Geometry-Image Mipmapping

• Geometry-image mipmapping is an extension of classical mipmaps that encodes 3D geometry into 2D images for continuous level-of-detail control.
• It leverages regular 2D grids to apply standard image operations and GPU trilinear interpolation for both rendering optimization and neural reconstruction.
• The approach addresses challenges in anisotropic filtering and connectivity preservation while enabling efficient compressed, decoder-free reconstruction.

Geometry-image mipmapping is the extension of mipmap pyramids from color textures to geometry images, that is, regular 2D parameterizations of 3D surfaces in which pixels store surface positions and, in some formulations, normals. In this setting, downsampled levels are not merely lower-frequency images; they are geometric levels of detail (LoD) that can be selected, interpolated, and processed with standard image-domain machinery. Contemporary work treats geometry-image mipmaps both as rendering primitives and as storage primitives: they support continuous LoD through GPU mipmapping and trilinear interpolation, and they also serve as compressed neural representations from which high-resolution geometry can be reconstructed in a single forward pass (Gao et al., 24 Nov 2025). Related neural material models explicitly describe themselves as direct generalizations of classical mipmapping, including geometry-image mipmapping, from low-dimensional textures to learned, scale-aware appearance functions (Kuznetsov et al., 2021).

1. Geometry images as mipmapped geometric signals

A geometry image parameterizes a surface onto a regular 2D domain and stores 3D coordinates as a 2D image. In the formulation used for neural geometry-image representations, the domain is a rectangular pixel grid $\Omega \subset \mathbb{R}^2$, each pixel $(u,v)$ stores a 3D position $(x,y,z)$ in RGB channels, and connectivity is implicitly given by the image grid: neighboring pixels imply neighboring samples on the surface (Gao et al., 24 Nov 2025). SwiftTailor adopts the same basic definition through a map $f : \mathcal{S} \rightarrow [0,1]^2$ and inverse $f^{-1} : [0,1]^2 \rightarrow \mathbb{R}^3$, then specializes it to garments by packing multiple sewing panels into a unified UV layout and storing aligned semantic, stitching, and geometry images (Pham et al., 19 Mar 2026).

A geometry-image mipmap is exactly analogous to a texture mipmap, but each pixel encodes geometry instead of color. In the OT-based neural geometry-image framework, a full-resolution position geometry image $I^{\text{pos}}_0$ of size $1024 \times 1024$ is downsampled by GPU mipmapping into the pyramid

$$I^{\text{pos}}_0 \to I^{\text{pos}}_1 \to I^{\text{pos}}_2 \to \cdots \to I^{\text{pos}}_7,$$

with resolutions

$$1024^2, 512^2, 256^2, 128^2, 64^2, 32^2, 16^2, 8^2,$$

and the same construction is used for normals $I^{\text{norm}}_\ell$ (Gao et al., 24 Nov 2025). Because GPUs already support trilinear filtering in mipmapped textures, fractional LoD values can be realized by hardware interpolation between adjacent levels, yielding smoothly varying geometry when choosing intermediate LoDs (Gao et al., 24 Nov 2025). This makes geometry-image mipmapping a direct route to continuous geometric LoD on regular grids.

The central attraction of this representation is regularity. By transforming irregular meshes into images, geometry processing becomes compatible with standard 2D convolutions, super-resolution networks, and GPU texture hardware (Gao et al., 24 Nov 2025). A plausible implication is that geometry-image mipmapping has become important not only as a rendering optimization, but also as a unifying data model for geometry compression, LoD control, and neural reconstruction.

2. Footprint estimation, level selection, and anisotropy

Geometry-image mipmapping inherits the classical resampling problem. Under projective or more general surface-to-screen mappings, some regions are magnified and require interpolation, while others are minified and require pre-filtering to avoid moiré, jagged edges, and flickering textures (Trusov et al., 2019). The projective-transform study on ARM/mobile platforms formulates image transformation as a three-step process—image reconstruction, spatial transformation, and sampling—and notes that the same resampling and aliasing issues arise for geometry images parameterized as regular images (Trusov et al., 2019).

