Self-Organizing Maps for the Reconstruction of Images in Pixel Permuted Image Stacks

Connor Price, David Kott, Chris Peterson, Michael Kirby
Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:362-374, 2026.

Abstract

A color digital photograph, of resolution $a\times b$, is typically stored as an $a\times b\times3$ array. The vector of length 3, sitting at a pixel, encodes its color in terms of intensity measurements of the red, green, and blue color bands. We call this length 3 vector a "pixel pole". Suppose we are given the $ab$ individual pixel poles as a jumbled collection of length 3 vectors and we wish to reconstruct the image, with no advanced knowledge concerning its content. In other words, we are given $ab$ color squares and we wish to "solve the pixel puzzle" meaning we want to reconstruct the original unknown image. As one can imagine, this is a difficult problem. In this paper, we show how to rebuild the images in a stack of $N$ distinct $a\times b$ color digital images from the $ab$ stacked pixel poles. More precisely, this paper shows how to use "Self Organizing Maps" (SOMs) to algorithmically reconstruct, unsupervised, a stack of distinct $a\times b$ color images from the collection of $1\times1\times3N$ stacked pixel poles using no apriori information about the original images. We evaluate the accuracy of the reconstructions as a function of $N$, we determine the effectiveness of the algorithm when the individual images are corrupted by noise, and we assess the model’s performance when pure noise images are included in the stack.

Cite this Paper

BibTeX
@InProceedings{pmlr-v321-price26a, title = {Self-Organizing Maps for the Reconstruction of Images in Pixel Permuted Image Stacks}, author = {Price, Connor and Kott, David and Peterson, Chris and Kirby, Michael}, booktitle = {Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025)}, pages = {362--374}, year = {2026}, editor = {Bernardez Gil, Guillermo and Black, Mitchell and Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Garcı́a-Rodondo, Ińes and Holtz, Chester and Kotak, Mit and Kvinge, Henry and Mishne, Gal and Papillon, Mathilde and Pouplin, Alison and Rainey, Katie and Rieck, Bastian and Telyatnikov, Lev and Yeats, Eric and Wang, Qingsong and Wang, Yusu and Wayland, Jeremy}, volume = {321}, series = {Proceedings of Machine Learning Research}, month = {01--02 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v321/main/assets/price26a/price26a.pdf}, url = {https://proceedings.mlr.press/v321/price26a.html}, abstract = {A color digital photograph, of resolution $a\times b$, is typically stored as an $a\times b\times3$ array. The vector of length 3, sitting at a pixel, encodes its color in terms of intensity measurements of the red, green, and blue color bands. We call this length 3 vector a "pixel pole". Suppose we are given the $ab$ individual pixel poles as a jumbled collection of length 3 vectors and we wish to reconstruct the image, with no advanced knowledge concerning its content. In other words, we are given $ab$ color squares and we wish to "solve the pixel puzzle" meaning we want to reconstruct the original unknown image. As one can imagine, this is a difficult problem. In this paper, we show how to rebuild the images in a stack of $N$ distinct $a\times b$ color digital images from the $ab$ stacked pixel poles. More precisely, this paper shows how to use "Self Organizing Maps" (SOMs) to algorithmically reconstruct, unsupervised, a stack of distinct $a\times b$ color images from the collection of $1\times1\times3N$ stacked pixel poles using no apriori information about the original images. We evaluate the accuracy of the reconstructions as a function of $N$, we determine the effectiveness of the algorithm when the individual images are corrupted by noise, and we assess the model’s performance when pure noise images are included in the stack.} }
Endnote
%0 Conference Paper %T Self-Organizing Maps for the Reconstruction of Images in Pixel Permuted Image Stacks %A Connor Price %A David Kott %A Chris Peterson %A Michael Kirby %B Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025) %C Proceedings of Machine Learning Research %D 2026 %E Guillermo Bernardez Gil %E Mitchell Black %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Ińes Garcı́a-Rodondo %E Chester Holtz %E Mit Kotak %E Henry Kvinge %E Gal Mishne %E Mathilde Papillon %E Alison Pouplin %E Katie Rainey %E Bastian Rieck %E Lev Telyatnikov %E Eric Yeats %E Qingsong Wang %E Yusu Wang %E Jeremy Wayland %F pmlr-v321-price26a %I PMLR %P 362--374 %U https://proceedings.mlr.press/v321/price26a.html %V 321 %X A color digital photograph, of resolution $a\times b$, is typically stored as an $a\times b\times3$ array. The vector of length 3, sitting at a pixel, encodes its color in terms of intensity measurements of the red, green, and blue color bands. We call this length 3 vector a "pixel pole". Suppose we are given the $ab$ individual pixel poles as a jumbled collection of length 3 vectors and we wish to reconstruct the image, with no advanced knowledge concerning its content. In other words, we are given $ab$ color squares and we wish to "solve the pixel puzzle" meaning we want to reconstruct the original unknown image. As one can imagine, this is a difficult problem. In this paper, we show how to rebuild the images in a stack of $N$ distinct $a\times b$ color digital images from the $ab$ stacked pixel poles. More precisely, this paper shows how to use "Self Organizing Maps" (SOMs) to algorithmically reconstruct, unsupervised, a stack of distinct $a\times b$ color images from the collection of $1\times1\times3N$ stacked pixel poles using no apriori information about the original images. We evaluate the accuracy of the reconstructions as a function of $N$, we determine the effectiveness of the algorithm when the individual images are corrupted by noise, and we assess the model’s performance when pure noise images are included in the stack.
APA
Price, C., Kott, D., Peterson, C. & Kirby, M.. (2026). Self-Organizing Maps for the Reconstruction of Images in Pixel Permuted Image Stacks. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), in Proceedings of Machine Learning Research 321:362-374 Available from https://proceedings.mlr.press/v321/price26a.html.

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