Lens Distortion Encoding System Version 1.0

Jakub Maksymilian Fober

REVIEW 1 major objections 1 minor 15 references

Lens Distortion Encoding System Version 1.0

T0 review · 1 major / 1 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A two-texture encoding lets any footage be re-lensed in post, from fisheye to anamorphic and back.

desk verdict A clean, well-structured specification for lens distortion interchange whose core accuracy claim is untested because the calibration methods are deferred to future work. read the letter →

arxiv 2411.16946 v2 pith:EY4EXZ77 submitted 2024-11-25 cs.CV cs.GRcs.MM

Jakub Maksymilian Fober This is my paper · ORCID

classification cs.CVcs.GRcs.MM

keywords LensdistortionencodingSTMapworkflowCameracalibrationAnamorphiclensesAximorphicFisheyeVisualspheremappingcorrection

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes the Lens Distortion Encoding System (LDES): a way to store a lens's distortion as a pair of texture maps so that any footage shot with one lens can be rewarped into the look of another lens, or into a synthetic projection, without reshooting. The two textures are the View Map, which records where each output pixel points in a shared spherical image space, and the Footage Map, which records where each point of that sphere lands in the footage. Direct conversion from one lens to another is a single sampling of the Footage Map through the View Map, and because View Maps live in a common spherical space they can be blended and animated. The stated benefit is that an expensive lens's distortion look could be emulated with cheaper glass, and that transitions such as anamorphic-to-spherical, previously impractical, become ordinary opacity ramps. The system intentionally stays inside the existing 32-bit STMap format so mainstream compositing tools can use it unchanged.

What carries the argument

The central object is the LDES profile pair: a View Map and a Footage Map, both in 32-bit STMap form (a texture whose channels store sample coordinates rather than colors). The Footage Map encodes absolute pixel positions in a spherical equidistant projection, with its alpha channel marking the footage boundary; the View Map encodes, per output pixel, the corresponding point of that spherical space, with its blue channel optionally storing linear-space vignetting. The load-bearing operation is Equation 4, sampling the Footage Map through the View Map, which synthesizes the final distortion STMap, and Equation 3's tile scaling that reconciles differing FOV labels. The mechanism is completed by the synthetic projection model parameterized by the fisheye factor k (rectilinear, stereographic, equidistant, equisolid, orthographic), the anamorphic and aximorphic extensions for axis-dependent distortion, and Equation 6's conversion of View Map coordinates into ray-tracing incidence vectors.

What would settle it

Calibrate one lens with both proposed methods, checkerboard fitting and the motorized gimbal with a target at infinity, and compare the derived View Maps; if corresponding pixels differ by more than one image pixel at the lens's native resolution, the claimed distortion-accurate interchange fails. Alternatively, shoot the same static scene through lens A and lens B, remap A's footage with an A-to-B map, and measure the pixel difference against B's actual footage.

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Extended reading notes

Core claim

The central claim is that lens distortion interchange can be reduced to composing two maps in a spherical equidistant coordinate system. A Footage Map assigns each footage pixel to its absolute position on the visual sphere, labeled by a field-of-view angle Ω; a View Map assigns each output-image pixel to a point on that same sphere, also labeled by Ω. The final distortion texture is obtained by sampling the Footage Map through the View Map (Equation 4), with a simple tile scaling correcting any FOV mismatch between the two maps (Equation 3). Because the View Map is defined in a shared spherical space rather than in the rectilinear space of a particular camera, view maps from different lenses can be opacity-blended, animated, or fed directly into a ray-tracing engine as incidence directions. The paper thereby claims that distortion becomes a fully exchangeable, animatable creative parameter rather than a fixed property of the lens that captured the image.

Load-bearing premise

The whole workflow assumes that real lenses can be calibrated into accurate View and Footage Maps in a single spherical equidistant coordinate space; the paper describes two calibration methods but defers their evaluation to future work, so if calibration is inaccurate the interchange and animation cannot deliver the claimed distortion accuracy.

