Resolving Shape Ambiguities
using Heat Conduction and Shading

Akihiko Oharazawa, Sriram Narayanan, Mani Ramanagopal, Srinivasa G. Narasimhan
Carnegie Mellon University
ICCP 2025
Paper Code (Coming Soon)

Abstract

Can Shape Laplacians and Shading uniquely determine the shape of an object?

We present a novel theory for 3D shape recovery that jointly leverages Laplacian — intrinsic geometry cues — and Shading to resolve longstanding ambiguities in Shape-from-Shading (SfS). While classical SfS suffers from per-pixel cone ambiguity — even under known lighting — and Shape Laplacian methods capture intrinsic surface geometry but are limited by local binary (concave/convex) ambiguities, our method combines Laplacian and shading cues to enable accurate shape recovery even under unknown lighting conditions. In contrast to recent analysis-by-synthesis approaches that require strong priors and often suffers from local minima. Our framework provides a principled solution to the fundamental ambiguities of shape reconstruction.

Theory: Shape from Laplacian and Shading (SFLS)

Laplacian constraint yields a binary ambiguity, Shading cone constraint with one solution.

Results

Our result demonstrates the effectiveness of our method in reconstructing shapes from Laplacian and shading cues. Notably, our method reconstructs 3D shapes without requiring any priors, even under unknown lighting conditions.

(Reconstructions shown on the right are interactive.)


Input Shading

Object 1

Input Laplacian

SfS

SfL

Ours (SFLS)

Object 2
Object 3
Object 4

Citation


  @inproceedings{Oharazawa_2025_ICCP,
  author    = {Oharazawa, Akihiko and Narayanan, Sriram and Ramanagopal, Mani and Narasimhan, Srinivasa G.},
  title     = {Resolving Shape Ambiguities using Heat Conduction and Shading},
  booktitle = {Proceedings of the IEEE/CVF International Conference on Computational Photography (ICCP)},
  month     = {July},
  year      = {2025},
  pages     = {xxxxx-xxxxx}
  }