A scanned well log is a picture of a decision that was already made. Somewhere a tool ran down a borehole, a pen swept across paper, and a curve was drawn. Decades later that paper gets photographed, and what a petrophysicist wants back is not the photograph. It is the curve: a value at every depth, the thing the pen was standing in for. The pixels are incidental. The geometry is the data. Once you have said that sentence out loud about a log, it is hard to stop noticing how many other engineering documents it also describes, and that noticing is the whole subject of this note.
We came to the observation from one direction. VeerNet is the model EarthScan uses to lift curves off raster logs, and building it forced us to be exact about what recovery means when the input is an image and the output is a line. But the exactness turned out to be portable. The same three questions that a log poses are posed, almost verbatim, by a piping and instrumentation diagram, by a contour map, by a wiring schematic, by a plotted figure in an old report. Each is a raster scan of a document whose meaning is carried by traced strokes rather than by the paper. Each needs those strokes turned back into structured geometry. This is a survey of that family for the reader who likes seeing a single idea recur in disguises, and it is deliberately not a walk back through how VeerNet itself was trained.
What "the geometry is the data" actually rules in
The framing does real work, because it excludes as much as it includes. A page of printed prose is a raster too, but the meaning there lives in glyphs that optical character recognition already handles as a solved category. The documents in this family are the ones where the load-bearing content is not text but drawn structure: a curve's shape against a depth axis, a network of pipes and the valves punctuating them, the nesting of contour lines, the path of a plotted series across its axes. You cannot read these with a text recogniser because there is no text to read at the level that matters. You have to recover the lines themselves.
That is the shared shape of the problem, and it has a shared shape of solution that the drawings survey literature has been circling for years. Moreno-Garcia and colleagues, reviewing the digitisation of complex engineering drawings, describe the same recurring pipeline independent of drawing type: isolate the meaningful strokes and symbols from the background, classify what they are, and reassemble them into a structured representation [3]. The class list differs between a P&ID and a floor plan, but the machine underneath does not, which is exactly the point Rezvanifar and coauthors make concrete when they spot symbols on architectural floor plans with a segmentation-first framework whose bones are recognisable from any other document in the family [4]. The documents look nothing alike. The problem they pose is nearly identical.
The playbook, stated as three steps
Here is the pipeline in the form that ports, described from the log case we measured but written so the log-specific words can be swapped out. It has three steps and no more.
The first step is data, and it is the step most likely to kill a project before it starts, because supervised segmentation needs pixel-accurate labels and no archive of scanned documents comes with them. The move that unblocks it is to stop annotating and start synthesising: draw the documents yourself, procedurally, so that every pixel's label is known at draw time because you placed it. For VeerNet we generated 15,000 labelled instances this way, which is the difference between a dataset you wait months for and one you regenerate over a weekend. The reason this is legitimate rather than a shortcut is the subject of Nikolenko's book-length treatment of synthetic data: for tasks where you can model the generative process of the document, procedurally labelled data is a genuine substitute for hand annotation rather than a poor imitation of it [5]. A log generator that knows where it drew each curve transfers directly to a schematic generator that knows where it drew each wire. The synthesiser changes; the principle that you label by construction does not.
The second step is the network, and it is the most stable part of the whole pipeline across domains. A single grayscale channel goes in, because these are line drawings and colour is rarely the signal. An encoder of 5 stages compresses the image into a 128-dimension representation, a decoder of 5 stages expands it back to a per-pixel mask, and 2 attention layers sit on the bottleneck to let the network relate parts of the drawing that are far apart on the page. The encoder-decoder-with-skip-connections shape is Ronneberger, Fischer, and Brox's U-Net, which made dense segmentation trainable from few images [1], and the attention refinement is the mechanism from Vaswani and colleagues that lets a model reason about long-range structure that convolution keeps stubbornly local [2]. A valve at the top of a P&ID and its paired instrument tag at the bottom are exactly the kind of distant relationship attention is for. Nothing in this description mentions logs. That is deliberate, and it is why the step carries over untouched.
The third step is recovery: turning the predicted mask back into the vector object a human wanted. For a log that means walking each curve's mask column by column and reading off a value against depth, producing a digital curve you can compare to ground truth. On the multiclass log task that recovery reached a peak R-squared of 0.9891 between the recovered curve and the true one, which is the number that tells you the mask actually became geometry and not just a plausible smear. The recovery arithmetic is document-specific in its bookkeeping and generic in its idea: every document in this family ends by converting labelled pixels back into the lines, contours, or connections they represent.
Where the fan opens
The exhibit is the argument in one frame. The core on the left is the playbook precisely as we ran it on logs, with its measured numbers attached. The spokes fan the same three steps out to the adjacent documents, and selecting one shows the only honest way the method differs between domains: the synthesis step and the recovery step carry over verbatim, and the segmentation step changes nothing but its class list. Porting from strip logs to schematics does not mean a new architecture. It means teaching the same network a different vocabulary of things to find, which is a labelling task, not an engineering one. That is a much smaller claim than "our model generalises," and it is the claim that actually holds.
