HyPlaneHead: Hybrid-Plane 3D GAN Synthesis

• HyPlaneHead is a full-head image synthesis method that combines planar symmetry with spherical anisotropy for enhanced 3D-aware GAN performance.
• It employs a near-equal-area sphere-to-square warping strategy to address non-uniform feature utilization and mirroring artifacts inherent in Cartesian projections.
• The unified feature map split into distinct panels eliminates cross-channel interference, leading to improved image fidelity and state-of-the-art performance.

HyPlaneHead is a full-head image synthesis method centered on a hybrid-plane representation for 3D-aware GANs. It is introduced in "HyPlaneHead: Rethinking Tri-plane-like Representations in Full-Head Image Synthesis" (Li et al., 20 Sep 2025). The method is motivated by three limitations identified in prior tri-plane-like representations: feature entanglement under Cartesian projection, non-uniform feature utilization in spherical tri-planes, and feature penetration across convolutional channels. HyPlaneHead addresses these issues by combining planar and spherical planes in a single representation, adopting a near-equal-area sphere-to-square warping strategy, and generating a single-channel unified feature map that is spatially split into plane-specific panels rather than emitted as multiple feature maps in separate channels (Li et al., 20 Sep 2025).

1. Problem setting and limitations of prior representations

Tri-plane-like representations are widely used in 3D-aware GANs for head image synthesis because they permit efficient feature lookup during volumetric rendering. In the Cartesian tri-plane formulation associated with EG3D, a 3D point is projected onto three axis-aligned planes, denoted $F_{xy}$, $F_{yz}$, and $F_{zx}$, by dropping one coordinate. This is computationally efficient, but symmetric 3D locations can share the same projected UV coordinates, which produces feature entanglement and visible mirroring artifacts in asymmetric regions, including face features appearing on the back of the head (Li et al., 20 Sep 2025).

SphereHead attempts to mitigate this problem by replacing Cartesian projection on one plane with direct $(\theta,\phi)$ lookup on a spherical plane $F_{\theta\phi}$. According to the HyPlaneHead analysis, this breaks Cartesian symmetry and reduces mirroring, but the mapping from a square feature map to the sphere through $(\theta,\phi)$ is highly non-uniform: features cluster near the poles and become sparse near the equator. The seam at $\phi=\pm\pi$ also introduces visible discontinuities unless two orthogonal spheres are used (Li et al., 20 Sep 2025).

HyPlaneHead further identifies a more subtle problem shared by both tri-plane and spherical tri-plane systems: feature penetration across channels. In these earlier formulations, three or four feature maps are generated as separate output channels of a single convolutional decoder. Because the same UV spatial location supplies the same input to all channels, the network must disentangle different spatial semantics through channel-wise filters alone. The reported consequence is that artifacts in one plane can leak into another, degrading image quality (Li et al., 20 Sep 2025).

This framing is significant because it recasts the limitations of prior 3D-aware head generators as a representational issue rather than only a rendering or training issue. A plausible implication is that improvements in image fidelity require not merely better discriminators or losses, but a reorganization of how 3D features are parameterized and emitted by the generator.

2. Hybrid-plane representation

HyPlaneHead introduces a hybrid-plane, or "hy-plane," representation that combines planar planes for symmetric features, a spherical plane for anisotropic features, and a unified feature-map design intended to eliminate inter-channel interference (Li et al., 20 Sep 2025). The representation includes three planar planes, $$P_{xy}, P_{yz}, P_{zx} \in \mathbb{R}^{H \times W \times C}$$, and one spherical plane, $P_{sph} \in \mathbb{R}^{H \times W \times C}$.

The planar planes are aligned as follows: $P_{yz}$ observes $F_{yz}$0 with $F_{yz}$1 forward and $F_{yz}$2 up; $F_{yz}$3 observes $F_{yz}$4 with $F_{yz}$5 to the left and $F_{yz}$6 forward; and $F_{yz}$7 observes $F_{yz}$8 with $F_{yz}$9 left and $F_{zx}$0 up. For a 3D point $F_{zx}$1, the planar feature query is defined as

$F_{zx}$2

with projected coordinates such as

$F_{zx}$3

The spherical plane caches features on the unit sphere using spherical coordinates aligned so that the polar axis is "up" the head (Li et al., 20 Sep 2025).

The overall feature vector for any 3D point is

$F_{zx}$4

and this $F_{zx}$5-dimensional feature is fed to a small volume-renderer MLP, following the overall rendering paradigm of EG3D (Li et al., 20 Sep 2025).

The conceptual role of the hybrid design is explicit in the formulation. Planar planes preserve efficiency and suit symmetric structure, while the spherical plane captures anisotropic features that are difficult to represent without mirroring. This suggests that HyPlaneHead treats head geometry and appearance as having mixed symmetry properties rather than forcing all features into one projection family.