Editorial extensions

If this is right

A well-calibrated LDES profile of a single lens becomes a reusable asset: any footage shot with that lens can be transformed to any other profile with a matching FOV, or to a synthetic projection, by a single STMap sample.
View Maps can be opacity-blended and animated, so a transition like anamorphic-to-spherical is a continuous interpolation between two textures rather than a lens change.
Because View Maps convert to ray directions, CGI can be rendered with the distortion baked in, letting three-dimensional scenes match live-action footage without a separate warp pass.
Existing STMap pipeline tools in compositing software can consume LDES maps directly, so adoption does not require new hardware or proprietary formats.
The FOV label and tile-scaling rule allow profiles shot at different field widths to be combined without reshooting, provided the FOV normalization of Equation 5 is applied.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Inference: if the calibration step were validated, the same two-map scheme could be extended beyond lenses to camera motion, using the View Map's rotation mechanism to simulate pan, tilt, and roll in post, a step the paper only sketches.
Inference: the encoding's resolution independence suggests it could serve real-time engines for games and virtual production as a distortion lookup that is cheaper than ray tracing, though the paper lists real-time support only as future work.
Inference: the perceptual claims of Table 2 invite a user study; if the aximorphic region-splitting in the paper's Exercise 1 measurably changes perceived speed, distance, and spaciousness, LDES would supply a direct control surface for cinematic directing.
Inference: a standard library of View Maps would make the system's value depend on calibration quality; comparing the two calibration methods on the same lens would quantify the interchange error that the paper leaves open.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a clear, well-put-together specification for a lens distortion interchange format, and the two-map idea is genuinely nice. But the central claim—that it enables a 'distortion-accurate workflow' with seamless interchange—is not tested anywhere in the paper. The calibration methods that would produce the maps are sketched and explicitly deferred to future work.

What's actually new: the View Map / Footage Map split, with the footage sampled through the view map to produce a final STMap, is a simple and clever way to separate lens characterization from per-shot distortion. Encoding coordinates in absolute spherical (equidistant) space and labeling maps by FOV avoids the rectilinear-only limitation of standard STMaps and makes transitions between profiles well-defined. The compatibility argument is reasonable: because the output is a standard 32-bit STMap, it should drop into After Effects or Resolve with existing plug-ins.

The paper does a good job of assembling standard material: the fisheye factor table, Brown-Conrady extensions, anamorphic and aximorphic variants are all sourced, and the author cites his own earlier work where relevant. The workflow example is concrete enough to show the intended usage. This is not a sloppy paper; the math is internally consistent as a specification.

The soft spots are real. The load-bearing assumption is that real lenses can be calibrated into accurate View and Footage Maps in a single spherical space using either the checkerboard fit or the motorized-gimbal rig. The paper provides no calibration output, no error metrics, no comparison to existing tools. Section 6 says so plainly. That means the abstract's promise of 'distortion accuracy' is not yet supported—it's a design goal. Also, Eqs. 9 and 12 have a few ambiguities (missing parentheses, unclear operator precedence) that would need cleanup before implementation. Table 2 is labeled as an empirical self study, which is honest, but it's not a result.

Who should read this: engineers and artists working on lens mapping standards, or anyone building on STMap pipelines. It gives you a concrete proposal to react against. Don't read it expecting validation of the accuracy claim.

Recommendation: send it to peer review. A specialist referee can assess whether the encoding design is sound and what it would take to validate it, but the review must insist on either an actual calibration evaluation or a clear reframing of the paper as a specification without the accuracy claim. I'd treat it as a conditional accept at best.

Referee Report

1 major / 1 minor

Summary. The paper introduces the Lens Distortion Encoding System (LDES) as a specification for representing lens distortion in a common spherical equidistant projection space using two 32-bit STMap textures: a View Map (mapping output image coordinates to equidistant-space coordinates) and a Footage Map (mapping equidistant-space coordinates to original footage coordinates). The core operation is a two-stage sample (Eq. 4) where the View Map is used to sample the Footage Map, producing an animatable and combineable distortion mapping texture. The paper also defines synthetic projection models (parameterized fisheye through an aximorphic extension), anamorphic and Brown-Conrady extensions, two calibration methods for real lenses (checkerboard fitting and a gimbal-based infinity-target rig), and a workflow example for compositing and ray-tracing. No experimental results, calibration outputs, or error metrics are reported; Section 6 explicitly defers calibration-method evaluation to future work.

