LocusGS: Spatially Grounded 3D Gaussian Splatting

• LocusGS is a feed-forward 3D Gaussian Splatting method that augments fixed query tokens with learnable 3D anchor centers and support radii for spatially coherent Gaussian reconstruction.
• It combines anchor-aware self-attention, anchor-to-camera-ray geometric biases, progressive anchor refinement, and anchor-centered Gaussian decoding to reduce the mixing of visually similar but spatially distant regions.
• At matched Gaussian budgets, LocusGS improves TokenGS performance, reaching 28.50 PSNR, 0.909 SSIM, and 0.135 LPIPS on RealEstate10K with 1,024 queries, while producing substantially tighter Gaussian groups.

LocusGS is a feed-forward 3D Gaussian Splatting (3DGS) method that introduces explicit spatial states into query-based Gaussian reconstruction. Each learnable query is augmented with a three-dimensional anchor center and a support radius, which are progressively refined and used in query interaction, multi-view feature aggregation, and Gaussian decoding. The method addresses the spatial diffuseness of latent Gaussian tokens, in which Gaussians generated by one query may be scattered across distant scene regions. By imposing anchor-to-ray geometric biases and anchor-centered Gaussian parameterization, LocusGS produces more spatially coherent Gaussian groups while improving novel-view synthesis under a fixed Gaussian budget (Li et al., 13 Aug 2026).

1. Position within feed-forward Gaussian reconstruction

3DGS represents a scene as anisotropic Gaussian primitives with 3D centers, scales, rotations, opacities, and appearance attributes. Conventional 3DGS generally optimizes these primitives independently for each scene, whereas feed-forward methods predict an entire Gaussian representation in one pass from a small set of posed input images.

Two principal feed-forward paradigms are distinguished:

1. Dense or pixel-aligned prediction: methods such as pixelSplat, MVSplat, and DepthSplat associate image features or pixels with Gaussian predictions. Their Gaussian budget is consequently tied to image resolution and often to the number of input views.
2. Query-based prediction: methods such as TokenGS maintain a fixed set of learnable tokens. Each token aggregates multi-view image evidence and decodes a group of Gaussian primitives. This makes the output budget independent of image resolution and input-view count.

Query-based prediction removes the natural correspondence between image features and spatial image locations. A latent query does not explicitly specify where in 3D it operates, which image regions should provide its evidence, the spatial extent of its responsibility, or where its decoded Gaussian group should be placed. Consequently, appearance-based aggregation may combine visually similar but spatially unrelated regions, producing spatially diffuse Gaussian groups.

LocusGS retains the fixed-budget query formulation but augments each query with an explicit spatial state. The resulting representation can be summarized as:

$$\text{query feature}+\text{3D anchor state} \longrightarrow \text{spatially grounded Gaussian group}.$$

The method is designed for novel-view synthesis rather than visual localization. The name should therefore be distinguished from unrelated systems using similar terminology, including the Locus Algorithm for differential photometry (Creaner et al., 2020), LiDAR place recognition using higher-order pooling (Vidanapathirana et al., 2020), and Gaussian-based localization methods such as GSLoc (Botashev et al., 2024).

2. Baseline query architecture

Given posed input images

$\mathcal{I}=\{I_v\}_{v=1}^{V}$

and camera parameters

$\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$

an image encoder produces multi-view visual tokens $\mathbf{F}$. A query-based decoder maintains $N$ learnable query features:

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$

A conventional decoder updates the queries through self-attention and cross-attention:

$\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$

After $L$ decoder layers, query $i$ predicts $K$ Gaussian primitives,

$\mathcal{I}=\{I_v\}_{v=1}^{V}$0

where $\mathcal{I}=\{I_v\}_{v=1}^{V}$1 is the Gaussian center, $\mathcal{I}=\{I_v\}_{v=1}^{V}$2 is its scale, $\mathcal{I}=\{I_v\}_{v=1}^{V}$3 its rotation, $\mathcal{I}=\{I_v\}_{v=1}^{V}$4 its color or appearance feature, and $\mathcal{I}=\{I_v\}_{v=1}^{V}$5 its opacity. The complete scene is

$\mathcal{I}=\{I_v\}_{v=1}^{V}$6

LocusGS preserves this set-to-set formulation. Its modification is not primarily a new Gaussian primitive or rasterizer, but the introduction of a spatial state that constrains the query’s evidence aggregation and output geometry.

3. Anchor state and spatially grounded attention

Anchor representation

For query $\mathcal{I}=\{I_v\}_{v=1}^{V}$7 at decoder layer $\mathcal{I}=\{I_v\}_{v=1}^{V}$8, LocusGS maintains both a feature $\mathcal{I}=\{I_v\}_{v=1}^{V}$9 and an anchor

$\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$0

where $\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$1 is the anchor center and $\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$2 is its support radius. The feature stores appearance, semantic, and reconstruction information; the anchor specifies spatial responsibility.

