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Spatial Perspective Transform Estimation from Fourier Spectrum Analysis of 2D Patterns in 3D Space

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Ian J. Maquignaz

Signal Processing · Submitted 27 Nov 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This work expands on previously derived affine Spatial-Fourier Transformation Pairs and characterizes its implications towards 3D surface imaging as a means of augmenting (X,Y,Z)-(R,G,B) point-clouds to include additional information from localized sampling of pattern transformations.

how it is stated · asserted 0.93 read the record →

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arXiv ID2211.14726 (version 1)
Pith IDEQ5PHGJ3, Pith's permanent record of this paper and its review
CitationIan J. Maquignaz. "Spatial Perspective Transform Estimation from Fourier Spectrum Analysis of 2D Patterns in 3D Space." arXiv:2211.14726 (2022). https://pith.science/paper/EQ5PHGJ3
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,725 input tokens.

What the abstract itself states, as probabilities: claims first 0.14 · states limitation 0.06 · human participants 0.03 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.37 · compares with prior results 0.59 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical relationship for Spatial-Fourier Transformation Pairs is derived, defining the transformation of spatial transformed planar surfaces in the Discrete Fourier Transform spectrum. The mathematical relationship for the twelve degrees of freedom in perspective transformation is defined and validated, asserting congruity with independent and uniform transform pairs for spatial Euclidean, similarity, affine and perspective transformations. This work expands on previously derived affine Spatial-Fourier Transformation Pairs and characterizes its implications towards 3D surface imaging as a means of augmenting (X,Y,Z)-(R,G,B) point-clouds to include additional information from localized sampling of pattern transformations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. contribution 0.98 0.74 0.38 asserted 0.92
s1 The mathematical relationship for Spatial-Fourier Transformation Pairs is derived, defining the transformation of spatial transformed planar surfaces in the Discrete Fourier Transform spectrum. contribution 0.49 0.88 0.08 asserted 1.00
s2 The mathematical relationship for the twelve degrees of freedom in perspective transformation is defined and validated, asserting congruity with independent and uniform transform pairs for spatial Euclidean, similarity, affine and perspective transformations. result 0.51 0.83 0.25 asserted 1.00
s3 This work expands on previously derived affine Spatial-Fourier Transformation Pairs and characterizes its implications towards 3D surface imaging as a means of augmenting (X,Y,Z)-(R,G,B) point-clouds to include additional information from localized sampling of pattern transformations. contribution 0.58 0.78 0.22 asserted 0.93

What kind of paper the classifier reports this is: method or tool 0.95 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • S sections
  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical relationship for Spatial-Fourier Transformation Pairs is derived, defining the transformation of spatial transformed planar surfaces in the Discrete Fourier Transform spectrum. The mathematical relationship for the twelve degrees of freedom in perspective transformation is defined and validated, asserting congruity with independent and uniform transform pairs for spatial Euclidean, similarity, affine and perspective transformations. This work expands on previously derived affine Spatial-Fourier Transformation Pairs and characterizes its implications towards 3D surface imaging as a means of augmenting (X,Y,Z)-(R,G,B) point-clouds to include additional information from localized sampling of pattern transformations.

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