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

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.