Do We Need Learned Targets? Classical Gradients as Supervision for 2D Gaussian Initialization

Kyungjune Baek

cs.CVOct 19, 2026

Do We Need Learned Targets? Classical Gradients as Supervision for 2D Gaussian Initialization

Authors: Kyungjune Baek

Organizations: Sejong University, Seoul, Republic of Korea

Abstract

Learning-based Gaussian image initializers can require costly supervision obtained by per-image optimization. We investigate whether the Pseudo-PPM targets used by Instant GaussianImage can be replaced by classical image gradients. Our framework uses normalized Sobel maps in two tracks. A training-free analytic initializer combines probability boosting, parallel grid-based sampling, and geometric processing, producing initial parameters in 0.32 seconds on average. A neural initializer is trained on DIV2K with online Sobel supervision, which removes offline target optimization and allows training to scale to 10,000 LSDIR images without additional preprocessing. Both tracks achieve competitive long-budget reconstruction on Kodak and DIV2K. Under domain shift, the DIV2K-trained neural initializer surpasses Instant-GI on Manga109 from 500 fitting iterations onward (by 1.40 dB at 5K iterations), and training on LSDIR increases this margin to 1.85 dB. On Kvasir-SEG, the training-free analytic initializer exceeds Instant-GI at every reported budget. A controlled pipeline-time comparison yields an estimated $4.9\times$ reduction for DIV2K. These results establish inexpensive analytic targets as a practical alternative to optimization-derived supervision for scalable Gaussian initialization.

Figures & tables

Figure 1: Cost and supervision quality are entangled. Quality of the optimized Pseudo-PPM target (DIV2K, $50K$ -point GaussianImage fitting) as a function of the per-image optimization budget. The generating reconstruction improves with the optimization budget ( $\approx$ 50s per image for the reported target-generation setting), illustrating the cost of obtaining optimized supervision. Our analytic target removes this trade-off by construction.

Figure 2: Overview of the proposed Gaussian initialization framework. Our framework supports two tracks: (Top) Neural Initialization, which trains a network to predict Gaussian parameters using the raw Sobel map as an online training target (Eq. 5 ), and (Bottom) Analytic Initialization, which provides a training-free approach via probability boosting and parallel grid-based sampling. Unlike prior work, both tracks enable online target generation, eliminating the need for expensive pre-optimization.

Figure 3: Visualization of Gradient-Driven Probability Map Generation. We compute an analytic probability map from Sobel gradient magnitudes. For the analytic initialization, we further apply Bias ( $\delta$ ), Gamma Correction ( $\gamma$ ), and Boosting to ensure coverage. The gradient structure serves as a dense supervisory signal for network training, eliminating offline target optimization.

Figure 4: Comparison of Floyd-Steinberg (FS) dithering and the proposed Grid-based Centroidal Approximation. The illustrated settings produce different candidate counts (151 $K$ for FS and $\sim$ 30 $K$ for the proposed sampler). This image is a qualitative illustration; the matched-budget reconstruction ablation is reported separately.

	$N=5K$		$N=10K$		$N=43K$
Method	PSNR	MS-SSIM	PSNR	MS-SSIM	PSNR	MS-SSIM
GaussianImage †	29.85	.962	32.48	.982	N/A	N/A
GaussianImage	28.53	.947	30.64	.972	38.23	.996
GI++ †	31.83	.960	35.41	.983	N/A	N/A
GI++	29.75	.954	31.69	.974	35.42	.986
Instant-GI	30.28	.958	33.41	.981	42.67	.997

Table 1: Reconstruction after

50K

fitting iterations on Kodak and DIV2K at the requested point budgets

N

. The

43K

and

77K

settings correspond to the average Instant-GI counts. PSNR (dB) and MS-SSIM: higher is better.

\dagger

: values reported in [ 15 ] ; other baseline rows are reproduced results. + indicates that the model is trained with 10K images of the LSDIR dataset.

Method	PSNR $\uparrow$	MS-SSIM $\uparrow$	#pts( $K$ )
GI	28.81	.992	199.4
Instant-GI	34.89	.997	199.4
Analytic (Ours)	35.87	.996	199.6
Neural (Ours)	36.29	.996	199.3
Neural+ (Ours)	36.74	.997	198.8
Neural+* † (Ours)	36.99	.997	221.5

Table 2: Generalization on out-of-distribution data. Reconstruction quality on Manga109 (drawn art), point-matched at

\sim

199K and optimized for

5K

iterations. This distribution departs from the DIV2K images on which Instant-GI’s targets are optimized. † Neural+* is point-unconstrained, listed for reference only.

Figure 5: Training Convergence and Qualitative Progression. PSNR curves and reconstructions for one DIV2K image. Random initialization (GaussianImage) is included. The plot illustrates fitting behavior on this image.