3. Near-equal-area sphere-to-square warping

A central component of HyPlaneHead is a near-equal-area warping strategy for packing spherical features into a square feature map. The method applies Lambert Azimuthal Equal-Area projection from sphere to circle and then an elliptical grid mapping from circle to square (Li et al., 20 Sep 2025).

For spherical coordinates with colatitude $F_{zx}$6 and longitude $F_{zx}$7, the first step is

$F_{zx}$8

The paper states that this mapping preserves area exactly from sphere to disk. It maps the North Pole $F_{zx}$9 to $(\theta,\phi)$0 at the center, and the South Pole $(\theta,\phi)$1 to $(\theta,\phi)$2 collapsed at the seam (Li et al., 20 Sep 2025).

The second step converts disk polar coordinates to Cartesian coordinates:

$(\theta,\phi)$3

The third step applies the elliptical grid mapping from disk to square:

$(\theta,\phi)$4

The resulting $(\theta,\phi)$5 are rescaled to $(\theta,\phi)$6 UV coordinates on $(\theta,\phi)$7 (Li et al., 20 Sep 2025).

The stated benefits of this two-step warp are threefold: it is nearly equal-area, it avoids the $(\theta,\phi)$8 seam by collapsing it to a single point at one square corner, and it greatly improves detail in equatorial regions (Li et al., 20 Sep 2025). In contrast to direct $(\theta,\phi)$9 warping, the method explicitly prioritizes more uniform feature-map utilization.

HyPlaneHead also presents a dual-sphere variant, denoted hy-plane $F_{\theta\phi}$0, to remove the residual South-Pole singularity. In this case two spherical planes $F_{\theta\phi}$1 and $F_{\theta\phi}$2 with opposite pole orientations are blended using

$F_{\theta\phi}$3

The weighting emphasizes the high-quality center region of each sphere over its edge region (Li et al., 20 Sep 2025).

4. Single-channel unified feature map and generator design

HyPlaneHead replaces the conventional design of emitting multiple $F_{\theta\phi}$4-channel planes with a single unified feature map, $F_{\theta\phi}$5, produced by the synthesis decoder and then spatially split into sub-rectangles, each corresponding to one hy-plane component (Li et al., 20 Sep 2025). This is termed the "unify-split" strategy.

The rationale is architectural rather than purely algorithmic. If separate planes are emitted as different channels at the same spatial location, the same local convolutional context is reused across planes with distinct semantics. HyPlaneHead instead carves the unified map into four rectangular panels, so that planes never share the same spatial pixel. The stated consequence is the elimination of cross-plane filter interference (Li et al., 20 Sep 2025).

The split can also be area-biased. The paper notes that more pixels, for example $F_{\theta\phi}$6, may be allocated to the spherical plane and fewer, for example $F_{\theta\phi}$7, to smaller planar panels when anisotropy and detail are critical (Li et al., 20 Sep 2025). This design turns feature-map area into an explicit resource allocation mechanism.

The generator architecture is described in relation to EG3D, PanoHead, and SphereHead. Its components are summarized below.

Component	Specification
Mapping network	$F_{\theta\phi}$8 via 8-layer MLP
Synthesis decoder	Up-sampling ConvBlocks with Conv–AdaIN–LeakyReLU
Feature output	Produces $F_{\theta\phi}$9 at resolution $(\theta,\phi)$0
Rendering core	Split panels, bilinear sampling, small $(\theta,\phi)$1 MLP
Post-processing	StyleGAN2-like super-resolution CNN to $(\theta,\phi)$2
Background	Separate 2D generator for environment

The synthesis decoder expands to produce $(\theta,\phi)$3 at resolution $(\theta,\phi)$4, exemplified by $(\theta,\phi)$5 with split panels whose total area equals $(\theta,\phi)$6. Features are bilinearly sampled for each ray point, passed through the volume-rendering MLP to obtain density and view-dependent color, and then refined by a super-resolution CNN to the final image size of $(\theta,\phi)$7 (Li et al., 20 Sep 2025).

Training uses an adversarial loss in the StyleGAN2-ADA style, a view-image consistency loss from SphereHead, and an optional perceptual loss using LPIPS between rendered and real images under conditioned poses (Li et al., 20 Sep 2025). The adversarial and view-image consistency objectives are given as

$(\theta,\phi)$8

and

$(\theta,\phi)$9

5. Experimental setup and reported results

HyPlaneHead is trained on a custom full-head dataset of approximately 100K–200K high-resolution portraits, using $\phi=\pm\pi$0 crops, random horizontal flip, 25M images seen on eight V100 GPUs, and batch size 32 (Li et al., 20 Sep 2025). Evaluation uses FID on 50K generated versus 50K real images under conditioned poses, and FID-random with decoupled conditioning and rendering views, $\phi=\pm\pi$1, to assess arbitrary-view fidelity (Li et al., 20 Sep 2025).