It is worth being blunt about what the spokes are and are not. Strip logs are the one member of this family we have measured end to end, and the exhibit marks them as such. Schematics, P&IDs, maps, and plots are drawn on the fan because they satisfy the same three conditions, not because we have benchmarked transfer to them. The value of the taxonomy is that it tells you where to point the playbook next and what work each new target actually requires, which is a synthesiser for that document type and a class list for its segmenter. Everything between those two is inherited.
Why the boring parts are the transferable parts
There is a pattern in which steps port and which do not, and it rewards attention. The two steps that carry over unchanged, synthesis and recovery, are the two that are least glamorous and most mechanical: generate labelled examples, convert masks to lines. The step that needs per-domain work, segmentation's class list, is the one closest to the specific meaning of the document. This is the usual arrangement in transfer, and it is good news, because it means the expensive, fiddly infrastructure is exactly the part you build once. When we describe the network without ever saying "log," we are not being coy. We are reporting that the network genuinely does not know it is looking at a log, and would not have to be told it was looking at a P&ID.
The grayscale, single-channel input deserves one more sentence, because it is a quiet load-bearing choice. Committing to one channel says the signal is in the strokes and not in the ink colour, and that assumption is true for logs and stays true for schematics, P&IDs, and most contour maps. It is the assumption that would break first on a document family where colour is categorical, a subway map say, and knowing that is knowing exactly one edge of where the fan stops opening.
The honest edge of the analogy
A survey earns its keep by marking its own boundary. The playbook fans out because the three documents share a structure, but sharing a structure is not sharing a difficulty. A P&ID packs far more distinct symbol classes into a page than a two-curve log track does, and more classes is harder supervision even when the pipeline is identical. Maps carry georeferencing that a log does not, so recovery there has an extra coordinate step the log case never needed. And every claim of transfer past strip logs is, in this note, an argument from shared structure rather than a measured result. The 0.9891, the 15,000 instances, the 5-plus-5 stages with 2 attention layers on a 128-dimension bottleneck: those are logs, measured. The rest of the fan is where the same method should reach, stated as a taxonomy for the curious and as a build order for us, not as a scoreboard.
References
[1] Ronneberger, O., Fischer, P., and Brox, T. U-Net: Convolutional Networks for Biomedical Image Segmentation. MICCAI 2015, LNCS 9351, pp. 234-241. The encoder-decoder with skip connections that made dense segmentation trainable from few annotated images. https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28
[2] Vaswani, A., Shazeer, N., Parmar, N., et al. Attention Is All You Need. Advances in Neural Information Processing Systems 30 (NIPS 2017). The attention mechanism used to relate distant parts of a drawing on the bottleneck. https://proceedings.neurips.cc/paper/2017/hash/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html
[3] Moreno-Garcia, C. F., Elyan, E., and Jayne, C. New Trends on Digitisation of Complex Engineering Drawings. Neural Computing and Applications 31 (2019), pp. 1695-1712. The recurring isolate-classify-reassemble pipeline shared across engineering drawing types. https://link.springer.com/article/10.1007/s00521-018-3583-1
[4] Rezvanifar, A., Cote, M., and Albu, A. B. Symbol Spotting on Digital Architectural Floor Plans Using a Deep Learning-based Framework. CVPR Workshops 2020, pp. 568-569. The same segmentation-first recovery on a different raster document family. https://openaccess.thecvf.com/content_CVPRW_2020/html/w34/Rezvanifar_Symbol_Spotting_on_Digital_Architectural_Floor_Plans_Using_a_Deep_CVPRW_2020_paper.html
[5] Nikolenko, S. I. Synthetic Data for Deep Learning. Springer Optimization and Its Applications 174 (2021). Why procedurally generated, automatically labelled data substitutes for hand annotation when the document's generation can be modelled. https://link.springer.com/book/10.1007/978-3-030-75178-4
Limitations
The measured claims in this note are the log ones and only the log ones. The 15,000 synthetic instances, the 5 encoder and 5 decoder stages with 2 attention layers on a 128-dimension bottleneck, the single grayscale channel, and the peak R-squared of 0.9891 are recorded on the strip-log task from one engagement. Every statement about schematics, P&IDs, maps, and scientific plots is an argument from shared structure, not a benchmarked transfer result, and the reader should treat the fan as a taxonomy of where the method should reach rather than a table of scores it has posted. Shared structure also does not equalise difficulty: documents with many symbol classes, with categorical colour, or with georeferencing pose supervision and recovery problems a two-curve log never raises, and any one of those can be the reason a port that looks trivial on paper is not. The peak R-squared is a best case on the multiclass task, not an average across curves or examples, so it states what the recovery can reach, not what it reaches on every log. Finally, this is a survey written for insight rather than a reproduction: it names the steps that carry over and the one that needs re-labelling, but it does not, and does not claim to, prove that the segmenter trained on one document family will land on another without its own synthetic data and its own class list.
