin to Appear
These are not announced weeks or months in advance
Gemini Links 21/04/2025: Remembering Pope Francis, Crystal Simulation
Links for the day
Doing Microsoft's Job. On IBM's Payroll.
today's Red Hat cannot recognise threats even after a head-on collision
Google News is Rewarding Slopfarms, Not Journalism
Don't read junk from chatbots
Teaching GAFAM in Schools is Like Teaching Children to Smoke Tobacco
So suggests an FSF presentation
Richard Stallman, Whose Site is Trusted by Greater Manchester, Has Come to the United Kingdom
He doesn't suck up to the Crown, so he'll never be "knighted"
On Desktops/Laptops in Singapore Does a Fifth of Users Run GNU/Linux?
Probably not, but it's growing fast there
Links 21/04/2025: Fake Ceasefire and Software Patents (Fake Patents) Thrown Out
Links for the day
Companies With Fake Values and a Fake Economic/Financial State (Phony Valuations)
It'll all go up in smoke, eventually
Links 21/04/2025: Microsoft LLM Slop (Plagiarism) Going Out of Control, CT Scans' Cancer Problems Was Underrated
Links for the day
4 Years Ago Freenode Crumbled From Within
there are still hundreds of thousands of users online at any given time
GNOME Has a Long History (Over a Decade) Misusing the Code of Conduct (CoC) to Censor (Cull) Legitimate Technical Criticism
This has nothing to do with manners, it's about control (by cover-up)
Microsoft Has Tainted GNOME, Which Has Key People Acting as a SLAPP Front Against Techrights (Trying to Censor the Site by Extortion and Many Threats)
One common denominator (other than Microsoft salaries) is GNOME, which was led by an actual professional crank until she quit so suddenly months ago
Homeland of Linux Kernel Turning to GNU/Linux?
Adoption of Vista 11 has been relatively low
According to StatCounter, This is What Linux Adoption Looks Like (Based on Web Requests Visible to StatCounter)
How much worse will it get for Microsoft?
Gemini Capsules Still Outsourcing to Certificate Authority Let's Encrypt Now Measured at Less Than 10 (or Less Than 0.3%)
In Geminispace, Let's Encrypt is not commonly used
Twisting Microsoft's Failure (Transmitting Malware) as "SSH Backdoors" and a Linux Problem
Somehow we almost always find that those FUD pieces about "Linux" are based on obvious falsehoods
Vista 11 Has Burned OEMs and Some Move to GNU/Linux
When people can finally avoid Windows (there's no reason to attach it to new PCs) there will be a lot more GNU/Linux users out there
Remember That Microsoft Mass Layoffs Are Imminent Because Its 'Empire' is Falling Apart
European politicians take a long, hard look a Free software
Richard Stallman in the UK This Week, Scheduled to Give Two Public Talks (London and Oxford)
Those talks do not cover the same topics
Gemini Links 21/04/2025: April, Autism, and ASN
Links for the day
Over at Tux Machines...
GNU/Linux news for the past day
IRC Proceedings: Sunday, April 20, 2025
IRC logs for Sunday, April 20, 2025