Significance. The proposed encoding concept is novel and potentially valuable: if accurate per-lens calibration maps can be produced, LDES could serve as an ACES-like interchange standard for lens distortion, enabling seamless emulation of expensive lens looks, animatable transitions (e.g., anamorphic to spherical), and direct integration with existing STMap workflows in compositing software. The mathematical construction of the two-stage sampling and the use of a common spherical space are internally coherent as a specification, and the paper honestly discloses that the calibration methods are not yet validated. However, the central abstract claims of a 'distortion-accurate workflow' and 'seamless interchange ... regardless of the lens source' rest entirely on the unverified accuracy of the View/Footage map calibration. The paper provides no data showing that real lenses can be encoded to production quality by either proposed method, nor any comparison with established STMap or calibration pipelines. As a specification, the paper is a useful contribution; as a demonstration of the promised capability, it is incomplete.

major comments (1)

[Section 4.1, Eq. (9a)] The anamorphic extension defines the radius as r = sqrt(v_x^2 + v_y^2 / s) without specifying the meaning, range, or reference of the squeeze factor s. For anamorphic lenses, the common convention is a horizontal squeeze (the image is compressed horizontally by a factor typically 1.33x or 2x); the presented formula instead scales the vertical contribution to the radius by 1/s, which is not a horizontal squeeze in the usual sense. This ambiguity directly affects synthetic View Map generation for anamorphic profiles, a key use case claimed in the abstract. The definition of s (e.g., 's is the anamorphic squeeze ratio such that the effective horizontal focal length is multiplied by s') should be stated explicitly, and the resulting equations checked against a known anamorphic projection model.

minor comments (1)

[Section 4.1, Eq. (8a)-(8c)] The synthetic projection model is plausible, but the definitions of f and r assume a specific relationship between image-space coordinates and pixel units; it would help to state explicitly that v is in aspect-corrected image-space units normalized to the horizontal FOV Ω.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: LDES defines the distortion mapping as a composition of two user-supplied map textures, so the core interchange result is a definitional construction rather than a fitted or self-cited prediction.

full rationale

The paper's central mechanism is Eq. (4): the final STMap is produced by sampling the Footage Map through the View Map. This is exactly the definition of the two-map encoding scheme, not a derived prediction. Both maps are external inputs to the system: the View Map encodes target-image coordinates in equidistant projection space (Eq. 2b), and the Footage Map encodes source footage coordinates in the same space (Eq. 1). Their composition is by construction and does not reduce to a parameter fitted from data. The accuracy claim in the Abstract depends on the maps being accurate for real lenses, but Section 6 explicitly defers evaluation of the calibration methods; this is a missing verification of an input assumption, not a circular derivation. The only self-referential elements are the citation [Fober 2021] for the optional aximorphic synthetic projection model and Table 2's 'Empirical self study' perception associations. Neither is load-bearing for the core interchange workflow: the aximorphic extension is one of several optional distortion models, and the perceptual table supports artistic exercises, not the encoding mechanism. No fitted parameter is renamed as a prediction, and no uniqueness theorem is imported from prior work. Therefore the derivation chain is self-contained with respect to its stated definitions, and the paper's limitations lie in validation rather than circularity.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The system's practical value depends on calibration-derived parameters that are not measured or validated in the paper: FOV labels, projection factors, anamorphic squeeze, and Brown-Conrady coefficients. The single-sphere model and the sufficiency of the described calibration and interpolation are assumed rather than demonstrated.

free parameters (4)