The reported baselines include tri-plane (EG3D), tri-grid (PanoHead), and spherical tri-plane (SphereHead), in single and dual variants, with feature map sizes at $\phi=\pm\pi$2 and $\phi=\pm\pi$3 (Li et al., 20 Sep 2025). The quantitative excerpt given in the paper is as follows.

Method	FID	FID-rand
Tri-plane (EG3D)	9.22	11.23
Spherical tri-plane	8.64	10.71
Tri-grid (PanoHead)	8.77	10.66
Hy-plane (3+1) w/o split/warp	8.54	10.66
Hy-plane (3+1) + unify-split	8.31	10.18
Hy-plane (3+1) + split + warp	8.18	9.96
Hy-plane (3+1) + split + warp + area-bias	8.14	9.88
Hy-plane (2+2) + split + warp + area-bias	8.17	9.84

Within this excerpt, the best FID is reported for Hy-plane $\phi=\pm\pi$4 with split, warp, and area-bias, while the best FID-rand is reported for Hy-plane $\phi=\pm\pi$5 with split, warp, and area-bias (Li et al., 20 Sep 2025). The progression across rows is used in the paper to isolate the contributions of unify-split, warping, and area-biased allocation.

Qualitatively, the paper reports that tri-plane and tri-grid exhibit clear mirroring, including faces on the back and symmetric hair; single spherical planes show seam and polar noise; dual spherical planes are smoother but over-smoothed in fine detail; and Hy-plane yields clean symmetric leaves from planar planes together with crisp face and back regions from the spherical plane, without seams and with uniform detail (Li et al., 20 Sep 2025). The phrase "clean symmetric leaves" appears in the source summary; in context, this suggests a distinction between regions benefiting from symmetry-preserving planar structure and those requiring anisotropic spherical encoding.

6. Ablations, interpretation, and position within 3D-aware head synthesis

The ablation results reported for HyPlaneHead assign distinct roles to its three principal modifications. First, unify-split alone reduces feature penetration and improves FID across models, although in pure tri-plane form FID-rand worsens because the reduction in channel interference exposes more mirroring (Li et al., 20 Sep 2025). Second, the near-equal-area warp defined by Equations (1)–(3) further reduces FID and FID-rand by approximately 0.2 (Li et al., 20 Sep 2025). Third, area-biased splitting, in which a larger spatial region is assigned to $\phi=\pm\pi$6, produces an additional 0.04–0.1 FID gain (Li et al., 20 Sep 2025).

The comparison between hy-plane $\phi=\pm\pi$7 and $\phi=\pm\pi$8 clarifies the trade-off between architectural simplicity and singularity handling. The paper reports that $\phi=\pm\pi$9 is marginally better at extreme poses, whereas $$P_{xy}, P_{yz}, P_{zx} \in \mathbb{R}^{H \times W \times C}$$0 is sufficient when the single seam point is hidden downward (Li et al., 20 Sep 2025). This suggests that the single-sphere variant retains most of the benefit of the hybrid representation while reducing redundancy.

In the broader context of full-head 3D-aware GANs, HyPlaneHead is presented as a systematic rethinking of tri-plane-like feature parameterizations rather than a replacement of the standard rendering pipeline. It retains the familiar sequence of latent mapping, feature synthesis, ray-based querying, volume rendering, and super-resolution, but changes the representational substrate on which those steps operate (Li et al., 20 Sep 2025). Its state-of-the-art characterization in the source material rests specifically on this combination of planar and spherical planes, near-equal-area warping, and single-channel unify-split generation.

A common misconception in this area is that mirroring artifacts arise solely from insufficient capacity or inadequate supervision. HyPlaneHead argues instead that they are structurally induced by Cartesian projection symmetries and that analogous structural issues also affect spherical tri-planes through non-uniform warping and cross-channel interference (Li et al., 20 Sep 2025). Another possible misconception is that spherical parameterizations uniformly dominate planar ones; the reported analysis does not support that conclusion. Instead, the hybrid design is premised on the coexistence of symmetric and anisotropic cues within full-head imagery.

From a methodological perspective, HyPlaneHead occupies an intermediate position between pure planar factorization and pure spherical parameterization. This suggests a more general design principle for 3D-aware generative representations: different subsets of head appearance may be most naturally encoded in different coordinate systems, and architectural separation of those coordinate systems can be as important as the choice of renderer or adversarial objective.