The radius is parameterized through an unconstrained scalar $\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$3:

$\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$4

where $\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$5 provides numerical stability. The initial centers and raw radii are learnable parameters shared across scenes and are randomly initialized in normalized 3D scene coordinates. Anchors do not receive direct ground-truth position or radius supervision; they are learned indirectly through rendering losses and visibility regularization.

Anchor-aware self-attention

The anchor center is converted into a positional embedding:

$\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$6

where $\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$7 is a sinusoidal positional encoding. The self-attention feature becomes

$\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$8

Self-attention is consequently conditioned on the spatial configuration of the anchors as well as latent query content. The reported visualizations show sparse query-to-query attention neighborhoods rather than uniform interaction among all queries.

Anchor-to-ray cross-attention

Each image patch token is associated with an approximate camera ray. LocusGS introduces a geometric bias based on the distance between the anchor and the ray:

$\mathcal{P}=\{\Pi_v\}_{v=1}^{V},$9

where $\mathbf{F}$0 is the ray corresponding to image token $\mathbf{F}$1, $\mathbf{F}$2 is the shortest point-to-ray distance, and $\mathbf{F}$3 is a fixed base bandwidth.

The content-based attention logit is

$\mathbf{F}$4

and the final attention weights are

$\mathbf{F}$5

with

$\mathbf{F}$6

The cross-attended feature is

$\mathbf{F}$7

This mechanism combines content compatibility with geometric compatibility. Image patches that look relevant but originate from rays distant from an anchor are penalized, reducing the aggregation of spatially unrelated evidence.

Plücker-ray formulation

LocusGS represents a camera ray using Plücker coordinates:

$\mathbf{F}$8

where $\mathbf{F}$9 is the ray direction and

$N$0

is the moment vector for camera center $N$1. Dense pixel-level Plücker maps are average-pooled according to the image patch size $N$2. For input images of spatial size $N$3, the pooled dimensions are

$N$4

The patch-ray tensor has shape

$N$5

After normalization,

$N$6

the point-to-ray distance is implemented as

$N$7

The default base bandwidth is $N$8. The squared bandwidth is lower-bounded for numerical stability, and the geometric bias is clamped to $N$9.

4. Progressive anchor refinement and Gaussian decoding

After the feature update at layer $$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$0, lightweight heads predict residual changes to the anchor:

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$1

The anchor state is updated as

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$2

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$3

with

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$4

Anchor refinement is therefore iterative. Early anchors provide an initial spatial hypothesis; subsequent decoder features update the center and radius, which then modify later self-attention, cross-attention, and Gaussian decoding.

The radius has two coupled functions. It determines the spatial bandwidth of anchor-to-ray attention and scales the local offsets used to generate Gaussian centers. At the final decoder layer, query $$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$5 predicts $$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$6 offsets:

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$7

and the Gaussian centers are decoded as

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$8

This anchor-centered parameterization constrains each query’s Gaussian group to a local region. It contrasts with free-center decoding,

$$\mathbf{Q}^{0} = [\mathbf{q}_1^{0},\mathbf{q}_2^{0},\ldots,\mathbf{q}_N^{0}]^\top \in\mathbb{R}^{N\times d}.$$9

which allows each Gaussian center to be placed independently in global coordinates.

The remaining Gaussian attributes—scale, rotation, opacity, and color or appearance feature—are predicted from the final query feature using the token-based Gaussian head inherited from TokenGS. Each query predicts $\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$0 Gaussians. Thus, 1024 queries produce 65,536 Gaussians, while 4096 queries produce 262,144 Gaussians. The Gaussian count is fixed and independent of the number of input views.

5. Training objectives and implementation

Reconstruction supervision

Selected decoder layers $\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$1 decode intermediate Gaussian sets $\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$2, which are rendered into target views:

$\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$3

The reconstruction loss follows TokenGS:

$\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$4

with

$\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$5

Visibility regularization

For a 3D point $\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$6, its normalized projection in supervision view $\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$7 is $\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$8. The out-of-view penalty is

$\mathbf{Q}^{l+1}=D(\mathbf{Q}^{l},\mathbf{F}).$9

For a point set $L$0,

$L$1

Unlike the baseline, LocusGS applies visibility regularization both to decoded Gaussian centers and to anchor centers:

$L$2

where

$L$3

Multi-layer loss

The total objective is

$L$4

Later decoder layers receive larger weights. In the main DL3DV ablation, supervision at layers $L$5 performs best among the tested schedules. The reported results are:

Supervised layers	PSNR	SSIM	LPIPS
$L$6	23.549	0.7575	0.3074
$L$7	24.284	0.7843	0.2709
$L$8	24.071	0.7793	0.2774

Training configuration

LocusGS is evaluated on RealEstate10K and DL3DV-10K. RealEstate10K uses two-view reconstruction at $L$9. DL3DV uses four input views during training, with base training at $i$0 followed by finetuning and evaluation at $i$1.