Omega_view_map and Omega_footage_map (FOV labels) = user-supplied whole-number degrees
Eq. 3 and Eq. 5 use these FOV values for tile scaling and normalization; the paper gives no calibration measurement or accuracy bound for them.
Projection factor k (including k_x, k_y, k_top, k_bottom) = not specified; examples in Table 1
Eqs. 8-11 define synthetic view maps for any k; values must be chosen or fitted per lens, and no fitted values are reported.
Anamorphic squeeze factor s = not specified
Eq. 9 scales vertical distortion; it is a lens-dependent parameter not measured in the paper.
Brown-Conrady coefficients (c1,c2,k1,k2,...,p1,p2,q1,q2) = not specified
Eqs. 12-13 require calibrated radial, decentering, and thin-prism coefficients to match real lenses; no calibration outputs are provided.

assumptions (4)

domain assumption Every lens can be represented as a map between image pixels and incidence directions on a single visual sphere (single viewpoint model).
Invoked in Sections 1.1 and 3; required for View Map and Footage Map bijections; not tested and likely violated by some non-central or compound lenses.
domain assumption The Brown-Conrady division model combined with cartographic mapping enables comprehensive mapping of all lenses.
Section 2.2 states this without quantitative support; it is load-bearing for covering all lens types.
domain assumption Spherical equidistant coordinates are a consistent common space for combining view maps and footage maps.
Eqs. 1-5 define the system in this space; real calibrated maps may not perfectly conform to equidistant encoding.
domain assumption Bilinear interpolation is sufficient for distortion-accurate sampling.
Section 4.2 claims this; no image quality or error metrics are provided.

invented entities (2)

View Map
purpose: Stores normalized equidistant-sphere coordinates per footage pixel, optionally vignetting, for use as the driver in sampling a Footage Map.
Core new file type of LDES; no shipped sample, independent implementation, or validation is provided.
Footage Map
purpose: Stores footage ST coordinates in equidistant spherical space and footprint boundaries; sampled through the View Map to produce the final warp.
Second core new file type; no sample or validation is provided.

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Cite this review

Pith. "Pith review of Lens Distortion Encoding System Version 1.0." pith.science (2026). https://pith.science/paper/EY4EXZ77

@misc{pith2026241116946,
  author       = {Pith},
  title        = {Pith review of: Lens Distortion Encoding System Version 1.0},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EY4EXZ77}},
  note         = {Machine review of arXiv:2411.16946}
}

read the original abstract

Lens Distortion Encoding System (LDES) allows for a distortion-accurate workflow, with a seamless interchange of high quality motion picture images regardless of the lens source. This system is similar in a concept to the Academy Color Encoding System (ACES), but for distortion. Presented solution is fully compatible with existing software/plug-in tools for STMapping found in popular production software like Adobe After Effects or DaVinci Resolve. LDES utilizes common distortion space and produces single high-quality, animatable STMap used for direct transformation of one view to another, neglecting the need of lens-swapping for each shoot. The LDES profile of a lens consist of two elements; View Map texture, and Footage Map texture, each labeled with the FOV value. Direct distortion mapping is produced by sampling of the Footage Map through the View Map. The result; animatable mapping texture, is then used to sample the footage to a desired distortion. While the Footage Map is specific to a footage, View Maps can be freely combined/transitioned and animated, allowing for effects like smooth shift from anamorphic to spherical distortion, previously impossible to achieve in practice. Presented LDES Version 1.0 uses common 32-bit STMap format for encoding, supported by most compositing software, directly or via plug-ins. The difference between standard STMap workflow and LDES is that it encodes absolute pixel position in the spherical image model. The main benefit of this approach is the ability to achieve a similar look of a highly expensive lens using some less expensive equipment in terms of distortion. It also provides greater artistic control and never seen before manipulation of footage.

Figures

Figures reproduced from arXiv: 2411.16946 by the authors.

**Figure 1.** Naming convention for the LDES files. The inclusion of the FOV value in the filename is mandatory, for the mapping process to function. The FOV is always specified as a whole number in degrees. If the exact lens value is a decimal numeral, the texture coordinates must be scaled appropriately to match the noted FOV value. For further details, see equation No. 5 on the following page. As a good practice, the FOV note… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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