The canonical isotropic mipmap level is selected from a local scale factor computed from the inverse map $(u,v)$0: $(u,v)$1 The selected mip level is the one whose scale best matches $(u,v)$2, and linear interpolation between adjacent levels suppresses visible seams at discrete level transitions (Trusov et al., 2019). For geometry images, the same Jacobian-based scale estimate transfers directly: build a mipmap pyramid over positions, normals, or colors, estimate the local screen-to-parameter-space footprint, and sample the corresponding level (Trusov et al., 2019).

The principal limitation of ordinary mipmaps is isotropy. Mipmaps approximate each pixel footprint by a square in source space, whereas perspective and parameterization distortions often produce elongated ellipses. Rip-maps improve this by allowing independent scaling along the two axes and approximating the footprint by an axis-aligned rectangle, while FAST combines mipmap pre-filtering with adaptive jittered supersampling to approximate the true anisotropic footprint more closely (Trusov et al., 2019).

Method	Footprint approximation	Additional memory
Mip-map pre-filtering	Square, isotropic	$(u,v)$3 of base image
Rip-map pre-filtering	Axis-aligned rectangle	$(u,v)$4 base image
FAST	Anisotropic footprint with jittered samples on a mip level	$(u,v)$5 of base image

For resource-constrained systems, bilinear interpolation combined with mip-map pre-filtering, or bilinear interpolation combined with FAST, is identified as the best practical choice for projective transformation on mobile devices (Trusov et al., 2019). In geometry-image terms, this establishes the baseline engineering trade-off: isotropic mipmaps are cheap and robust, while anisotropic schemes are needed when the parameterization or viewpoint induces strong directional stretching.

3. Fidelity, sampling error, and connectivity-preserving variants

Traditional geometry images represent a three-dimensional mesh using an image-like structure with the connectivity information encoded in the image space, but their reconstruction error includes both sampling error and round-off error (Wang et al., 2013). Sampling error depends on the parametrization methods, the sampling methods, geometry-image resolutions, and interpolating functions; round-off error is produced in the scaling step that maps coordinates to RGB (Wang et al., 2013). In the context of mipmapping, this means that coarser levels are ordinarily approximations of an already sampled surface representation.

Connectivity-preserving geometry images (CGIMs) alter this premise. CGIMs construct a V-matrix whose elements are vertices of the original mesh, possibly repeated, such that the induced vertex-set equals the original vertex-set and the induced edge-set equals the original edge-set (Wang et al., 2013). The paper states that the reconstructed mesh produces no sampling errors, but merely round-off errors over the coordinates of vertices (Wang et al., 2013). If a connectivity-preserving V-matrix is encoded in a $(u,v)$6-bit CGIM, both the max Hausdorff distance and the root-mean-square Hausdorff distance are bounded by

$(u,v)$7

This exactness at a single level has important consequences for geometry-image mipmapping. CGIMs provide a high-fidelity base representation, but their guarantees depend on repetition patterns that encode adjacency. The detailed synthesis of the paper notes that arbitrary filtering or averaging of CGIM pixels disrupts those patterns, and that direct mipmapping of a CGIM image is not connectivity-preserving (Wang et al., 2013). This suggests that CGIMs are better suited to hierarchies built from separately simplified meshes, each re-encoded as its own CGIM, than to classical hardware-generated mip pyramids.

The same paper explicitly points toward hierarchical directions. Future work is described as developing multi-chart CGIMs with smaller resolutions and applying CGIMs to hierarchical mesh compression, including geometry images that preserve details, features, or regions of interest by using CGIM patches (Wang et al., 2013). Within the broader history of geometry-image mipmapping, CGIMs therefore occupy a precise niche: they maximize per-level reconstruction fidelity, but they do not natively solve the problem of safe multilevel filtering.