The reported training setup uses AdamW, a cosine learning-rate schedule, base learning rate $i$2, 2,000 warmup iterations for base training, finetuning learning rate $i$3, 400 finetuning warmup iterations, 300 base-training epochs, and 20 finetuning epochs. Evaluation uses PSNR, SSIM, and LPIPS.

6. Evaluation, spatial coherence, and limitations

Novel-view synthesis results

On RealEstate10K with two input views at $i$4, LocusGS improves over TokenGS at matched query and Gaussian budgets:

Method	PSNR	SSIM	LPIPS	Gaussians
TokenGS, 1024 tokens	28.02	0.896	0.147	66K
LocusGS, 1024 tokens	28.50	0.909	0.135	66K
TokenGS, 4096 tokens	28.41	0.903	0.135	262K
LocusGS, 4096 tokens	28.89	0.916	0.124	262K

The 1024-token LocusGS model surpasses GS-LRM in PSNR and SSIM while using approximately half as many Gaussians.

On DL3DV, the model is trained with four views but evaluated with two, four, and six input views. LocusGS outperforms TokenGS in all tested conditions while retaining a fixed Gaussian budget:

Input views	LocusGS PSNR	LocusGS SSIM	LocusGS LPIPS	Gaussians
2	20.90	0.678	0.377	262K
4	24.80	0.812	0.248	262K
6	25.78	0.836	0.225	262K

Dense methods such as MVSplat and DepthSplat increase their Gaussian count with the number of input views, whereas LocusGS and TokenGS retain a fixed output budget.

Ablation findings

The structural ablation supports the interaction of the principal components:

Variant	PSNR	SSIM	LPIPS
Full LocusGS	24.284	0.7843	0.2709
No radius state	23.640	0.7618	0.3007
Static radius without refinement	23.979	0.7746	0.2866
Content-only self-attention	24.171	0.7807	0.2764
Content-only cross-attention	22.751	0.7220	0.3500
Center-only geometric bias	23.770	0.7670	0.2940
Free Gaussian centers	22.079	0.6860	0.3970

Removing the radius state, preventing radius refinement, removing anchor-aware attention, or allowing free Gaussian centers all reduce performance. The largest degradation occurs with free-center decoding, indicating that anchor-centered output parameterization is central to the method. The cross-attention ablation also shows that geometric grounding of image evidence is more consequential than content-only cross-attention.

Spatial coherence

For query $i$5, the centroid of its Gaussian centers is

$i$6

Within-token dispersion is measured by

$i$7

The reported dispersion values are:

Dataset	Method	Mean	Variance	Median
RE10K	TokenGS	5.1164	34.1712	2.7911
RE10K	LocusGS	0.1978	0.1371	0.1117
DL3DV	TokenGS	0.5881	0.0139	0.5531
DL3DV	LocusGS	0.0433	0.0004	0.0383

The absolute values are dataset-dependent because scene-normalization conventions differ, but within each dataset LocusGS exhibits substantially tighter query-associated Gaussian groups. Visualizations show TokenGS producing diffuse or disconnected primitives, whereas LocusGS produces compact groups around learned anchors. Learned radii tend to be smaller in detailed or strongly constrained regions and larger in sparse or weakly constrained regions. This behavior is consistent with an adaptive support scale, although the radius is not presented as a calibrated uncertainty estimate.

Efficiency and limitations

The anchor machinery increases model size and forward time. On an NVIDIA A100 40GB using DL3DV four-view evaluation:

Model	Parameters	Storage	Forward time
TokenGS	222.0M	846.93 MiB	$i$8 ms
LocusGS	241.5M	921.31 MiB	$i$9 ms

The forward-time measurements exclude rendering. LocusGS therefore trades approximately 19.5 million additional parameters and approximately 66 ms of pure forward time in this configuration for improved rendering quality and spatial organization.

The principal explicitly identified limitations are:

• Calibrated-camera requirement: anchor-to-ray attention requires known camera intrinsics and extrinsics, so the method is not directly pose-free.
• Isotropic support: each anchor uses a scalar radius. This may be inadequate for elongated structures, thin surfaces, long corridors, walls, or regions with strongly directional uncertainty.
• Potential anchor errors: incorrectly initialized or refined anchors may bias cross-attention toward inappropriate rays.
• Support-scale trade-offs: large radii can make attention diffuse and Gaussian groups broad, whereas small radii can overconstrain queries assigned to geometrically extended regions.
• Disconnected structures: anchor-centered decoding improves locality but may limit a query’s ability to represent genuinely disconnected or highly nonlocal structures.

The proposed extensions include anisotropic supports and visibility-aware uncertainty. More generally, LocusGS demonstrates that explicit geometric state can constrain latent-token reconstruction without abandoning fixed-budget feed-forward prediction. Its central architectural principle is that a query responsible for a spatial Gaussian group should carry not only a feature representation, but also an explicitly refined location and spatial scale.