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

GNU/Linux is Replacing Microsoft Windows. But We Need to Eradicate Microsoft, It's a Hub of Crime.
I have been writing about Microsoft since the 1990s when I was in school
Microsoft Staff Harassing Women, Strangling Women, Telling Women to Kill Themselves and Worse? Not a Problem!
Two women have left Brett Wilson LLP
 
Happy Independence Day to Our American Readers
Maybe tomorrow will be a good opportunity to explain to American people - in terms of concepts, not brands - which tools respect their independence
Slopwatch: Linux Journal, Linuxsecurity, and Google News Getting Even Worse (More Slopfarms Added Which Attack Linux With Bruce-Force SPAM)
Google News is part of the same problem
Links 03/07/2025: More Cuts and Cancellations at Microsoft Revealed
Links for the day
Gemini Links 03/07/2025: Favourite Child and Launching WikiGem
Links for the day
Mystery Surrounding the PCLinuxOS Sites and PCLinuxOS Magazine
Let's hope this isn't something major
People and Companies Do Learn Some Lessons From Their Mistakes (Stubborn Ones Don't)
Brett Wilson LLP is an example of one that would rather drown in mistakes
Links 03/07/2025: 'Hey Hi' Slop Ridiculed Some More and Microsoft's Layoffs Tally for 2025 Reaches About 29,000 in Just 6 Months (Almost 5,000 Per Month)
Links for the day
The Slopfarms Are Losing the Plot (and Google is Propping Up Rogue Sites)
Google is part of the attack on the Web, on information, and on technology
New BetaNews Realises There's No Potential or Future in Slopfarms, Prior Editor Wayne Williams is Back
They realise that slop (so-called "AI") cannot replace humans
Claims That Microsoft Looks for Staff That Works More and Gets Paid Less (or Can Only Code by Grabbing Other People's Code, Under the Guise of "AI")
People can form their own opinion
Richard Stallman Was Right About Reasons Not to Use Microsoft
last updated 2017
Over at Tux Machines...
GNU/Linux news for the past day
IRC Proceedings: Wednesday, July 02, 2025
IRC logs for Wednesday, July 02, 2025
Gemini Links 03/07/2025: No to Cloudflare and Small Web July
Links for the day
Links 02/07/2025: Deep Microsoft Cuts, Macron Speaks to Putin
Links for the day
Confirmed: Microsoft Shutdowns Today, Not Only Mass Layoffs
"The Initiative is the only studio closure planned today, although some other teams have seen cuts of varying degrees."
Microsoft Windows Nosedives in Switzerland While GNU/Linux Leaps Above 6%
sooner or later they might have to make the move anyway
Anxiety at Microsoft: Many Workers (Maybe Over 10,000) Still Don't Know They're Being Laid Off Just Before US Independence Day
"Has anyone gotten the notification yet?"
Microsoft "Declined to Say How Many People Would be Laid Off," According to Associated Press
Some other prominent publications said they reached out for comment from Microsoft and received none
The X War is Over and the "Wayland People" Lost
People will gravitate towards what works for them
20 Years Since My Thesis
It's still online
GNU/Linux is Replacing Windows in Laptops/Desktops
The world will move on while Windows and Microsoft shrink
Now Comes the Expected Webspam, Framing Microsoft Layoffs as "Hey Hi" Success Story (False Marketing That's Piggybacking the Layoffs)
falsely marketed as "intelligence"
Hungary: Microsoft Windows Sinks to 17% "Market Share"
In many nations in Europe it seems like the era of Windows is coming to an end
Microsoft Media Operatives and Bill Epsteingate-Funded Sites Said Microsoft Lays Off 9,000, But Other Sites Say More (Including 2,300 in Redmond Alone)
We might never know the real number/s (Microsoft will keep the cards close to its chest) until there are leakers or unless there are whistleblowers with hard proof
Microsoft Layoffs in Spain, Portugal Record for GNU/Linux
in Portugal we see GNU/Linux at record levels
GNU/Linux Reaches All-Time High in the United States of America
Windows is trending down
Yes, Microsoft is Again Using Its Favourite Liars (Stenographers) to Seed Fake Layoff Numbers, Much Lower Than What's Really Happening
It is Jordan Novet again, just as we predicted
Will Microsoft Once Again Choose Its Favourite Liar to Spread Lies About Today's Layoffs, Quickly to be Replicated and Spread by Slopfarms?
What lies is Microsoft briefing its media moles to tell today?