4. Area-preserving geometry-image mipmaps and decoder-free neural reconstruction

A major contemporary development is the use of Optimal Transport (OT) to construct strictly area-preserving geometry images so that each surface area element gets proportional image area, thereby reducing oversampling in flat regions and undersampling in feature-rich regions (Gao et al., 24 Nov 2025). This is introduced specifically as a way to enable continuous levels of detail through geometry-image mipmapping (Gao et al., 24 Nov 2025). The construction begins with a conformal initialization via discrete Ricci flow and then refines the parameterization with a variational OT formulation based on power diagrams and Brenier’s theorem (Gao et al., 24 Nov 2025).

In this framework, the stored representation is a pair of geometry images: a position image $(u,v)$8 and a normal image $(u,v)$9, both generated at high base resolution, stored as 16-bit RGB PNGs, and then mipmapped on the GPU (Gao et al., 24 Nov 2025). Compression is achieved by storing only one low-resolution mip level of the position image and the corresponding low-resolution normal image. A standard 2D image super-resolution CNN then reconstructs the full-resolution geometry image in a single forward pass: $(x,y,z)$0 After reconstruction, the GPU generates a fresh mipmap pyramid from the reconstructed full-resolution geometry image, and the renderer can select arbitrary LoD levels on the fly (Gao et al., 24 Nov 2025).

The stored mip level $(x,y,z)$1 determines the compression ratio

$(x,y,z)$2

Stored resolution	CR
$(x,y,z)$3	1024
$(x,y,z)$4	256
$(x,y,z)$5	64
$(x,y,z)$6	16
$(x,y,z)$7	4

The LoD ablation identifies $(x,y,z)$8 as a sweet spot between storage and accuracy, with $(x,y,z)$9 and $f : \mathcal{S} \rightarrow [0,1]^2$0, while $f : \mathcal{S} \rightarrow [0,1]^2$1 yields $f : \mathcal{S} \rightarrow [0,1]^2$2 and $f : \mathcal{S} \rightarrow [0,1]^2$3 (Gao et al., 24 Nov 2025). At CR $f : \mathcal{S} \rightarrow [0,1]^2$4, the method is reported to outperform ACORN, NGLOD, and NCS in CD and HD, while remaining decoder-free in the sense that runtime LoD is handled by image mipmapping and hardware filtering rather than mesh-specific progressive decoders (Gao et al., 24 Nov 2025).

The method also clarifies a frequent misconception: continuous LoD through geometry-image mipmapping does not remove all topological assumptions. The OT and Ricci-flow pipeline assumes genus-zero meshes with a single boundary for the square-domain parameterization, and seams may appear along mesh boundaries in reconstructed meshes (Gao et al., 24 Nov 2025). Geometry-image mipmapping solves multiresolution access on a regular domain; it does not by itself eliminate charting or seam-management problems.

5. Neural generalizations of geometry-image mipmapping

NeuMIP makes the relationship to geometry-image mipmapping explicit. It is described as a direct generalization of classical mipmapping, including geometry-image mipmapping, from low-dimensional textures to a learned, high-dimensional, scale-aware material representation (Kuznetsov et al., 2021). Instead of storing prefiltered RGB or scalar height values, NeuMIP stores a pyramid of learned latent textures

$f : \mathcal{S} \rightarrow [0,1]^2$5

with $f : \mathcal{S} \rightarrow [0,1]^2$6 channels in the feature pyramid, and queries them using the same mipmap logic as classical LoD selection. Given footprint radius $f : \mathcal{S} \rightarrow [0,1]^2$7,

$f : \mathcal{S} \rightarrow [0,1]^2$8

with bilinear interpolation in each level and linear interpolation across scale (Kuznetsov et al., 2021). A small fully connected network with 4 layers and 25 hidden channels decodes the feature together with incoming and outgoing directions into RGB reflectance (Kuznetsov et al., 2021).

