Binocular rendering requires two nearby views of the same scene and therefore repeats substantial visibility and shading work. We present a 2D Gaussian Splatting (2DGS) pipeline that fully renders a dominant-eye RGB image and an alpha-weighted depth proxy, reprojects that image to the affiliated eye, and repairs uncovered pixels. Small interior gaps are interpolated, whereas larger disoccluded regions are identified as regions of interest (ROIs) and selectively re-rendered. The depth proxy reuses the alpha-blending weights computed during dominant-eye rasterization, avoiding a separate depth-rendering pass. An adaptive ROI generator localizes the required updates using reprojected image boundaries and optional connected center-hole detection. On DTU, Tanks and Temples, and MipNeRF-360, the method reduces the measured time of a sequential two-pass binocular reference by 15.5\% to 28.8\% and peak GPU memory by 6\% to 11\%. The corresponding affiliated-eye quality degradation is at most 1.3 dB PSNR, 0.02 SSIM, and 0.02 LPIPS, representing a measurable trade-off that requires application-specific perceptual validation. These results establish a practical efficiency-quality trade-off for controlled static-scene stereo rendering and motivate future evaluation under continuous motion and on physical VR hardware.

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