Depth from gradient fields and control points: Bias correction in photometric stereo

Itsik Horovitz, Nahum Kiryati

Research output: Contribution to journalArticlepeer-review


Photometric stereo is capable of high quality reconstruction of fine shape details, but is prone to systematic errors due to nonideal illumination or imperfect calibration. We present methods for correcting the bias, using sparse control points of known 3D location. An easy way to obtain control points is via the projection of a dot-matrix pattern using a laser pointer with a suitable adapter, and triangulation. Straight forward incorporation of control points as constraints in the computation of depth from the gradient field leads to singularities. We propose two well-behaved methods for bias correction using control points. One is based on constrained weighted least squares extension of depth from gradient-field computation. The other adds an interpolation surface to the reconstructed shape. Practical computation of depth from a gradient field requires an efficient numerical scheme. We employ full-multigrid computation with successive over-relaxation and show how to propagate the gradient field and the control points through the pyramid. Experimental results demonstrate significant bias reduction in photometric stereo, allowing high reconstruction quality even in the presence of severe setup errors.

Original languageEnglish
Pages (from-to)681-694
Number of pages14
JournalImage and Vision Computing
Issue number9
StatePublished - 20 Aug 2004


  • Control points
  • Depth from gradient field
  • Full multigrid
  • Photometric stereo
  • Thin plate spline interpolation
  • Weighted least squares


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