"OSS Fetishism" Wins After Ferenc Zsolt Szabó Ousted (Microsoft Mole From Capgemini)
Many people said 2025 would be the "year of Linux on the desktop"
There is Nothing That LLMs Can Offer Honest People
LLMs are a passing fad; they're expensive and offer poor "value" for energy; they usually offer no value at all unless you are a cheater, spammer, and liar
What statCounter Shows Today Helps Explain Microsoft's Helplessness, Mass Layoffs
Since many US journalists are already away on holiday almost nobody will dare ask the difficult questions or give a voice to whistleblowers
Microsoft Gets the Chop in South America
The notion of digital sovereignty gained a lot of popularity
Europe Has an 'Exit'
Let's see what happens the rest of this year
El Presidente Talks, Canada Walks (Away From Windows)
GNU/Linux rising
Cities in France and Germany Move to GNU/Linux and statCounter Detects Big Differences
Will governments lead by example?
Microsoft Lost Its Foothold in Africa
How many of these are "old" Windows machines converted to GNU/Linux? Probably a lot.
Led by Europe, GNU/Linux Makes Big Gains This Month
statCounter started showing new/fresh stats
Links 02/07/2025: Massive Microsoft Layoffs About to Commence, "Tesla's Robotaxi Program Is Failing"
Links for the day
Why the Microsoft People Who Started SLAPPs Against Techrights Could Very Well be Sent Back to Prison
White-collar crime is also a crime
The Company Run by Former (and Last Proper) Red Hat CEO, Promoting Microsoft Mono, Faces Shock as Senior Partner Jailed for 33 Sexual Offenses Including Pedophilia
"As reported by The Oxford Mail in April 2025, the offenses include rape, sexual assault, engaging in non-penetrative activity with a child, and more."
Microsoft Lost 29% of Windows Users, Based on Microsoft, Now Come Massive Layoffs
Microsoft collapse is today
Slopwatch: Google Serves to People Linux Slop and Linux FUD (Made by Bots)
"Slopwatch" finds it difficult to ignore Google's role in encouraging LLM slop
Over at Tux Machines...
GNU/Linux news for the past day
IRC Proceedings: Tuesday, July 01, 2025
IRC logs for Tuesday, July 01, 2025
"Wayland People" Behave Like the Googles and Microsofts of This World
Published yesterday by Igor Ljubuncic
Gemini Links 02/07/2025: Arch Linux and Fulfillment in Gemini
Links for the day
Links 01/07/2025: "Independence Day in Taiwan", Bounties on Software Patents
Links for the day
What Happens When Your Law Firm is Preoccupied With Harassing and Trying to Extort a Humble Couple in Manchester, Even on Behalf of Violent Microsoft Staff From Another Continent
It's good to see that law firms which operate in bad faith are perishing
Lawyer X, Law Firm X and Elon Musk's X: scandals linked by Old Xaverian
Reprinted with permission from Daniel Pocock
Gemini Links 01/07/2025: Distraction-Free Writing and Hytale Mismanagement
Links for the day
Links 01/07/2025: "Beauty of Blogging" and "Etiquette of Collapse"
Links for the day
Microsoft Uses LLM Slop to Defraud (or Rob) Shareholders
Microsoft is basically defrauding its shareholders by LLM slop
The Web is a Dead End
We need to adopt alternatives
When Words Lose Their Intended Meaning
examples of words that, at least in the technical spheres, don't mean what they sound like
People Who Disagree With You on Technical Matters May or May Not Agree With You on Political Things (But Usually They Do)
What bothers me a great deal is seeing left-leaning people accusing other left-leaning people of being "nazis"
"Too Much Choice" and "Too Many Programming Languages"
What IBM and its apologists aim for was attempted in the 1930s and it failed
Microsoft Lost 400,000,000 Windows Users, According to Microsoft
more people adopt smaller computers and many people replace Windows with GNU/Linux, as they don't really need a new computer
The "Davos Effect": Tarnishing the Reputation of Places Not by Overtourism But by Oligarch Infestation
The last Venice needs is an affiliation with Venetian oligarchs
Half a Year Gone, What's to Come Next
In the second half of 2025 we expect to be done with the Microsoft SLAPPs
Over at Tux Machines...
GNU/Linux news for the past day
IRC Proceedings: Monday, June 30, 2025
IRC logs for Monday, June 30, 2025
People at the Very Top of Microsoft Know How Bad Things Really Are
There's no product that can replace the former profitability of Windows licensing and stuff that went on top of Windows
Gemini Links 01/07/2025: Mid Year and a Tour of Old Languages
Links for the day