Depth from Dual Differential Defocus and Stereo (D³S) Consensus

Under Review
*Indicates Equal Contribution

aPurdue University, West Lafayette, IN, USA

bNorthwestern University, Evanston, IL, USA

Abstract

We introduce D³S Consensus, a physics-based, closed-form algorithm that unifies depth-from-defocus (DfD) and stereo to achieve highly accurate depth estimation throughout an extended working range beyond the depth-of-field (DoF) of cameras. Given a pair of dual-defocus stereo images, the method estimates an overdetermined set of depth using a novel DfD theory, Dual Differential Defocus (D³), and (S)tereo in a coupled fashion. It then picks the most confident depth prediction from the set by enforcing consensus between these physically independent cues to reject unreliable estimates.

Analysis shows that D³S achieves a comparable working range under the same error tolerance with 10× smaller baseline than previous triangulation-based depth estimation systems. This enables compact passive binocular rangefinders with substantially smaller form factors than conventional stereo and DfD designs. We demonstrate the first D³S prototype with only 4 mm baseline and 12 mm EFL. It generates up to 900×1800-pixel depth maps with 1-cm mean absolute error over 0.3–1.64 m from a snapshot acquisition. This has surpassed the reported accuracy of certain commercially available stereo cameras with much larger form factors.

BibTeX

@misc{luo2026d3s,
  title  = {Depth from Dual Differential Defocus and Stereo ({D$^3$S}) Consensus},
  author = {Luo, Junjie and Xu, Wei and Chu, Dylan and Alexander, Emma and Guo, Qi},
  year   = {2026},
  note   = {Under review}
}