Method	100	250	500	1000	5000
Instant-GI	28.67	30.22	31.51	32.69	34.89
Analytic	20.66	24.51	28.71	32.37	35.87
Neural	24.92	29.05	31.65	33.71	36.29
Neural+	25.91	30.76	32.98	34.55	36.74
Neural+* †	29.72	32.13	33.70	34.95	36.99

Table 3: Convergence on Manga109. PSNR (dB) at increasing optimization budgets (point-matched

\sim

199K). Bold marks the best point-matched method per column; Instant-GI leads at step 100; Neural+ leads from step 250. † Point-unconstrained, reference only.

Method	100	250	500	1000	5000
Random	11.30	14.87	22.44	34.29	43.57
Instant-GI	26.35	33.81	38.50	42.14	46.18
Analytic	33.26	38.40	41.63	44.13	46.80
Neural	36.50	40.48	42.28	43.63	45.69
Neural+	36.35	40.31	42.28	43.84	45.90

Table 4: Convergence on Kvasir-SEG. PSNR (dB) at increasing optimization budgets (

20K

-point budget, all 1000 images, long side resized to 512). Kvasir-SEG provides an image-reconstruction evaluation under domain shift. Bold marks the best per column. Under this strong shift, our analytic prior already leads Instant-GI at every budget, and the neural variants lead earlier still. Random is included as a poor-initialization baseline.

Figure 6: Absolute error maps on Manga109. Our methods (Analytic, Neural, Neural+) achieve better fidelity than Instant-GI and GaussianImage. Instant-GI shows error concentrations in high-frequency regions (line art, hatching), whereas our methods maintain a consistently lower error profile.

Method	Pre-proc.	Network	Total
Instant-GI	40,000s	10,200s	50,211s
Neural (Ours)	0s	10,200s	10,211s
Analytic (Ours)	0.3s	0s	11.3s

Table 5: Pipeline efficiency on DIV2K. A controlled single-resolution sample-count comparison isolating target-generation cost: the official Instant-GI recipe uses three-resolution samples, whereas our reported model uses one. Online generation removes offline target preprocessing; its cost is included in training. Total additionally includes 11s of per-image GaussianImage fitting.

5 $K$ iterations	Kodak		DIV2K
Method	PSNR $\uparrow$	MS-SSIM $\uparrow$	PSNR $\uparrow$	MS-SSIM $\uparrow$
- GC & Bias	38.94	.991	37.17	.988
- $\gamma$ Correction (GC)	39.58	.993	38.76	.995
- Bias	40.87	.996	39.15	.995
Kernel-size ( $k$ ) = 3	40.13	.997	38.06	.997
Local Variance	39.34	.992	38.79	.994

Table 6: Analytic-initializer ablations after

5K

fitting iterations on Kodak and DIV2K. GC denotes gamma correction; Bias is the additive probability offset. PSNR and MS-SSIM: higher is better.

Gamma ( $\gamma$ )	PSNR $\uparrow$	MS-SSIM $\uparrow$
0.1	38.54	.997
0.2	38.59	.997
0.3	39.41	.997
0.4	40.42	.997
0.5	40.92	.997
0.6	40.95	.996

Table 7: Sensitivity to

\gamma

on Kodak after

5K

fitting iterations.

	Kvasir-SEG			Manga109
Method	HGC $\uparrow$	Emp. $\downarrow$	Low	HGC $\uparrow$	Emp. $\downarrow$	Low
Random	.545	.0039	.196	.593	.0020	.283
Instant-GI	.873	.0002	.117	.945	.0000	.097
Analytic	.884	.0002	.043	.929	.0001	.020
Neural	.875	.0004	.082	.946	.0003	.074
Neural+	.867	.0006	.103	.946	.0021	.063

Table 8: Direct initialization-quality diagnostics. Metrics on initialized Gaussian centers before reconstruction optimization. HGC: high-gradient coverage (fraction of top-20% Sobel-gradient energy covered by centers,

\uparrow

); Emp.: empty high-gradient cell ratio (

\downarrow

); Low: fraction of points in low-gradient regions. These metrics characterize the initial point placement. Kvasir on all 1000 images; Manga109 on a 100-image subset (seed 42).

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2D Gaussian splatting provides an efficient explicit representation for image reconstruction, but existing methods still require costly per-image iterative optimization or rely on handcrafted priors for primitive allocation. We present AIR, a self-supervised feed-forward framework that amortizes iterative Gaussian fitting into a single network pass, eliminating per-image test-time optimization. AIR adopts a stage-wise residual architecture that progressively predicts additional Gaussian primitives from reconstruction residuals, together with an explicit Stage Control mechanism that activates new primitives only in under-reconstructed regions. A Predict--Optimize--Distill training strategy stabilizes multi-stage prediction by distilling short-horizon optimized Gaussian increments back into the predictor. The stabilized predictor is then jointly finetuned across stages and equipped with an image-adaptive quantizer for compact Gaussian storage. Experiments on Kodak and DIV2K show that AIR achieves better reconstruction quality than representative Gaussian-based baselines while reducing encoding time to 160--300,ms. Code: https://github.com/whoiszzj/AIR.git

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