The conceptual shift is that geometry-image mipmapping is no longer restricted to explicit geometry. NeuMIP prefilters reflected radiance as a function of spatial position, incoming direction, outgoing direction, and filter size, and supplements the pyramid with neural offsets that generalize classical parallax mapping without an explicit heightfield (Kuznetsov et al., 2021). The paper describes this as prefiltering the appearance of microgeometry rather than prefiltering normals or heights directly. This suggests that the defining idea of geometry-image mipmapping is increasingly the scale-aware query of a filtered rendering function on a 2D parameterized domain, not merely the storage of explicit positions.

Tri-MipRF extends the same mipmap logic to volumetric neural fields. It factorizes a prefiltered 3D feature space into three orthogonal 2D mipmap pyramids,

$f : \mathcal{S} \rightarrow [0,1]^2$9

and selects levels from projected spherical footprints using

$f^{-1} : [0,1]^2 \rightarrow \mathbb{R}^3$0

with analogous formulas for the other planes (Hu et al., 2023). The paper characterizes the method as a 3D mipmap or prefiltering scheme implemented via three orthogonal 2D geometry-image-like mipmaps (Hu et al., 2023). While this is not a surface geometry image in the strict sense, it preserves the essential structure of geometry-image mipmapping: factorization onto regular 2D domains, explicit multiscale prefiltering, and footprint-conditioned LoD selection.

6. Multiview rendering, garment charts, and persistent limitations

Light-field display point rendering introduces multiview mipmapping because compute shaders do not support hardware mipmapping, yet all visible pixels are generated by point splats rather than by the fixed-function rasterizer (Gavane et al., 6 Nov 2025). The method computes, for each triangle and across all views, the minimum and maximum effective footprint of a view pixel on the triangle in texture space,

$f^{-1} : [0,1]^2 \rightarrow \mathbb{R}^3$1

converts these to min and max LODs, samples each texture once at those two levels, and then interpolates the prefiltered values per view and per splat (Gavane et al., 6 Nov 2025). The paper explicitly notes that these principles transfer to geometry images or multi-view geometry parameterized into textures (Gavane et al., 6 Nov 2025). In encyclopedia terms, this is a multiview generalization of geometry-image mipmapping: the mipmap is still spatial, but LoD selection is controlled by a view-set footprint envelope rather than by a single-view gradient.

SwiftTailor shows how geometry-image representations naturally invite mipmap-style processing even when the paper does not explicitly implement it. Its Garment Geometry Image packs multiple garment panels into a square UV layout and stores aligned semantic, stitching, and geometry images, with the geometry image filled by linear edge interpolation and barycentric interior interpolation (Pham et al., 19 Mar 2026). The source analysis states that SwiftTailor does not construct an explicit pyramid of geometry images, does not train multi-scale reconstruction losses across different resolutions, and does not use LoD for fast preview versus final reconstruction (Pham et al., 19 Mar 2026). A plausible implication is that geometry-image mipmapping in multi-chart domains requires seam-aware downsampling rules, because filtering geometry images changes the shape and can change topology, whereas filtering ordinary textures affects only appearance (Pham et al., 19 Mar 2026).

Across the literature, several limitations recur. Isotropic mipmaps approximate footprints by squares and cannot fully avoid directional aliasing under strong anisotropy (Trusov et al., 2019). Continuous LoD quality depends strongly on parameterization quality; OT-based geometry images address this by enforcing area preservation, but only under specific topological assumptions (Gao et al., 24 Nov 2025). Connectivity-preserving encodings minimize per-level reconstruction error, but direct filtering breaks their structural guarantees (Wang et al., 2013). Neural generalizations capture far richer appearance and volumetric effects, yet they inherit their own approximation limits, such as difficulty with very sharp, glinty specular effects or reliance on basic importance sampling in complex BRDF regimes (Kuznetsov et al., 2021). Geometry-image mipmapping is therefore best understood not as a solved primitive, but as an evolving multiresolution framework whose success depends on how faithfully a 2D regular domain can encode the geometry, appearance, or volumetric signal being filtered.